Option a) t= 4 years. The effective interest rate for the specified account is 9.31%. This is because the effective interest rate is the rate that actually applies to the balance in the account, taking into account the compounding frequency. The formula for the effective interest rate is:
Effective interest rate = (1 + nominal yield / compounding frequency) ^ compounding frequency - 1
In this case, the nominal yield is 9% and the compounding frequency is 2 (since it is compounded twice a year). Plugging these values into the formula, we get:
Effective interest rate = (1 + 0.09 / 2) ^ 2 - 1
Effective interest rate = (1.045) ^ 2 - 1
Effective interest rate = 1.092025 - 1
Effective interest rate = 0.092025
Converting this to a percentage, we get:
Effective interest rate = 9.31%
Therefore, the correct answer is 9.31%.
For the second part of the question, we can use the formula for future value to find the missing quantity. The formula is:
A = P(1 + rt)
Plugging in the given values, we get:
5580 = 4500(1 + 0.06t)
Solving for t, we get:
5580 = 4500 + 270t
1080 = 270t
t = 4
Therefore, the correct answer is t = 4 years, or choice A.
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TB The number is 27% of the pupils in a school are in Primary Six. There are 540 Primary Six pupils How many pupils are there in the school? % % There are 20 pupils in the school. 27%-> 1% →>> 100%->
In linear equation, 2000 pupils are there in the school.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
= 540/27%
= 54000/27
= 2000
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Exit
3-2: Practice & Problem Solving week of 2/27
Find the least common multiple (LCM) for the pair of numbers.
45,7
The LCM of 45 and 7 is
Answer:
315
Step-by-step explanation:
The LCM for 45 and 7 is 315
One way to find the LCM of 7 and 45 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 7?What are the Factors of 45?
Here is the prime factorization of 7:
7171
And this is the prime factorization of 45:
32×5132×51
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 7, 3, 5
what are 3 numbers that equal 18.75 with a range of 1.75 and a median of 6
Answer:
5.5, 6, and 7.25
Step-by-step explanation:
3 numbers equal 18.75 tells us:
a + b + c = 18.75, where a, b, and c are the 3 unknown numbers respectively.
Next, we know that the range is 1.75. Let us consider that c is the greatest value and a is the smallest value. Thus, we can write
c - a = 1.75
Lastly, we know that there is a median of 6. This tells us that the "middle" number (which in this case would be b if c is greatest and a is smallest) should be 6.
b = 6.
Substituting we can write,
a + c + 6 = 18.75
a + c = 12.75
Also,
c - a = 1.75
c = a + 1.75
Substituting back into the other equation we get,
a + ( a + 1.75) = 12.75
2a + 1.75 = 12.75
2a = 11
a = 5.5
Now, we can find the last number.
c = (5.5) + 1.75
c = 7.25
Plug all 3 numbers back into the original equation to verify if our numbers are correct:
5.5 + 6 + 7.25 = 18.75
Thus, we know we are correct.
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Two hikers, Alan and Ben, are 12.6 miles apart and walking towards each other. They meet in 3 hours. Find the rate of each hiker if Ben walks 0.8 mph faster than Alan.
Alan's rate of speed is _____ mph. (Round to one decimal place.)
Ben's rate of speed is ___ mph. (Round to one decimal place.)
In response to the supplied query, we may state that Ben's speed, equation rounded to one decimal place, is x + 0.8 = 2.5 mph.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
Rate times distance
Let x represent Alan's speed in mph. Ben's speed will then be x + 0.8 mph.
They will have travelled 12.6 kilometres in total when they finally cross paths. The formula is as follows:
[tex]12.6 = (x + x + 0.8) × 3\\12.6 = 6x + 2.4 \s10.2 = 6x \sx = 1.7[/tex]
Alan is moving at a speed of 1.7 mph, decimal place included.
Ben's speed, rounded to one decimal place, is x + 0.8 = 2.5 mph.
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Answer:
Alan's rate of speed is 1.7 mph.
Ben's rate of speed is 2.5 mph.
Step-by-step explanation:
We can use the distance-rate-time formula to solve the given problem.
[tex]\boxed{\sf Distance=rate \times time}[/tex]
Create a distance equation for each of the hikers.
AlanDistance = dSpeed = rTime = 3 hoursTherefore, the equation for Alan's distance in terms of r is:
[tex]\implies \sf d = 3r[/tex]
BenDistance = dSpeed = r + 0.8 (as Ben walks 0.8 mph faster than Alan)Time = 3 hoursTherefore, the equation for Ben's distance in terms of r is:
[tex]\implies \sf d = 3(r+0.8)[/tex]
Alan and Ben are 12.6 miles apart and walking toward each other.
Therefore, their combined distances will equal 12.6 miles.
Set the sum of the found expressions for distance equal to 12.6 and solve for r:
[tex]\implies \sf d_{Alan}+d_{Ben}=12.6[/tex]
[tex]\implies \sf 3r+3(r+0.8)=12.6[/tex]
[tex]\implies \sf 3r+3r+2.4=12.6[/tex]
[tex]\implies \sf 6r+2.4=12.6[/tex]
[tex]\implies \sf 6r=10.2[/tex]
[tex]\implies \sf r=1.7[/tex]
Therefore:
Ben = r = 1.7 mphAlan = r + 0.8 = 1.7 + 0.8 = 2.5 mphSolutionAlan's rate of speed is 1.7 mph.
Ben's rate of speed is 2.5 mph.
Given: PQ ≈ QS and QS = ST
Prove: PQ = ST
Proof:
Answer:
Proof:
Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.
Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.
To prove that PQ is exactly equal to ST, we must use the transitive property of equality.
Transitive Property of Equality: If a = b and b = c, then a = c.
Using the transitive property, we can say:
PQ ≈ QS and QS = ST → PQ ≈ ST
Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:
PQ ≈ ST ≈ rounded value
Therefore, PQ is exactly equal to ST because they have the same rounded value.
The amount of orange juice that can be obtained from a single orange is normally distributed. A manufacturing company selects an srs of size n
The shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population is approximately Normal
If the amount of orange juice that can be obtained from a single orange is Normally distributed, then the distribution of the sample mean of orange juice obtained from a sample of size 5 from this population will also be Normally distributed.
The mean of the sample mean distribution will be equal to the population mean, which is the mean amount of orange juice that can be obtained from a single orange.
The standard deviation of the sample mean distribution, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size.
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The given question is incomplete, the complete question is:
The amount of orange juice that can be obtained from a single orange is Normally distributed. A manufacturing company selects an SRS of size n = 5 from the population of all oranges in their inventory and calculates the sample mean amount of orange juice that is obtained. What is the shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population?
Kyle’s handful of trail mix has 2 almonds, 4 peanuts, 3 raisins, and 5 sunflower seeds. If he picks one item from the handful of trail mix at random, what is the probability that the item is a peanut?
StartFraction 1 over 14 EndFraction
StartFraction 1 over 7 EndFraction
StartFraction 2 over 7 EndFraction
Two-fifths
The answer is Start Fractiοn 2 οver 7 End Fractiοn.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
Kyle's handful οf trail mix cοntains a tοtal οf 2 + 4 + 3 + 5 = 14 items.
The prοbability οf picking a peanut is the number οf peanuts in the handful divided by the tοtal number οf items in the handful:
prοbability οf picking a peanut = number οf peanuts / tοtal number οf items
prοbability οf picking a peanut = 4 / 14
Simplifying the fractiοn by dividing bοth the numeratοr and denοminatοr by 2, we get:
prοbability οf picking a peanut = 2 / 7
Therefοre, the answer is StartFractiοn 2 οver 7 EndFractiοn.
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Please show your work.
The slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.
Opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.
What are parallelograms and rhombus?A parallelogram is a quadrilateral (a four-sided polygon) in which opposite sides are parallel.
A rhombus is a special type of parallelogram in which all four sides are congruent.
To prove that quadrilateral JKLM is a parallelogram, we need to show that opposite sides are parallel.
We can find the slope of each side by using the formula:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of JK:
(-5 - 1) / (1 - (-3)) = -6/4 = -3/2
The slope of LM:
(4 - (-2)) / (3 - 7) = 6/-4 = -3/2
The slope of KL:
(-2 - (-5)) / (7 - 1) = 3/6 = 1/2
The slope of MJ:
(1 - (-5)) / (-3 - 1) = 6/-4 = -3/2
We can see that the slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.
To prove that JKLM is not a rhombus, we need to show that at least one pair of opposite sides are not congruent.
We can find the length of each side using the distance formula:
Length of JK:
√[(1 - (-5))² + (1 - (-3))²] = √[36 + 16] = √[52]
Length of KL:
√[(-2 - (-5))² + (7 - 1)²] = √[9 + 36] = √[45]
Length of LM:
√[(4 - (-2))² + (3 - 7)²] = √[36 + 16] = √[52]
Length of MJ:
√[(-5 - 1)² + (-3 - 1)²] = √[36 + 16] = √[52]
We can see that all four sides have the same length, which means that they are congruent. Therefore, JKLM is a rhombus.
However, we can also see that opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.
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A lighthouse casts a 144-foot shadow. A nearby lamppost that measures 5.5 feet casts an 9-foot shadow. What is the height (in feet) of the lighthouse?
Therefore, the height (in feet) of the lighthouse is 88 feet.
What is an illustration of height?A person's or something's height can be described as their vertical position or their vertical extension (how "tall" they are) (how "high" a point is). For example, "The height of the structure is 50 m" or "The height of an airplane in-flight is roughly 10,000 m".
Let's use proportions to solve the problem. We can set up a ratio of the height of the lighthouse to the length of its shadow, and another ratio of the height of the lamppost to the length of its shadow, and then equate the two ratios:
height of lighthouse / length of shadow of lighthouse = height of lamppost / length of shadow of lamppost
Let's plug in the given values:
h / 144 = 5.5 / 9
To solve for the height of the lighthouse, we can cross-multiply and simplify:
9h = 144 × 5.5
9h = 792
h = 88
Therefore, the height of the lighthouse is 88 feet.
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Use pythagorean theorem to answer.
The unknown side 'x' is found using pythagorean theorem as: x = 12.69.
Explain about the Pythagorean theorem?The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.
The Pythagoras equation applies to any triangle with a 90° angle solely on a single side.The Pythagorean Theorem states that a right triangle's hypotenuse (the side across from the right angle) has a square that is equal to the sum of its legs.Pythagorean Theorem is also known as:
a²+ b² = c²
Given sides are:
13, 3 and x.
Then,
3²+ x² = 13²
x² = 13² - 3²
x² = 169 - 9
x² = 160
x = √160
x = 12.69
Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.
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an investment of $12,000 earns an interest of 2.5% per year
compounded monthly, for 6 years. calculate the Future value and
effective annual interest rate
The future value of the investment after 6 years is $14,370.88; while the effective annual interest rate is 2.56%.
To calculate the future value of the investment, we can use the formula: FV = PV (1 + r/n)^(nt), where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, PV = $12,000, r = 0.025, n = 12 (compounded monthly), and t = 6.
Plugging these values into the formula, we get:
FV = $12,000 (1 + 0.025/12)^(12*6)
FV = $12,000 (1.002083333)^72
FV = $14,370.88
Therefore, the future value of the investment after 6 years is $14,370.88.
To calculate the effective annual interest rate, we can use the formula: EAR = (1 + r/n)^(n) - 1, where r is the annual interest rate and n is the number of times the interest is compounded per year.
In this case, r = 0.025 and n = 12 (compounded monthly).
Plugging these values into the formula, we get:
EAR = (1 + 0.025/12)^(12) - 1
EAR = (1.002083333)^12 - 1
EAR = 0.02568245
Therefore, the effective annual interest rate is 2.568245%.
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help please!!!!!!!!$!!!
4. What is the simplest form of the expression?
√20+√45-√5
04√5
13 √5
5√5
Answer:
4√5
Step-by-step explanation:
To simplify √20+√45-√5, we need to look for factors that can be simplified under the square root. We can simplify 20 and 45 by factoring out perfect squares:
√20 + √45 - √5 = √(4×5) + √(9×5) - √5
= 2√5 + 3√5 - √5
= 4√5
Therefore, the simplest form of the expression is 4√5
35+=7(_+_) i need help asp
Answer:
dddiejehehegeheheheh
the techniques of shifting, compressing, stretching, an(d)/(o)r reflecting. g(x)=-x^(3)+7
The techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.
The techniques of shifting, compressing, stretching, and reflecting are used to transform functions. These techniques allow us to move the graph of a function up, down, left, or right, to make it wider or narrower, and to flip it over the x-axis or y-axis.
The function g(x)=-x^(3)+7 can be transformed using these techniques. For example, we can shift the graph of g(x) up by 2 units by adding 2 to the function: g(x)=-x^(3)+7+2=-x^(3)+9. We can also stretch the graph of g(x) vertically by multiplying the function by a constant greater than 1: g(x)=2(-x^(3)+7)=-2x^(3)+14.
Similarly, we can compress the graph of g(x) vertically by multiplying the function by a constant between 0 and 1: g(x)=0.5(-x^(3)+7)=-0.5x^(3)+3.5. We can also reflect the graph of g(x) over the x-axis by multiplying the function by -1: g(x)=-(-x^(3)+7)=x^(3)-7.
These are just a few examples of how the techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.
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4. Write the function rule for g(x) from f(x) = √x. Shift up 5, then vertical stretch by a factor of 2, followed by a shift to the right 3 units.
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
The function rule for g(x) from f(x) = √x can be found by applying the given transformations to f(x). First, we shift up 5 units by adding 5 to the function. Then, we apply a vertical stretch by a factor of 2 by multiplying the function by 2. Finally, we shift to the right 3 units by replacing x with (x - 3) in the function. The resulting function rule for g(x) is:
g(x) = 2√(x - 3) + 5
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
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the base of a parallelogram is one third its height if the area is 768 square cm find the base and height
The base and height of the parallelogram is B = 16 cm and H = 48 cm
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be represented as A
Now , area of parallelogram A = bh
And , base of a parallelogram is one third its height
So , B = ( 1/3 )H
And , area of parallelogram is A = 768 cm²
On simplifying , we get
768 = ( 1/3 )H²
Multiply by 3 on both sides , we get
H² = 2304
Taking square roots on both sides , we get
H = 48 cm
So , the height of the parallelogram is 48 cm
And , the base of the parallelogram is 16 cm
Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively
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Does anyone know how to answer this?
Following surgery, a patient has been receiving a pain relief medication intravenously. The concentration C� (in milligrams per liter) of the medication in the patient's bloodstream t� hours after this process started is given by
C(t)=60t+12t+6,t≥0�(�)=60�+12�+6,�≥0
a) The patient will not receive pain relief unless the concentration of the medication is 1010 or more milligrams per liter. Use this function to determine the time interval for which the concentration of the medication, C� , will be greater than or equal to 1010 milligrams per liter.
The time interval for which the patient will receive pain relief is hours. (Express your answer in interval notation and round any decimals to the nearest tenth of an hour).
The time interval for which the patient will receive pain relief is [1.3, 8.3] hours.
To determine this, we can use the equation C(t) = 60t + 12t + 6, where t is the number of hours after the surgery. Setting C(t) = 1010 and solving for t, we get t = 13.3, so the patient will receive pain relief for t > 13.3 hours, or [1.3, 8.3] hours.
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(Quick!) Can you show work as well please?
The value of x would be equal to 20 degrees.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
We are given the parameters as;
7x and (x + 20)
The sum of angle is equal to 180.
7x + (x + 20) = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160/8
x = 20
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0 A community center offers classes for students.
. The range of the number of students in each class is 13.
. The median number of students in each class is 9.
Which of the following box-and-whisker plots could represent the numbers of students in the classes?
Numbers of Students
Numbers of Students
in Classes
in Classes
C₂
+++
2 4 6 8 10 12 14 16 18 20 22 24
Numbers of Students
in Classes
+++
2 4 6 8 10 12 14 16 18 20 22 24
B.
D.
++
2 4 6 8 10 12 14 16 18 20 22 24
Numbers of Students
in Classes
+111*
2 4 6 8 10 12 14 16 18 20 22 24
T
The response is A.
Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.
what is the range?The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.
As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
from the question:
According to the information provided, the number of pupils in each class might range from 9+6 = 15 to 9+6 = 3. Because the maximum value exceeds 15, options C and D cannot accurately represent the number of students in the classes.
Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.
Option B's median value is 9, but its range (from 9-5 = 4 to 9+5 = 14) is only 11, which is less than the range that could be achieved by the number of students. As a result, option B cannot accurately reflect the number of students enrolled in each class.
Thus, the response is A.
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Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
The investment οf $1,000 will be wοrth $1,225.04 after 3 years.
What is Cοmpοund interest?Cοmpοund interest is interest οn the principal amοunt οr lοan which is calculated accοrding tο the number οf cοmpοunds in οne year.
In this, the interest earned in each periοd is based οn the tοtal amοunt, which includes bοth the principal and the accumulated interest.
The fοrmula used fοr cοmpοund interest is
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]Here we have
The principal amοunt is $ 1000
The annual interest rate here is 7.5%
The interest is cοmpounded annually.
The time periοd is 3 years
Using the fοrmula,
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
A = 1,000 (1 + 0.075/1)⁽¹⁽³⁾⁾
= 1,000 (1.075)³
= $1,225.04
Therefοre,
The investment of $1,000 will be wοrth $1,225.04 after 3 years.
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Let's relax a bit before we keep answering! What's your fav song and singer?
shirt by sza and fav singer ariana grande!
thanks so much!
Answer:
Love The Way You Lie - Eminem
13. R(x) (2x+6)(x-1) (4-x)(x+2) Find any vertical asymptote(s) and any horizontal asymptote(s)
The vertical asymptote(s) for R(x) is x=1 and x=-2. The horizontal asymptote(s) is y=0.
To find the vertical asymptotes, we look at each factor and look for any x-values that would make the factor equal to zero.
The factors are (2x+6), (x-1), (4-x), and (x+2).
So, x=1 would make (x-1) equal to zero and x=-2 would make (x+2) equal to zero.
To find the horizontal asymptote, we look at the degree of the highest exponent and divide it into the coefficient of the term with the highest degree.
Since the highest exponent is 1 and there is no coefficient, the answer is y=0.
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please help with my this just write the letters in the order it should go in please
The correct match of the accounting terms such as assets, debits, and credit, would be:
Asset - ODebit - KCredit - RCapital - G Liabilities - QCash payments - NProfit - BCash receipts - DOwner's equity - LTransactions - ESole trader - CIncome - Q Expenses - HAccounting equation - F Loss - J Bank - M Subsidiary journal - AWhat are some accounting terms ?This is a matching exercise that matches various accounting terms with their definitions. Here are the meanings of the terms:
Asset: Possessions of the business that can be used to generate income.Debit: An entry on the left-hand side of the ledger that records an increase in assets or a decrease in liabilities.Book of first entry: Also known as a subsidiary journal, this is a book where transactions are first recorded before being transferred to the general ledger.Profit: This is the excess of income over expenses. When income is greater than expenses, the business makes a profit.Sole trader: This refers to a business that is owned and operated by one person.Cash receipts: This refers to transactions that generate cash for the business, such as sales.These are some terms in accounting which are used to ensure that proper records are taken.
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A line / is said to be tangent to a circle Cat a point P if and only if I meets Cat P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, show that lis tangent to the circle at P if and only if /is perpendicular to the line OP.
Yes, a line / is said to be tangent to a circle at a point P if and only if it meets the circle at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, we can show that / is tangent to the circle at P if and only if it is perpendicular to the line OP.
To show this, first consider a line / that is perpendicular to the line OP. Since the line OP is the line connecting the point P and the center of the circle, O, the line / must intersect the circle at P and nowhere else. This means that / is tangent to the circle at P.
Now, consider a line / that is not perpendicular to the line OP. Since / is not perpendicular to the line OP, it will either intersect the circle at two points or not at all. Since it is not tangent to the circle, it cannot intersect the circle at only one point, P. Therefore, we have shown that a line / is tangent to a circle at a point P if and only if it is perpendicular to the line OP.
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16x^2 - 81=
Factor completely
Answer:
Below
Step-by-step explanation:
(4x- 9)(4x + 9) Just by looking.....
Can someone please answer and explain a & b please, thank you.
A roll of ribbon was 12 meters long. Diego cut 9 pieces of ribbon that were 0.4 meter
each to tie some presents. He then used the remaining ribbon to make some
wreaths. Each wreath required 0.6 meter. For each question, explain your reasoning.
a. How many meters of ribbon were available for making wreaths?
b.
How many wreaths could Diego make with the available ribbon?
Answer: a. 8.4 meters b. 14 wreaths
Step-by-step explanation:
The following equation shows the problem, with x representing the number of wreaths made:
12 = 9(0.4) + 0.6x
To answer a, get 0.6x alone:
12 = 9(0.4) + 0.6x
12 = 3.6 + 0.6x
8.4 = 0.6x
There were 8.4 meters available to make wreaths
To answer b, get x alone
8.4 = 0.6x
14 = x
Diego could make 14 wreaths with the available ribbon
Hope this helps!
use the image below to find the requested values?
find the measure of hdg
Answer:
<HDG = 39°
Step-by-step explanation:
Red square is a right angle which mean its a 90°
Those two angle <CDG and <HDG are complementary angle which mean they both add up to 90°
<CDG + <HDG = 90°
51° + (3t+15)° = 90°
Solve for t.
3t + 51 + 15 = 90°
3t + 66 = 90°
3t = 24
t = 8
Plug t = 8 into <HDG to find the measurement.
<HDG = 3t + 15
<HDG = 3*8 + 15
<HDG = 24 + 15
<HDG = 39°
Select the two real roots of the polynomial fun S(r)=r^(5)+5r^(4)-7r^(3)-43r^(2)-8r-48
The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 are r = -8 and r = 3.
The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 can be found by factoring the polynomial and finding the values of r that make the function equal to zero.
First, we can factor the polynomial using the Rational Root Theorem, which states that if a polynomial has rational roots, they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is -48 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.
We can use synthetic division to test these possible roots and find the ones that make the function equal to zero. After testing the possible roots, we find that the two real roots are r = -8 and r = 3.
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Find the measure of the missing arc lengt. pt. 2
Answer:
100°
Step-by-step explanation:
You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.
Crossing chordsThe angle where chords cross is the average of the two arcs that they intercept. Here, that means ...
85° = (AE +BC)/2
Solving for BC, we get ...
2(85°) = AE +BC
BC = 170° -AE = 100°
The missing arc measure is 100°.