Let P(2, 3) be a point on a figure. The figure is dilated by a scale factor of 4.

What are the coordinates of P′?

Write the ordered pair.

the answer is b hoped i helped

The length of the blue line segment is 11 units.

For any point P on an ellipse, the sum of the distances from P to the two foci is equal to the length of the major axis of the ellipse. This is known as the "distance property" of an ellipse.

To see why this is true, consider an ellipse with foci F₁ and F₂ and major axis length 2a. Let P be any point on the ellipse, and let D₁ and D₂ be the distances from P to F₁ and F₂, respectively. Then, by definition of an ellipse, we know that:

D₁+ D₂ = 2a

Given that,

Two line segments

Red segments of length = 3 unit

So from the definition we know that,

The sum of segments = the length of major axis

The length of major axis  =  2a

2a  = D₁+ D₂

14=  3 + D₂

D₂ =  11

Therefore, the length of the blue line segment is 11 units.

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The better deal is the loan with the 600% APR.

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum).

Given that, Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.

There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.

600/365 = 1.643

The daily interest rate of the loan will be 1.643%.

The following equation is used to find the total interest payment:

[tex]A = P(1+\frac{r}{365} )^{t} -P[/tex]

A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.

Plug in your values into the equation.

P = 380 r = 1.643 and t = 7

380(1+1.643/365)^7 - 380 = 12.136

Rounded to the nearest hundredths value, the total interest paid will be $12.14.

Compare the total amounts paid for both loans.

$12.14 < $45

Hence, The better deal is the loan with the 600% APR.

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A circle with an area of 254.47 square inches is given.

We have to determine the circumference of the circle.

Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.

[tex] \Pi r^{2}=254.47 [/tex]

[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]

[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]

[tex] r^{2}=80.97 [/tex]

[tex] r=\sqrt{80.97} [/tex]

r = 8.99

Therefore, r = 9 inches (approximately)

Circumference of a circle = [tex] 2\Pi r [/tex]

= [tex] 2 \times \frac{22}{7} \times 9 [/tex]

= 56.57 inches

= 56.6 inches (approximately).

Therefore, the circumference of the circle is 56.6 inches.

The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).

This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).

To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).

By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.

Therefore, the limit of the sequence as n tends to infinity is 0.

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Answer:

b

Step-by-step explanation:

Using the correlation coefficient, mean test scores, and mean GPA, we can predict that a freshman with a GPA of 2.9 would have an approximate combined test score of 1260.71.

Since we know the mean combined application test score is 1225, the standard deviation is 120, the mean GPA is 2.64, and the standard deviation for GPA is 0.58, we can use this information to predict scores.

First, we will use the correlation coefficient (r), which in this case is 0.44, to calculate the slope (b) of the best-fit line. The slope (b) is calculated by dividing the product of the standard deviations by the mean test score, and then multiplying by the correlation coefficient.

b = r * (Sy / Sx)
b = 0.44 * (0.58 / 120)
b = 0.44 * 0.0048333
b ≈ 0.0021

Next, we need to find the intercept (a) of the best-fit line, which can be calculated using the means of the two variables (mean test score and mean GPA).

a = mean of GPA - b * mean of test scores
a = 2.64 - 0.0021 * 1225
a ≈ 0.10

With the slope (b) and the intercept (a), we can now predict the combined test score for a student with a GPA of 2.9.

Predicted Test Score = a + b * GPA
Predicted Test Score = 0.10 + 0.0021 * 2.9
Predicted Test Score ≈ 1260.71

Thus, for a freshman with a first-semester GPA of 2.9, the predicted combined test score would be approximately 1260.71.

Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.

To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.

To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps:

B. 22 : 2. 22 : 2 is equivalent to 11 : 1.

C. 55 : 5. 55 : 5 is equivalent to 11 : 1.

E. 110 : 10. 110 : 10 is equivalent to 11 : 1.

In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective common multiple (numerator or denominator):

For 22 : 2, we would divide all through by 11;

22 : 2 = 11 : 1

For 55 : 5, we would divide all through by 5;

55 : 5 = 11 : 1

For 110 : 10, we would divide all through by 10;

110 : 10 = 11 : 1

Complete Question:

Select three ratios that are equivalent to 11 : 1.

Choose 3 answers:

1 :11

22 : 2

55 : 5

9 : 99

110 : 10