This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
we can assume that the graph of Cera's and Bethany's savings accounts will show the total amount of money in their accounts after a certain number of weeks.
Since both Cera and Bethany deposit the same amount of money and make the same additional deposits each week, their savings will increase at the same rate. Therefore, the graph will likely show two parallel lines that start at $20 and increase by $15 per week.
The number of solutions modeled by the graph will depend on whether the two lines ever intersect. If the lines do not intersect, then there is no solution to the system of equations that model the two savings accounts. In other words, there is no point at which the total amount of money in both accounts is the same.
On the other hand, if the lines do intersect, then there is at least one solution to the system of equations. In this case, the point of intersection represents the week at which the total amount of money in both accounts is the same.
To change the situation so that the graphs model a different number of solutions, we could change the initial deposit or the amount of money deposited each week for one or both of the savings accounts. For example, if Cera starts with a higher initial deposit than Bethany, or if Cera deposits more money each week, then their savings will increase at different rates and the lines on the graph will not be parallel.
Therefore, This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.
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Please help asap!
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 29 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The total number of cards sold for Mother's Day is 290 cards.
What is the proportions?
Proportion is a mathematical concept that expresses the equality of two ratios. Two ratios are said to be proportional if they have the same relative size or relationship.
Let x be the total number of cards sold for Mother's Day. We know that one salesman sold 29 cards, which is 10% of the total number of cards sold. Using this information, we can set up the following proportion:
(10/100) * x = 29
Simplifying, we get:
x = 290
Hence, the total number of cards sold for Mother's Day is 290 cards.
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Q+9p when q = 18 and p = 4
Answer: 48
Step-by-step explanation: 9p p=4 9*4=36 +18 = 48
ASAP 40 points
Graphs of exponential functions either increase or decrease for all x-values.
True or
False
It is true that graphs exponential functions either increase or decrease for all x-values.
How to define an exponential function?An exponential function is defined as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change, as a decimal.An exponential function can either increase or decrease depending on the values of a and b, however the behavior is uniform, meaning that it is true that graphs exponential functions either increase or decrease for all x-values.
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Data from 2020 indicate the U.S. was growing at yearly rate of 0.59%. The population of the U.S. that year was about 332 million, so a formula for the population P of the U.S. at time/ years after 2020 can be given by P(t) = 332(1.0059)^t, in
millions.
(a) Write a formula for the population of the U.S. at time/ years after 2020, of the form
P(t)=aekt. Show your work. Round the growth factor k to 5 decimals.
please please please could someone explain how to do this and show work!!!
The exponential growth equation is P ( t ) = 332 ( 1.0059 )^t , where t is the number of years and P ( t ) is the population after 2020
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the initial population be represented as x₀
Now , the value of x₀ = 332 million
And , the exponential growth rate r = 0.59 %
where the population of the U.S. at time/ years after 2020 is of the form equation P( t ) = aekt
On simplifying , we get
The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.59% )^t
Now , the value of P ( t ) is
The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.0059 )^t
The population of the U.S. at a time P ( t ) = 332 ( 1.0059 )^t
where the growth factor k = 1.0059
Hence , the exponential growth equation is P ( t ) = 332 ( 1.0059 )^t
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i need help now i have like so much questions that need to be done
The measure of ∠M and ∠N = 76
Define an isoscales triangle?An isosceles triangle is a triangle that has two sides of equal length and two equal angles opposite those sides.
Given:- ∠NLM = 28°
The given triangle is an isosceles triangle as sides LM and LN are equal.
Therefore ,∠LMN and ∠LNM will be equal.
Let us assume ∠M as x
Therefore,
∠LMN = ∠LNM = x
Sum of all angles of a triangle =180°
Therefore,
∠NLM + ∠LNM + ∠LMN = 180°
28 + x + x = 180
28 + 2x = 180
2x = 180 – 28
2x = 152
x = 152/2
x = 76
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What does each expression or equation represent in this situation? (What does the notation mean in English?)
The cost of apples when the number of apples bought is n can be found using the function:
C(n) = 0.9n
What is a function?
A mathematical statement or rule that establishes the link between an independent variable and a dependent variable is called a function. Relationships called functions provide an output for each input. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Often, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
Assuming the question is the one given below.
Given a function C which gives the cost of buying the n apples in dollars.
The first expression given is:
1) C(5) = 4.50
The input of the function is 5 and the output is 4.50.
This means that when the number of apples is 5 the total cost is $4.50.
Let us assume the general equation of the function as below:
C(n) = kn
When n = 5
C(5) = 5k = 4.50
k = 4.50/5 = 0.9
Hence the function is C(n) = 0.9n
2) We found the function as C(n) = 0.9n
C(2) means the cost when the number of apples is 2.
C(2) = 0.9 * 2 = $1.8
Therefore the cost of apples when the number of apples bought is n can be found using the function:
C(n) = 0.9n
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What would the hypotenuse have to be if the legs of a right triangle are 9 and 5?
Answer:
Roughly 10.30
Step-by-step explanation:
Use Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where [tex]c[/tex] is your hypotenuse
So:
[tex]c^2 = (9)^2 + (5)^2[/tex]
[tex]c= \sqrt{106}[/tex]
[tex]c[/tex] ≈ [tex]10.30[/tex]
Answer:10.3
Step-by-step explanation:
(100 POINTS AND BRAINLYEST)
(SOLVE ALL)
24.2 miles above
2. The line of site to the horizon would be tangent to the Earth’s surface. What kind of angle is formed between the radius of the Earth and the line of site? (1 point)
3. You will be setting up a right triangle to solve this problem using the radius of the Earth (3,959 miles), the distance to the horizon (which is unknown), and the altitude of Felix. Sketch and image of this scenario. Include distances on the right triangle. (3 points)
4. Use the Pythagorean Theorem to find the distance from Felix in the image to the horizon. (3 points)
5. Standing on the ground, the surface of the Earth appears to be flat. How far would a person on the ground have to travel to get a point on the horizon that Felix could see. Sketch a right triangle of this scenario using the altitude of Felix, the distance to the horizon, and the distance on the ground to the horizon (which is unknown). Include distances on the right triangle. Use the Pythagorean Theorem to find the missing side of the triangle. (5 points)
6. Use the answer from number 5 to determine the central angle of the Earth that Felix is viewing from his altitude. Treat the answer from number 5 like an arc length. You will need to use the radius of the Earth in this problem. Answer in radians or degrees. (2 points)
The analysis of the distances and angles viewed by Felix are presented as follows;
2. The angle formed is a right angle
3. Please find the drawing of the scenario created with MS Word
4. The distance obtained using Pythagorean Theorem is about 438.53 miles
5. The distance the person travels is about 437.86 miles
6. The central angle Felix is viewing from his altitude is about 6.34°
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the right triangle.
2. The angle formed by a tangent to a spherical surface, such as the Earth's approximately spherical surface and the radius of the sphere is a right angle.
Therefore;
The angle formed between the radius of the Earth and the tangential line of sight is a right angle3. The possible elevation of Felix above the Earth's surface, obtained from a similar question is; 24.214 miles
Therefore;
The legs of the right triangle are the radius of the Earth and the distance from Felix's to the point on the horizon.
The hypotenuse sum of Felix's altitude and the radius of the Earth
Please find attached the drawing of the scenario created with MS Word
4. Pythagorean Theorem indicates that the distance from Felix to the image on the horizon, d, can be obtained as follows;
d = √((3,959 + 24.214)² - 3,959²) ≈ 438.53
The distance from Felix to the image on the horizon is about 438.53 miles
5. The distance the person has to travel can be found as follows;
The surface of the Earth is assumed to be flat
The distance to the horizon from Felix is about 438.53 miles
The distance, l, the person on the ground has to travel is therefore;
l = √(438.53² - 24.214²) ≈ 437.86
The distance the person on the ground has to travel to get to a point on the horizon Felix could see is about 437.86 miles6. The central angle, θ, of the Earth that Felix is viewing, with an arc length of 437.86 miles can be found using the formula for finding the arc length of a sector of a circle as follows;
θ/360 × 2 × π × 3,959 ≈ 437.86
θ ≈ 437.86 × 360/(3,959 × 2 × π) ≈ 6.34°
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The quality control manager at a computer manufacturing company believes that the mean life of a computer is 83 months, with a standard deviation of 9 months.
If he is correct, what is the probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months? Round your answer to four decimal places.
The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:
P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035
What do you mean by probability?By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Moreover, the proportion of positive outcomes cannot be negative.
Here we have,
μ = 83,0 = 9, n = 78
Since sample size is large so we can assume normal distribution using CLT.
The z-score for x= μ-0.4 is
z=(μ-0.4-μ)/o/√n
=-0.4/9/√78
= -0.39
The z-score for x= μ +0.4 is
z=(μ+0.4-μ)/σ/√n
= 0.4/9/√78
= 0.39
The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:
P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035.
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Select ALL the correct answers. Which of the following statements are true about the equation below? The solutions are . The solutions are . The extreme value is at the point (7,-3). The graph of the quadratic equation has a minimum value. The extreme value is at the point (3,-7). The graph of the quadratic equation has a maximum value.
None of the statements (1) to (6) are true about the equation [tex]x^2-6x+2=0[/tex].
What does a math quadratic equation mean?Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a variable. a 0. It has at least 1 solution since it is a 2nd polynomial equation, which is guaranteed by the algebraic theorem. The solution might be simple or difficult.
None of the statements (1) to (6) are true about the equation. [tex]x^2-6x+2=0[/tex].
Reason why:
(1) The coefficient of the [tex]x^2[/tex] term is positive, so the graph of the quadratic equation is a parabola that opens upward. Therefore, it does not have a minimum value, but instead has a minimum point.
(2) The coordinates of the minimum point can be found using the formula x = -b/2a, which gives x = 6/2 = 3. Substituting x = 3 into the equation gives y = 2, so the minimum point is (3, 2).
(3) The point (7,-3) is not on the graph of the equation.
(4) The solutions to the equation are given by the quadratic formula x = [tex][6\± \sqrt{(6^2 - 4(1)(2))]}/2 = [6\± \sqrt{(28)]}/2 = 3\± \sqrt{7}[/tex]. So, statement (4) is partially correct, but the value of -3 is incorrect.
(5) Statement (5) is correct, as the solutions to the equation are x = [tex]3\±\sqrt7}[/tex].
(6) The graph of the quadratic equation has a minimum value, not a maximum value.
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Complete question is: Which of the following statements are true about the equation below?
x^2-6x+2=0
( 1 ) The graph of the quadratic equation has a minimum value.
( 2 ) The extreme value is at the point (3,-7).
( 3 ) The extreme value is at the point (7,-3).
( 4 ) The solutions are x = -3 + or - the square root of 7 .
( 5 ) The solutions arex = 3 + or - the square root of 7.
( 6 ) The graph of the quadratic equation has a maximum value.
Is (0, 6) a solution to the equation y = -x + 6?
Yes or No
Answer:
Yes
Step-by-step explanation:
We just need to (0,6) in the equation to see if it gives a true answer or not!
y = -x + 6
6 = 0 + 6
6 = 6
So, (0,6) is a solution to the equation y = -x + 6
I need help anyone please ?!!!!!!!
Answer:its a
Step-by-step explanation:you did it wrong
Please help as fast as possible! I know that’s what everyone asks but seriously I’ll give you points
Answer:
Number 2 and number 1
Step-by-step explanation:
youre all good
4.3 GRE scores, Part I. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.
(a) Write down the short-hand for these two normal distributions.
(b) What is Sophia’s Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section? Draw a standard normal distribution curve and mark these two Z-scores.
(c) What do these Z-scores tell you?
(d) Relative to others, which section did she do better on?
(e) Find her percentile scores for the two exams.
(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?
The normal distribution is N(151, 7), the z-score for verbal and quantitative reasoning are 1.29 and 0.52 respectively.
What is the short-hand for these two normal distribution(a) The shorthand for the normal distribution of the Verbal Reasoning section is N(151, 7), where 151 is the mean score and 7 is the standard deviation. The shorthand for the normal distribution of the Quantitative Reasoning section is N(153, 7.67), where 153 is the mean score and 7.67 is the standard deviation.
(b) Sophia’s Z-score on the Verbal Reasoning section is (160-151)/7 = 1.29. Her Z-score on the Quantitative Reasoning section is (157-153)/7.67 = 0.52.
(c) The Z-scores represent how many standard deviations above or below the mean Sophia’s scores are. A Z-score of 1.29 on the Verbal Reasoning section means Sophia’s score is 1.29 standard deviations above the mean score of all test takers. A Z-score of 0.52 on the Quantitative Reasoning section means Sophia’s score is 0.52 standard deviations above the mean score of all test takers.
(d) Sophia did better on the Verbal Reasoning section because her Z-score is higher for that section.
(e) To find the percentile scores, we use the standard normal distribution table. Sophia’s percentile score on the Verbal Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 1.29 and the table, we find that her percentile score is approximately 90.7%. Her percentile score on the Quantitative Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 0.52 and the table, we find that her percentile score is approximately 69.4%.
(f) To find the percentage of test takers who did better than Sophia on each section, we can use the standard normal distribution table again. For the Verbal Reasoning section, we need to find the area to the right of Sophia’s Z-score of 1.29. Using the table, we find that this area is approximately 9.3%. Therefore, approximately 9.3% of test takers did better than Sophia on the Verbal Reasoning section. For the Quantitative Reasoning section, we need to find the area to the right of Sophia’s Z-score of 0.52. Using the table, we find that this area is approximately 30.4%. Therefore, approximately 30.4% of test takers did better than Sophia on the Quantitative Reasoning section.
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1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
Using the graphs, Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.
What are graphs?An organised-representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.
Information and data have different purposes: Data is an unadorned truth; information is the meaning that can be inferred from data.
Challenge 1
Olivia may have, for example, translated 10 units to the right after reflecting over the x axis.
Let's use point C to apply this series of steps.
C = (-2,-4) (-2,-4)
After reversing the x axis, C' becomes (-2,4); the y coordinate changes sign, and C" becomes (8,4) after moving to the right by 10 units. The x coordinate is then increased by 10.
The graphic shows that point C (-2, -4) shifts to C"(8,4). The other four points I'll let you investigate.
Olivia may have also tried shifting 10 units to the right before reflecting across the x axis. The sequence here is irrelevant. Order does important, though, for several other combinations of transformations.
Challenge 2
The point (x,y) will become after reflection across the y axis (-x,y). Here, the sign is reversed, and only the x coordinate changes. The y coordinate remains constant.
With the y axis reflection, a point like C (-2, -4) becomes C'(2, -4). By moving up 8 units, we get at C"(2,4) by adding 8 to the y coordinate, but this is not what the graphic displays. Thus, Angelica's approach is flawed.
The last four points should also contain other contradictions, as well.
Challenge 3
Even Michael's approach is flawed. Instead of using an x axis reflection, he completely relies on translations to change ABCDE into A"B"C"D"E".
Quick inspection suggests that Michael might be right. Yet, if you examine much more closely, you'll notice that things aren't exactly in line.
This time, we'll choose point D rather than point C.
D can be found at (-6, -2). To reach D' if we move up 8 units, we must add 8 to the y coordinate (-6,6). Then, to move 10 units to the right, add 10 to the x coordinate. And brings us to D" (4,6).
The diagram, however, reveals that D" is actually at (4,2)
Let you examine the other points, please. The only points that should go to the right places are C and E; the remaining points should not. Once more, Michael's failure to apply an x axis reflection is to blame. His A"B"C"D"E" figure is reversed from how it should have been.
To sum up, the strategies mentioned in problem 1 are the proper ones to use in order to make ABCDE go to A"B"C"D"E. Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.
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What are all possible values of x that satisfy the inequality x3−8≥1?
By answering the above question, we may state that Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.
[tex]x^3[/tex] - 8 ≥ 1
[tex]x^3[/tex] ≥ 9
Taking the cube root of both sides, we get:
x ≥ ∛9
Since ∛9 ≈ 2.08, the solution to the inequality is:
x ≥ 2.08
Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.
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If a populstion takes 10 years to double in size then find to the nearest tenths of a percent the relative frowth rate of the population
Classify the triangle below as Right, Obtuse, or Acute
The triangles are classified as:
4. Acute 5. Obtuse 6. Obtuse 7. Acute 8. Obtuse 9. Acute 10. Obtuse
How to Classify Triangles as Right, Obtuse, or Acute?To classify a triangle as right, obtuse, or acute, we need to apply the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
If the square of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is obtuse. If the square of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is acute.
4. To check if this is a right triangle, we need to find if 9² is equal to 4² + 6², which is not true, so the triangle is acute.
5. To check if this is a right triangle, we need to find if 16² is equal to 10² + 12², which is not true, so the triangle is obtuse.
6. To check if this is a right triangle, we need to find if (8√6)² is equal to 8² + 16², which is not true, so the triangle is obtuse.
7. To check if this is a right triangle, we need to find if 29² is equal to 20² + 21², which is true, so the triangle is acute.
8. To check if this is a right triangle, we need to find if √73² is equal to 3² + 8², which is not true, so the triangle is obtuse.
9. To check if this is a right triangle, we need to find if 12² is equal to 8² + 10², which is true, so the triangle is acute.
10. To check if this is a right triangle, we need to find if (3√34)² is equal to 9² + 15², which is not true, so the triangle is obtuse.
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help please
John's family cell phone bill is $143. the family plan cost $68 plus $15 for each person on the plan.
John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A
What is the total of the cost?
Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.
Let the number of people on John's family plan be represented by p.
According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:
C = $68 + $15p
We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:
$143 = C + A
where A represents any additional charges.
Substituting C into this equation, we get:
$143 = ($68 + $15p) + A
Simplifying, we can write:
$75 = $15p + A
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help!! Find the missing length and round it to the nearest tenth.
The length of the hypotenuse is approximately 6.7.
What is the Pythagorean theorem and how is it used to find the hypotenuse of a right triangle?
The Pythagorean theorem is a fundamental relationship in Euclidean geometry that relates the lengths of the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Mathematically, the Pythagorean theorem can be expressed as:
[tex]c^2 = a^2+ b^2[/tex]
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Finding the missing length :
In the given problem, we are given the lengths of two sides of a right triangle, which are 3 and 6. We can use these values to find the length of the hypotenuse using the Pythagorean theorem:
[tex]h^2 = 3^2+ 6^2[/tex]
[tex]h^2 = 9 + 36[/tex]
[tex]h^2 = 45[/tex]
Taking the square root of both sides gives:
[tex]h = \sqrt{45}[/tex]
Using a calculator, we can simplify this to:
[tex]h \approx 6.7[/tex] (rounded to the nearest tenth)
Therefore, the value of the hypotenuse of the right triangle with sides 3 and 6 is approximately 6.7.
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Write the equation of the trigonometric graph. Use a positive coefficient on cosine for this activity.
The required equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.
What is the cosine function?The cosine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.
The graph of the cosine function is a wave-like curve that oscillates between -1 and 1, with a period of 2π radians or 360 degrees.
As we can see, the function's behavior repeats itself. In terms of the form of the function, we may select any interval of length 2π and the following interval of length 2π will be equal to the previous one.
Here, y = 2cos[(π/8)(x-2)-2]
Thus, the equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.
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Given AD = BC and AD || BC Prove: ABCD is a paralleologram
The response to the given question would be that As a result, we have demonstrated that ABCD's opposing sides are parallel, proving that ABCD is a parallelogram.
What is parallelograms?A simple quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. Both sets of opposite sides are parallel and equal in a particular type of quadrilateral known as a parallelogram.
We must demonstrate that the opposing sides of ABCD's parallelogram are parallel.
CBA = DAB (Alternate interior angles)
Alternative interior angles (ABD = BAC; ADC = CBD) (Alternate interior angles)
DCA = ACD (Alternate interior angles)
Considering that AD = BC, we also have:
A + B Equals A + C. (Also on both sides)
AD = BC
Think about the two pairs of sides that are diagonally opposed: AB and CD and AD and BC.
We have these for AB and CD:
Interior angles of a quadrilateral: DAB + ABD + BCD + CDA = 180°; CBA + BAC + ADC + DCA = 180°. (Substituting corresponding angles)
We may insert them in and simplify to get: since DAB = CBA and ABD = BAC.
BCD = ADC
As a result of having the same transversal CD and equal alternative interior angles, AD and BC are also parallel. As a result, we have demonstrated that ABCD's opposing sides are parallel, proving that ABCD is a parallelogram.
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3.1 divided by 992
I don’t know this questin
Answer:
Step-by-step explanation:
0.003125
Answer:0.003125
When dividing by a bigger number to turn it to a decimals with 0s because it will always help and also use the simple way of division writing it down ex. 3.1 I 992 and put it in as many times as possible
Review the graph of function g(x). On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4). A curve starts at open circle (4, 2) and curves up through (8, 5). What are Limit of g (x) as x approaches 4 negative and Limit of g (x) as x approaches 4 plus, if they exist? Limit of g (x) = 2 as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) = negative 2 as x approaches 4 plus Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) D N E as x approaches 4 plus Limit of g (x) D N E as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus
The lateral limits of the function g(x) at x = 4 are given as follows:
[tex]\lim_{x \rightarrow 4^-} g(x) = -4, \lim_{x \rightarrow 4^+} g(x) = 2[/tex]
How to calculate the lateral limits?
To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.
If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.
On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4), hence the lateral limit to the left of x = 4, where x is less than 4, is given as follows:
[tex]\lim_{x \rightarrow 4^-} g(x) = -4[/tex]
A curve starts at open circle (4, 2) and curves up through (8, 5), hence the lateral limit to the right of x = 4, where x is greater than 4, is given as follows:
[tex]\lim_{x \rightarrow 4^+} g(x) = 2[/tex]
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A grocer wants to mix two kinds of coffee. One kind sells for $0.90
per pound, and the other sells for $2.40
per pound. He wants to mix a total of 28
pounds and sell it for $1.45
per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
In order to create a 28-pound blend that he can sell for $1.45 per pound, the grocer should combine approximately 17.73 pounds of the less costly coffee and 10.27 pounds of the more expensive coffee.
How many pounds of each kind should he use in the new mix?Let's designate the quantity of the less expensive coffee X and the more expensive coffee Y. Since we are aware that the grocer wishes to combine 28 pounds altogether, we can write:
x + y = 28
The total profit from selling the mixture would be: 28($1.45) = $40.60 because we also know that he intends to sell it for $1.45 per pound.
The costs and quantities of the two varieties of coffee can be used to create a new equation.
0.9x + 2.4y = $40.60
With two variables in each equation, we now have two equations that we can solve by substitution or elimination. Use of substitution
28 + y = x - 0.9x + 2.4y = 40.60
0.9x + 2.4(28 - x) = $40.60
0.9x + 67.2 - 2.4x = $40.60\s-1.5x = -$26.60\sx = 17.73
We can apply the first equation to determine y now that we know x: x + y = 28.
17.73 + y = 28 \sy = 10.27
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Summarize in your own words a quantity in the life-science that is modelled by a function of time. For your function, if you knew some values of its derivative, what would those values be telling you about your model? Be specific (don’t just say “rate-of-change”).
One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.
How can this be modeled?This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.
If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.
A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.
If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.
A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.
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Nora left her house and drove to the store. She stopped and went inside. From there,
she drove in the same direction until she got to the bank. She stopped and went
inside the bank. Then she drove home. The graph below shows the number of blocks
away from home Nora x is a minutes after she left her house, until she got back home.
Distance (Blocks from Home)
How long was Nora in the bank?
Answer:
7 minutes
Step-by-step explanation:
It is 7 minutes because the bank it the top straight line and it elapses for 7 minutes
Does this represent a function yes or no because??????????
Answer:
Step-by-step explanation: It is a function. Because one input goes to exact one output.
In 50 words or fewer, describe the relationship between the volumes of a cylinder
and a cone that have the same size base and equal heights.
These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.
When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.
Find the length of the third side. If necessary, write in simplest radical form. 7 √51
The third side of the triangle is 8
Pythagoras' theorem:Pythagoras' theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle.
It states that: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Here we have
A right-angled triangle
From the figure
The sides of the triangle are 7 and √15
As we know from Pythagoras' theorem
=> Hypotenuse² = side² + side²
Substitute the above values in the condition
=> Hypotenuse² = (7)² + (√15)²
=> Hypotenuse² = 49 + 15
=> Hypotenuse² = 64
=> Hypotenuse = 8
Therefore,
The third side of the triangle is 8
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Complete Question is given picture