AABC was dilated to create AEFD. What is the scale factor that was applied to triangle ABC?
A
4
B
24
C
10
D
60
F

Answer:

p(8p + 7)

Step-by-step explanation:

8p² + 7p

p(8p + 7)

Answer:

x = 12

Explanation:

Given the expression

17-5(2x-9)=-(-6x+10)+4

​Open the parenthesis

17 - 5(2x) - 5(-9) = -6x + 10 + 4

17 - 10x + 45 = -6x + 14

-10x + 62 = -6x + 14

Collect the like terms

-10x + 6x = 14 - 62

-4x = -48

Divide both sides by -4

-4x/-4 = -48/-4

x = 48/4

x = 12

Hence the value of x that makes the equation true is 12

1. The present value of the security is approximately $7,224.45.

2. The annual interest rate they must earn is approximately 14.75%.

3. The present value of the investment is approximately $825.05 and the future value is approximately $1,319.41.

4. The most expensive car they can afford if financed for 48 months is approximately $21,875.88 and if financed for 60 months is approximately $25,951.46.

1. To calculate the present value of a security that will pay $14,000 in 20 years with an annual interest rate of 3%, we can use the formula for present value:

Present Value = \(\[\frac{{\text{{Future Value}}}}{{(1 + \text{{Interest Rate}})^{\text{{Number of Periods}}}}}\]\)

Present Value = \(\[\frac{\$14,000}{{(1 + 0.03)^{20}}} = \$7,224.45\]\)

Therefore, the present value of the security is approximately $7,224.45.

2. To determine the annual interest rate your parents must earn to reach a retirement goal of $1,300,000 in 19 years, we can use the formula for compound interest:

Future Value =\(\[\text{{Present Value}} \times (1 + \text{{Interest Rate}})^{\text{{Number of Periods}}}\]\)

$1,300,000 = \(\[\$260,000 \times (1 + \text{{Interest Rate}})^{19}\]\)

\(\[(1 + \text{{Interest Rate}})^{19} = \frac{\$1,300,000}{\$260,000}\]\)

\(\[(1 + \text{{Interest Rate}})^{19} = 5\]\)

Taking the 19th root of both sides:

\(\[1 + \text{{Interest Rate}} = 5^{\frac{1}{19}}\]\\\\\[\text{{Interest Rate}} = 5^{\frac{1}{19}} - 1\]\)

Interest Rate ≈ 0.1475

Therefore, your parents must earn an annual interest rate of approximately 14.75% to reach their retirement goal.

3. To calculate the present value and future value of the investment with different cash flows and a 12% annual interest rate, we can use the present value and future value formulas:

Present Value = \(\[\frac{{\text{{Cash Flow}}_1}}{{(1 + \text{{Interest Rate}})^1}} + \frac{{\text{{Cash Flow}}_2}}{{(1 + \text{{Interest Rate}})^2}} + \ldots + \frac{{\text{{Cash Flow}}_N}}{{(1 + \text{{Interest Rate}})^N}}\]\)

Future Value = \(\text{{Cash Flow}}_1 \times (1 + \text{{Interest Rate}})^N + \text{{Cash Flow}}_2 \times (1 + \text{{Interest Rate}})^{N-1} + \ldots + \text{{Cash Flow}}_N \times (1 + \text{{Interest Rate}})^1\)

Using the given cash flows and interest rate:

Present Value = \(\[\frac{{150}}{{(1 + 0.12)^1}} + \frac{{150}}{{(1 + 0.12)^2}} + \frac{{150}}{{(1 + 0.12)^3}} + \frac{{250}}{{(1 + 0.12)^4}} + \frac{{350}}{{(1 + 0.12)^5}} + \frac{{500}}{{(1 + 0.12)^6}} \approx 825.05\]\)

Future Value = \(\[\$150 \times (1 + 0.12)^3 + \$250 \times (1 + 0.12)^2 + \$350 \times (1 + 0.12)^1 + \$500 \approx \$1,319.41\]\)

Therefore, the present value of the investment is approximately $825.05, and the future value is approximately $1,319.41.

4. To determine the maximum car price that can be afforded with a $5,000 down payment and monthly payments of $300, we need to consider the loan amount, interest rate, and loan term.

For a 48-month loan:

Loan Amount = $5,000 + ($300 \(\times\) 48) = $5,000 + $14,400 = $19,400

Using an APR of 9% and end-of-month payments, we can calculate the maximum car price using a loan calculator or financial formula. Assuming an ordinary annuity, the maximum car price is approximately $21,875.88.

For a 60-month loan:

Loan Amount = $5,000 + ($300 \(\times\) 60) = $5,000 + $18,000 = $23,000

Using the same APR of 9% and end-of-month payments, the maximum car price is approximately $25,951.46.

Therefore, with a 48-month loan, the most expensive car that can be afforded is approximately $21,875.88, and with a 60-month loan, the most expensive car that can be afforded is approximately $25,951.46.

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The line passes through the point (4, 3)

The line has a slope of m=-1/3

The equation of the line can be written in the form

Since the slope is -1/3

Then the equation becomes

Since the line passes through the point (4, 3)

Substitute x = 4, y= 3 into the equation

Simplify the equation and solve for c

Hence, the equation becomes

Using an online graphing calculator.

The graph of the line is shown

Answer: 4

Step-by-step explanation: a is three units away from o and a’ is 9 units away from o. you add 9+3 to get the total distance and divide that number by 3 to get the scale factor. 12/3=4

The scale factor for the given dilation is 3

Dilation is a transformation of an object which changes its size. if the dilated image is larger then it is called enlargement. If the dilated image is smaller it is called reduction.

If the dilation has the origin as the center of dilation, we can find points on the image formed by dilation by multiplying the coordinates of the original geometric object like triangle multiplying by the scale factor. For scale factor k, the transformation of the dilation is written as :  (x, y) → (k x, k y).

The scale factor ,k  = coordinate of image / coordinate of original

Given that Triangle ABC is dilated to create triangle A’B’C’ using point O as the center of dilation as shown in the figure

Scale Factor = coordinate of image / coordinate of original

                    = OA' / OA = 9/3 = 3

Therefore, the scale factor for the given dilation is 3.

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Answer:   x = 7

====================================================

Work Shown:

The third unmarked angle is (9x-25) because the base angles are congruent. Recall the base angles are opposite the congruent sides in an isosceles triangle. The congruent sides are shown with the tickmarks.

Add up the three angles, set the sum equal to 180, and solve for x

(9x-25)+(9x-25)+(104) = 180

18x+54 = 180

18x = 180-54

18x = 126

x = 126/18

x = 7

Answer: 1. C and number 2 is A

Step-by-step explanation: Hope this helps

Answer:

A: 19.3 and 19.25

Step-by-step explanation:

When rounding decimals if the number in the decimal place to the right is higher than 5 you round up. If not keep keep the same.

The rounding off 19.254 to the nearest tenth and the nearest hundredth will be 19.3 and 19.25 respectively.

What is rounding off ?

Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.

To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here, The number 19.254 at tenth place is 5 so round up the hundredths place digit, hence the rounded off to the nearest tenth will be 19.3.

and also,

To round off the number to the nearest hundredth we need to look at the thousandth place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here, The number 19.254 at hundredth place is 4 so round up the thousandth place digit, hence the rounded off to the nearest hundredth will be 19.25.

Therefore, the rounding off 19.254 to the nearest tenth and the nearest hundredth will be 19.3 and 19.25 respectively.

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The median of the given data set as required to be determined in the task content is; 4.

It follows from the task content that the value which represents the median of the data set is to be determined.

By observation, the number of data values in the data set is; 15. On this note, the median value would be the eighth term in an orderly arrange of the values.

Consequently, the median of the data set as required is; 4.

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Answer:

3

Step-by-step explanation:

The correct answer is Stratified Random Sampling

Given that,

In a study, the sample is selected by dividing the class into gender-based groups, then choosing 10 men and 10 women.

Researchers split a population into homogeneous subpopulations called strata (plural of stratum) depending on particular traits in a stratified sample (e.g., race, gender identity, location, etc.).

In order to estimate statistical measures for each subpopulation, each stratum is then sampled using a different probability sampling technique, such as cluster sampling or simple random sampling.

When a population's traits are varied and researchers want to make sure that each characteristic is accurately represented in the sample, they rely on stratified sampling. This aids in the study's validity and generalizability while preventing biases in the research process like undercoverage bias.

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Answer:

103.5

Step-by-step explanation:

90-76.5=13.5

90+13.5= 103.5

Answer:

A= 254.34mm2

Step-by-step explanation:

Area of the circle can be calculated as

\(a = \pi \: {r}^{2} \)

So area can be calculated as

A= πr^2

A= (3.14) (9mm)^2

A= 254.34mm2

so area is 254.34 .

Answer: Area of circular object =254.34 mm²

Step-by-step explanation:  According to the question,

Radius of circular object (r)= 9mm

Area of a circle is given by the formula= πr²

Area of the circular object =π(9²)

                                            =254.34 mm²

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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Answer:

x = 138°

Step-by-step explanation:

This is a hexagon since it has 6 angles.

The sum of interior angles for a hexagon is equal to 720° so to find the value of x we need to find the sum of given angles and subtract from 720:

86 + 145 + 120 + 119 + 112 + x = 720 add given angles

582 + x = 720 subtract 582 from both sides

x = 138°

Answer:

\(-y^2+6y+16\)

Step-by-step explanation:

\(-(y+2)(y-8)\)

\(-1(y+2) \times (y-8)\)

\((-y-2)\times (y-8)\)

\(-y(y-8)-2(y-8)\)

\(-y^2+8y-2y+16\)

\(-y^2+6y+16\)

Answer:

420% of 85 = 357

Step-by-step explanation:

85/x=100/420

(85/x)*x=(100/420)*x       - we multiply both sides of the equation by x

85=0.23809523809524*x       - we divide both sides of the equation by (0.23809523809524) to get x

85/0.23809523809524=x

357=x

x=357

The distance between the given two points on the coordinate grid is 17 units.

A coordinate grid has two perpendicular lines, or axes labelled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.

Given that, are two points (7, 8) and (-8, 0) on a coordinate grid, we need to find the distance between the points

We know that, the distance between two points on a coordinate grid is given by;

D = √(x₂-x₁)²+(y₂-y₁)²

Here, x₁ = 7, x₂ = -8 and y₂ = 0, y₁ = 8

Therefore,

D = √(-7-8)²+(0-8)²

D = √(-15)²+(-8)²

D = √225+64

D = √289

D = 17

Hence, the required distance is 17 units.

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Answer:

vertical angles are =

Step-by-step explanation:

The solution is, The correct option is (C).

The graph of G(x) is the graph of F(x) shifted 5 units up.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

here, we have,

Given:

G(x) = F(x) + 5

As, the transformation takes place so there is a positive five.

The value of the function for a given x is the vertical position of the point on the graph.

Adding 5 to the function value shifts the graph up 5 units.

Hence, The graph of G(x) is the graph of F(x) shifted 5 units up.

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A(n) MODEL is a mathematical representation of an object created by a special software.

In computer science, a model is a mathematical abstraction of a system, process, or phenomenon that is intended to be simulated or executed on a computer system. A model is used to represent a system or process as a set of mathematical equations or logical rules in order to simulate or analyze it with a computer program.

                                                  It can be a physical object, such as a car or building, or an abstract concept, such as an economic system or a social network. In general, a model can be a simple or complex representation of a real-world object or process, and it can be used for a variety of purposes, such as predicting future outcomes, testing hypotheses, or designing new systems.

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Answer:

0.003

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

t = 3 meters

Step-by-step explanation:

From the given figure,

Perimeter = 16 meters

Now, the formula for perimeter of a rectangle = 2(l + b)

Where,

'l' is the length of the rectangle

and

'b' is the breadth of the rectangle.

Since length is the longest side of a rectangle, therefore from the given figure

=> l = 5 meters

and

=> b = t meters

Substituting values in the formula,

16 = 2(5 + t)

=> 16/2 = 5 + t

=> 8 = 5 + t

=> 8 - 5 = t

=> t = 3 meters

Answer:

a₇ = - 0.4

Step-by-step explanation:

The n th term of a geometric progression is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = - 6250 and r = \(\frac{1250}{-6250}\) = - \(\frac{1}{5}\) , thus

a₇ = - 6250 × \((-\frac{1}{5}) ^{6}\)

    = - 6250 × \(\frac{1}{15625}\) = - \(\frac{6250}{15625}\) = - 0.4

Answer:

25%

Step-by-step explanation:

1/4 is 25% of 4 areas please Brainliest

To determine the fraction of automotive batteries that would be expected to survive beyond 1000 days, we need to calculate the probability that a battery's life exceeds 1000 days, given that it follows a normal distribution with a mean of 900 days and a standard deviation of 35 days.

We can use the standard normal distribution (Z-distribution) to calculate this probability. We need to convert the value of 1000 days into a standardized Z-score using the formula:

Z = (X - μ) / σ

where X is the value we want to convert (1000 days in this case), μ is the mean (900 days), and σ is the standard deviation (35 days).

Z = (1000 - 900) / 35 = 2.857

Using a Z-table or a statistical calculator, we can find the area/probability to the right of Z = 2.857. This area represents the fraction of batteries expected to survive beyond 1000 days.

Looking up the Z-score of 2.857 in a standard normal distribution table, we find that the area to the right is approximately 0.00215.

Therefore, the fraction of automotive batteries expected to survive beyond 1000 days is approximately 0.00215 or 0.215%.

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Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation: