If the length of the rectangle is represented by x, then the height and width can be represented by the factors a and b, respectively. Therefore, the expression for the height and width in terms of the length can be written as:
Height = a * x
Width = b * x
These expressions can be used to find the height and width of the rectangle if the length and the factors are known.
For example, if the length is 10 and the factors are 2 and 3, then the height would be 2 * 10 = 20 and the width would be 3 * 10 = 30.
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1.) How can we get Equation B from Equation A?
A: Add/subtract the same quantity to/from both sides.
B: Add/subtract a quantity to/from only one side.
C: Multiply/divide both sides by the same non-zero constant.
D: Multiply/divide only one side by a non-zero constant.
2.) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
A: Yes
B: No
Multiply/divide both sides by the same non-zero constant (option C).
Both equations can be considered equivalent (yes).
How to solveTo solve the equation, we can start by simplifying equation A by opening the brackets:
3(x + 2) = 18
3x + 6 = 18
We can then solve for x by dividing both sides of the equation by a non-zero constant (3):
3x + 6 = 18
3x = 18 - 6
3x = 12
x = 4
From this solution, we can simplify equation A to obtain equation B:
x + 2 = 6
x = 6 - 2
x = 4
Hence, equation B can be obtained from equation A.
Part 2: Equivalent equations are algebraic equations that have the same solutions.
To determine if both equations are equivalent, we can solve them to their simplest form:
Equation A:
3(x + 2) = 18
3x + 6 = 18
3x = 18 - 6
3x = 12
x = 4
Equation B:
x + 2 = 6
x = 6 - 2
x = 4
Since both equations have the same solution, we can conclude that they are equivalent.
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You rolla fair 6-sided die what is p? ( rollgreater than 4)?
This is on kahn acedmy
The probability of rolling the dies and getting greater than 4 will be [tex]\dfrac{2}{6}[/tex].
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Given that the 6-sided die is rolled, the probability of getting a number greater than 4 will be calculated as,
Sample space = {1, 2, 3, 4, 5, 6} = 6
Favourable outcomes = {5,6} = 2
[tex]\rm Probability = \dfrac{Favourable \ events}{Sample\ space}[/tex]
[tex]\rm Probability = \dfrac{2}{6}[/tex]
Therefore, the probability will be [tex]\dfrac{2}{6}[/tex].
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Omar ordered a set of purple and red pins. He received 60 pins in all. 33 of the pins were purple. What percentage of the pins were purple?
55% of the pins were purple if Omar ordered a set of purple and red pins. He received 60 pins in all. 33 of the pins were purple.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To find the percentage of purple pins, we need to divide the number of purple pins by the total number of pins and multiply by 100.
Number of purple pins = 33
Total number of pins = 60
Percentage of purple pins = (Number of purple pins / Total number of pins) x 100
= (33 / 60) x 100
= 55%
Therefore, 55% of the pins were purple.
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I neeeeedddd helppppp
Answer:
∠A + ∠B + ∠C = 180° （∠sum of triangle）90°+ 4x+19°+5x-10°=180°9x=81x=9°∠A=90°∠B=55°∠C=35°Find an equation of the line that satisfies the given conditions. Through (1,6); parallel to the line y = 9x - 4
The equation of the line satisfying the given conditions. It passes through (1,6); parallel to the line y = 9x - 4 is y = 9x - 3.
To find an equation of the line that satisfies the given conditions, we need to use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Since the line we are looking for is parallel to the line y = 9x - 4, it will have the same slope, which is 9. Therefore, the equation of the line we are looking for will be y = 9x + b.
Now, we need to find the value of b. We can do this by plugging in the given point (1,6) into the equation and solving for b:
6 = 9(1) + b
6 = 9 + b
b = -3
So the equation of the line that satisfies the given conditions is y = 9x - 3.
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Find the length of the third side if necessary round to the nearest tenth 8 14
Answer:
Step-by-step explanation:
based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest who
Question 5 of 5
The graph shows the number of weeks of practice (x) and the number of
shots missed in a free-throw drill (y). The equation of the trend line that best
fits the data is y = -x + 6. Predict the number of missed shots after 6
weeks of practice.
Number of shots missed
987654321
•
123456789
Weeks of practice
According to the information, it can be predicted that the number of missed shots after six weeks of practice is zero (0).
How to calculate the number of lost shots after six weeks of practice?To calculate the number of lost shots after six weeks of practice, we must take into account the function that relates the weeks of practice with lost shots. In this case we must replace the value of X that corresponds to the weeks of practice and we will obtain as a result the amount of lost shots as shown below:
y = -x + 6y = - 6 + 6y = 0According to this function, we can infer that after six weeks of practice there will be 0 missed shots.
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From point A, Stanley walks 200 m due east to point B. From B, he then walks 160 m due south to point C. Work out the length of AC. Give your answer correct to 3 significant figures
The length of AC is 224 meters to 3 significant figures.
a² + b² = c²
where c is the hypotenuse (the side opposite the right angle) and a and b are the two legs (the sides adjacent to the right angle).
In this case, we can treat Stanley's path as a right triangle with legs AB and BC, and hypotenuse AC. Since we are given the lengths of AB and BC, we can plug those into the Pythagorean theorem and solve for AC.
AC² = AB² + BC²
AC² = (200 m)² + (160 m)
AC² = 40,000 m² + 25,600 m²
AC² = 65,600 m²
To find AC, we take the square root of both sides:
AC = [tex]\sqrt{65600}[/tex] m
AC ≈ 256
Finally, we round to 3 significant figures to get length of AC ≈ 224 meters.
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Polling agency is investigating the voter support for_ regions have equal number of voters ballot measure in an upcoming city election The City is divided in two in them: The agency will select _ random regions Region A and region B. Both population proportion of voters who would sample of 500 voters from one region, Region A of the city Assume that support the ballot measure in Region A is 0. 47. The What is the probability that the proportion of voters in the sample of Region who support the ballot measure greater than 0. 50 ? The polling agency will take another sample from different region, Region B, of the city: The the population proportion of voters who would agency plans to select random sample of 400 voters. Assume that support the ballot measure in Region B is 0. 51 What is the probability that , measure might pass?
The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is approximately 0.1736 or 17.36%. The probability that the ballot measure might pass in Region B can be calculated using a confidence interval approach.
The confidence interval for the population proportion of voters who support the ballot measure in Region B:
CI = p ± z × SE
where p is the sample proportion, z is the critical value for the desired confidence level (e.g., z=1.96 for 95% confidence), and SE is the standard error of the sample proportion.
the standard error of the sample proportion:
SE = [tex]sqrt [p ×\frac{(1-p)}{n} ][/tex] = [tex]sqrt[0.51 ×\frac{(1-0.51)}{400} ][/tex] = 0.025
where p is the sample proportion and n is the sample size.
the confidence interval using a 95% confidence level:
CI = 0.51 ± 1.96 0.025 = (0.46, 0.56)
Therefore, we can be 95% confident that the true population proportion of voters who support the ballot measure in Region B falls within the range of 0.46 to 0.56. Since the lower bound of the confidence interval is above 0.50, there is a possibility that the ballot measure might pass in Region B. However, the exact probability would depend on the actual population proportion and the sample size.
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sky can run 3 miles per hour faster than her sister rose can walk. If Sky ran 12 miles in the same time it took Rose to walk 8 miles, what is the speed of each sister in this case?
Sky can run 3 miles per hour faster than her sister rose can walk. If Sky ran 12 miles in the same time it took Rose to walk 8 miles, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.
To find the speed of each sister, we can use the formula distance = speed × time. We can set up a system of equations to solve for the speeds of Sky and Rose. Let s be the speed of Sky and r be the speed of Rose. Then we have:
12 = s × t (equation 1)
8 = r × t (equation 2)
We are also told that Sky can run 3 miles per hour faster than Rose, so we can write:
s = r + 3 (equation 3)
Now we can substitute equation 3 into equation 1 and solve for t:
12 = (r + 3) × t
t = 12 / (r + 3)
Next, we can substitute this value of t into equation 2 and solve for r:
8 = r × (12 / (r + 3))
8(r + 3) = 12r
8r + 24 = 12r
24 = 4r
r = 6
So the speed of Rose is 6 miles per hour. We can use equation 3 to find the speed of Sky:
s = 6 + 3
s = 9
So the speed of Sky is 9 miles per hour. Therefore, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.
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The speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.
Let's begin by defining some variables: let x be Rose's walking speed, and x + 3 be Sky's running speed. Since we know that Sky ran 12 miles and Rose walked 8 miles in the same amount of time, we can write an equation to represent this:
12 / (x + 3) = 8 / x
Cross-multiplying and simplifying gives us:
12x = 8x + 24
4x = 24
x = 6
So Rose's walking speed is 6 miles per hour, and Sky's running speed is 6 + 3 = 9 miles per hour.
Therefore, the speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.
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marys florist charges $3 per rose and plus $35 for a delivery. sam bought a bunch of roses and delivered to his mom. which value is the cost?
a) $69
b) $70
c) $71
d) $72
3. For a matrixAof sizem×n, explain why the following statements are logically equivalent: (a) For eachb∈Rm, the matrix equationAx=bhas a solution. (b) Eachb∈Rmis a linear combination of the columns inA(c) The columns ofAspanRm(d) The reduced echelon form ofAhas a pivot in every row.
All four statements are logically equivalent.
The statements (a), (b), (c), and (d) are all logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.
Let's start with statement (a): For each b∈Rm, the matrix equation Ax=b has a solution. This means that for any vector b in Rm, there exists a vector x in Rn such that Ax=b.
Now, let's look at statement (b): Each b∈Rm is a linear combination of the columns in A. This means that for any vector b in Rm, we can write b as a linear combination of the columns of A, which is equivalent to saying that Ax=b has a solution.
Statement (c) says that the columns of A span Rm. This means that the columns of A can be combined in a linear combination to produce any vector in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.
Finally, statement (d) says that the reduced echelon form of A has a pivot in every row. This means that the matrix A is of full rank and that there are no free variables in the equation Ax=b. This implies that there is a unique solution for every vector b in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.
Therefore, all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.
The solution to this question is to understand that all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.
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In a basket 5/6 of the fruits are apples. 4/5 of the apples are red apples. What fraction of the fruits in the basket red apples? Give the answer in simplest form
Answer:
2/3 of the fruits in the basket are red apples.
Step-by-step explanation:
5 apples of 6 total fruit are in a basket.
4 apples are red.
Take 4 and divide it by 6, you will get 0.67 or 2/3.
2/3 cannot be simplified.
3. ( 2 points) Find the value of \( a \) for which \[ v=\left[\begin{array}{c} -4 \\ a \\ -5 \\ -9 \end{array}\right] \] is in the set \[ H=\operatorname{span}\left\{\left[\begin{array}{c} 4 \\ 4 \\ 4
-4
The equation for the vector v given is: \( v=\left[\begin{array}{c} -4 \\ a \\ -5 \\ -9 \end{array}\right] \).
The set \( H \) is defined as the span of the vector \( \left[\begin{array}{c} 4 \\ 4 \\ 4\end{array}\right] \).
To find the value of a, we need to express the vector v in terms of the basis vector for H.
We can solve for a using the following equation: \( v = -4\left[\begin{array}{c} 4 \\ 4 \\ 4 \end{array}\right] + a\left[\begin{array}{c} 4 \\ 4 \\ 4 \end{array}\right] \)
Since the vector v has the same magnitude in each component, we can set the components equal:
\(-4 = a\)
Therefore, the value of a is -4.
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Question 4 options:
In a ratio of 3:4:5, three entrepreneurs invested in a project
an amount of $ 875,000 altogether.
Calculate the second largest share of the three. Round off to
the nearest 100th.
The ratio of investment is 3:4:5, which means the total ratio is 3+4+5 = 12.
Let the common ratio be x, then the amount invested by each entrepreneur is:
3x + 4x + 5x = 12x
According to the problem, 12x = $875,000
So, x = $875,000/12 = $72,916.67
Therefore, the second largest share is 4x = 4*$72,916.67 = $291,666.68
Rounding off to the nearest 100th, the second largest share is $291,666.67.
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Can someone answer this for me
uestion 3 of 19, Step 1 of 1 (1)/(19) Correct etermine whether the following statement is true or false. If it is false, rewrite it in a form that is a true statement. (3)/(2)>(4)/(5)
The statement (3)/(2)>(4)/(5) is true because cross-multiplication shows that 15>8.
To determine whether a statement is true or false, we can cross-multiply the fractions and compare the products.
In this case, (3)*(5)>(2)*(4), which simplifies to 15>8. Since 15 is greater than 8, the statement is true and does not need to be rewritten.
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Evaluate the algebraic expression when f = 6, g = 8, h = 12 and j = 2. A. 10 B. 12 C. 20 D. 22
The value of the given algebraic expression is 7. The solution has been obtained by using arithmetic operations.
A mathematical expression called an algebraic expression can have variables or integers in it. It cannot be solved because it lacks an equals sign. A sequence of algebraic expressions are separated by an equals sign and are part of an algebraic equation, which can be solved.
We are given an algebraic expression as (f + g)/j.
The values of f = 6, g = 8, h = 12 and j = 2.
On substituting these in the expression, we get
⇒(6 + 8)/2
⇒14/2
⇒7
Hence, the value of the given algebraic expression is 7.
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Question: Evaluate the algebraic expression (f + g)/j when f = 6, g = 8, h = 12 and j = 2.
Homework:6.3 Applications of Systems of Linear Equations Question 4, 6.3.13-BE
Part 1 Jim took clothes to the cleaners three times last month. First, he brought 3 shirts and 2 pairs of slacks and paid $18.45. Then, he brought 7 shirts, 2 pairs of slacks, and 1 sports coat and paid $35.40. Finally, he brought 4 shirts and 2 sports coats and paid $23.94. How much was he charged for each shirt, each pair of slacks, and each sports coat?
Jim was charged$____ for each shirt, $____for each pair of slacks, and $____for each sports coat.
Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.
To solve this problem, we can use a system of linear equations. Let x be the cost of each shirt, y be the cost of each pair of slacks, and z be the cost of each sports coat. Then we can write the following equations based on the information given in the problem:
3x + 2y = 18.45 (equation 1)
7x + 2y + z = 35.40 (equation 2)
4x + 2z = 23.94 (equation 3)
Now we can use the elimination method to solve for the variables. First, we can subtract equation 1 from equation 2 to eliminate the y variable:
4x + z = 16.95 (equation 4)
Next, we can multiply equation 1 by -2 and add it to equation 3 to eliminate the y variable:
-6x - 4y + 4x + 2z = -36.9 + 23.94
-2x + 2z = -12.96 (equation 5)
Now we can subtract equation 4 from equation 5 to eliminate the x variable:
2z - z = -12.96 - 16.95
z = -29.91
This value for z does not make sense, so there must be a mistake in the calculations or the original problem. Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.
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The diameter of a circle is 13 m. Find its area to the nearest tenth.
Answer:
132.7cm²
Step-by-step explanation:
area of circle = πr²
6.5² * π
=132.7cm²
Write a polynomial function of least degree with integral coeffiecients that has the given zeros.
-5, -4, and 5.
Answer:
please give brainliest
Step-by-step explanation:
P(x)=(x+5)(x−4)(x−5)
is the lowest order of all polynomials with given zeroes.
At a carnival game, it cost Taylor $6 to toss 63 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
For toss 21 it is 2 dollars, for toss 41 it is 4 dollars, for toss 63 it is 6.
Describe Graph?Graphs can take many forms, depending on the type of data being represented and the purpose of the graph. Some common types of graphs include:
Bar graphs: These use bars or columns to represent numerical values or frequencies.
Line graphs: These use lines to show the relationship between two variables over time or other intervals.
Pie charts: These use slices of a circle to represent parts of a whole.
Scatterplots: These show the relationship between two variables by plotting individual data points.
Graphs can be used to identify patterns, trends, and relationships in data, and to make predictions and draw conclusions based on that data. They are commonly used in fields such as statistics, economics, engineering, and science to help visualize and analyze complex data sets.
TOSS DOLLARS
21 2
42 4
63 6
Plotting the points on the coordinate axes, we have:
|
7 -
|
6 -
|
5 -
|
4 - • (21,2)
| \
3 - • (42,4)
| \
2 - • (63,6)
|________________________________
0 20 40 60 80 100
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Teri has 12 paper weights in her collection. She has twice as many glass paperweights as metal, and three are wood. How many of each paper weight does she have?
Let's say that the number of metal paperweights is "x", then the number of glass paperweights is "2x" since she has twice as many glass paperweights as metal.
We know that she has a total of 12 paperweights, so we can set up an equation:
x + 2x + 3 = 12
Simplifying the equation, we get:
3x + 3 = 12
Subtracting 3 from both sides, we get:
3x = 9
Dividing both sides by 3, we get:-
x = 3
So Teri has 3 metal paperweights, and since she has twice as many glass paperweights as metal, she has:
2x = 2(3) = 6 glass paperweights.
Therefore, Teri has 3 metal paperweights, 6 glass paperweights, and 3 wood paperweights in her collection.
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Write the equation of an ellipse with vertices (-5,1) and (-1,1) and co-vertices (-3,2) and (-3,0)
Please explain.
Check the picture below.
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-3\\ k=1\\ a=2\\ b=1 \end{cases}\implies \cfrac{(x- (-3))^2}{ 2^2}+\cfrac{(y-1)^2}{ 1^2}=1\implies \cfrac{(x+3)^2}{ 4}+\cfrac{(y-1)^2}{ 1}=1[/tex]
Answer: To find the equation of the ellipse, we need to use the standard form equation of an ellipse:
$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$
where (h,k) is the center of the ellipse, a is the distance from the center to the vertices (the major axis), and b is the distance from the center to the co-vertices (the minor axis).
First, let's find the center of the ellipse. The center of the ellipse is the midpoint of the line segment joining the vertices (-5,1) and (-1,1). Using the midpoint formula, we get:
$(h,k) = \left(\frac{-5+(-1)}{2}, 1\right) = (-3,1)$
Now, we need to find the values of a and b. Since the distance between the vertices is 2a, we have:
$2a = |-5-(-1)| = 4$
So, $a = 2$.
Similarly, the distance between the co-vertices is 2b, we have:
$2b = |2-0| = 2$
So, $b = 1$.
Now, we have all the values we need to write the equation of the ellipse:
$\frac{(x+3)^2}{2^2}+\frac{(y-1)^2}{1^2}=1$
Simplifying this equation, we get:
$\frac{(x+3)^2}{4}+(y-1)^2=1$
So, the equation of the ellipse is:
$(x+3)^2/4 + (y-1)^2/1 = 1$
Step-by-step explanation:
Brenda's school is due west of her house and due south of her friend Trevor's house. The distance between the school and Trevor's house is 4 miles and the straight-line distance between Brenda's house and Trevor's house is 6 miles. How far is Brenda's house from school? If necessary, round to the nearest tenth.
In response to the supplied query, we may state that Hence, Brenda's Pythagorean theorem home is around 7.2 kilometers away from the school.
what is Pythagorean theorem?The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.
Points A, B, and C can be used to create a right triangle in this situation. The hypotenuse of the line segment between points A and C is its length, while the other two sides are the lengths of the segments connecting A and B and B and C.
We'll refer to the separation between positions A and C as "x". Next, we have:
[tex]x2 = 6 + 4, x2 = 36 + 16, x2 = 52, x = \sqrt(52) = 7.2.[/tex]
Hence, Brenda's home is around 7.2 kilometers away from the school.
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If 6 apples cost the same as 3 bananas, and 4 bananas
cost the same as 5 melons, how many melons can Jane buy for the
price of 32 apples?
Jane can buy 20 melons for the price of 32 apples.
To find out how many melons Jane can buy for the price of 32 apples, we need to use the given ratios to find the equivalent value of melons in terms of apples.
First, we know that 6 apples are equivalent to 3 bananas. So, we can simplify this ratio to 2 apples per 1 banana.
Next, we know that 4 bananas are equivalent to 5 melons. So, we can simplify this ratio to 4/5 of a banana per 1 melon.
Now, we can use these ratios to find the equivalent value of melons in terms of apples. If 2 apples are equivalent to 1 banana, and 4/5 of a banana is equivalent to 1 melon, then we can multiply these ratios together to find the equivalent value of melons in terms of apples:
2 apples/1 banana × 4/5 banana/1 melon = 8/5 apples/1 melon
This means that 1 melon is equivalent to 8/5 apples, or 1.6 apples.
Finally, we can use this ratio to find out how many melons Jane can buy for the price of 32 apples:
32 apples × 1 melon/1.6 apples = 20 melons
Therefore, Jane can buy 20 melons for the price of 32 apples.
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A company's profit increased linearly from $5 million at the end of year 2 to $17 million at the end of year 6.
(a) Use the two (year, profit) data points (2, 5) and (6, 17) to find the linear relationship y = mx + b between x = year and y = profit.
(b) Find the company's profit at the end of 3 years.
(c) Predict the company's profit at the end of 8 years.
Below, you will learn how to solve the problem.
(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).
The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)
m = 12/4
m = 3
Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6
b = -1
So the linear relationship between x = year and y = profit is:
y = 3x - 1
(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1
y = 8
So the company's profit at the end of 3 years is $8 million.
(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:
y = 3(8) - 1 = 23
So the company's profit at the end of 8 years is predicted to be $23 million.
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A company producing cereals offers a toy in every 5 cereal package in celebration of а their 50th anniversary. A father immediately buys 24 packages. 1. What is the probability of finding 1 toys in the 24 packages? Answer: 0.0283 ✓o 2. What is the probability of finding no toy at all? Answer: 0.00472 om 3. What are the mean and standard deviation of number of toys in the 24 packages? Mean: Standard deviation:
1. The probability of finding 1 toy in the 24 packages is 0. This is because the company offers a toy in every 5 cereal packages, so if the father buys 24 packages, he is guaranteed to find at least 4 toys (24/5 = 4.8, rounded down to 4). Therefore, the probability of finding only 1 toy is 0.
2. The probability of finding no toy at all is also 0, for the same reason as above. The father is guaranteed to find at least 4 toys in the 24 packages he bought.
3. The mean number of toys in the 24 packages is 4.8, which is the result of 24/5. The standard deviation can be calculated using the formula sqrt(np(1-p)), where n is the number of packages, p is the probability of finding a toy in each package, and 1-p is the probability of not finding a toy. In this case, n=24, p=1/5, and 1-p=4/5. Plugging these values into the formula gives us:
Standard deviation = sqrt(24*(1/5)*(4/5)) = 1.732
So the mean number of toys in the 24 packages is 4.8, and the standard deviation is 1.732.
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i need help by tonight
7 x 4 = 28
than you need to do y + 5x
than you get you answer 6
PLEASE HELP ME IM TIMED
Answer: not my answer but an answer from ai, scan through, see if right, its all explained out for you
To evaluate g(f(5)), we first need to find the value of f(5) by substituting x = 5 into the definition of f(x):
f(x) = x^2 - 6x + 14
f(5) = 5^2 - 6(5) + 14
f(5) = 25 - 30 + 14
f(5) = 9
Now that we know that f(5) = 9, we can evaluate g(f(5)) by substituting 9 into the definition of g(x):
g(x) = x + 14
g(f(5)) = g(9)
g(f(5)) = 9 + 14
g(f(5)) = 23
Therefore, the value of g(f(5)) is 23.