Use the 30-60-90 rule to find the lengths of the sides labeled e and d

To dilate an image with a scale factor, multiply the scale factor with the dimensions of the image

The dilation is the process of changing the size of the given shape or figure ,the shape of the figure will be always same. Therefore dilation is one form transformation of shapes

The scale factor is the ratio of the measurement of the new shape to the measurement of the original shape.

We can use the scale factor for the dilation

To get the dilate and image with scale factor, we have to multiply the scale factor with the measurement of the original shape

The equation will be

The dimension after dilation = scale factor × original dimensions

Therefore, to dilate an image, multiply the scale factor and the original dimensions

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President Richard Nixon proposed the creation of The Environmental Protection Agency (EPA).

What is the Environmental Protection Agency?

The Environmental Protection Agency is an independent government agency of the United States, which was considered mandatory by the government for environmental issues.

The Agency followed a series of measures to improve air quality, decrease greenhouse gas emissions, forbid water pollution, and invest in oil spill control measures.

The EPA had many obligations in the United States, two of which were to set industry standards to reduce their impact on the environment and investigate air pollution.

How did the EPA launch?

The operation of the agency began on December 2, 1970, after President Nixon had signed an executive order. The order established by the EPA was made official by signing by the committee hearings in the House and Senate.

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A school show had sold the ticket sales of first and second nights. The price of a student ticket is $3.54, a So, the correct answer is option (d).

Total sale on tickets at the first night = $1345

Total sale on tickets at the second night = $935

Let the price of student ticket and adult ticket in school show be "$x" and "$y" respectively. According to problem,

On first night total sale,

180x + 110y = $1345 --(1)

On Second night total sale,

100x + 90y = $935 --(2)

we have to determine the price of student ticket i.e x and price of adult ticket i.e y .. We have a system of linear equation which consists two equations (1) and (2) . Now, we solve these equations using Substitution method,

From equation (2), 100x = 935 - 90y

=> x = (935 - 90y )/100 --(*)

Substitute the value of x in equation (1) 180x + 110y = $1345

=> 180(935 - 90y )/100 + 110y = 1345

Simplify ..

=> 168120 - 16200y + 11000y = 134500

=> 168120 - 134500 = 16200y - 11000y

=> 33620 = 5200y

=> y = 33620/5200

=> y = 6.46

put the value of y in equation (*) we get,

x = (935 - 90× 6.46)/100 = 3.536

Hence, the value of x is $3.536 and value of y is $6.46..

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The number of inches of a segment is 1.06 inches if a segment is 2.7 centimeters long.

In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.

In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.

Given,

In 1 inch there are about 2.54centimeters

And the segment is 2.7 centimeters long

The number of inches=?

2.7/2.54=1.0629

When it is rounded to the nearest 100, we get

1.06 inches.

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Answer:

3.75

Step-by-step explanation:

I BELIVE YOUR ANSWER IS 3.75

Answer:

3.75

Step-by-step explanation:

1) The value of the expression x + y is; 30

2) The value of the expression m + n is; 16

1) We are told that segments LJ and A F are perpendicular. This means that; 4x + 50 = 90 and 7y - 50 = 90

Let us solve for x and y;

4x + 50 = 90

4x = 90 - 50

4x = 40

x = 10

Similarly;

7y - 50 = 90

7y = 90 + 50

7y = 140

y = 140/7

y = 20

Thus;

x + y = 10 + 20

x + y = 30

2) We are told that LJ is a perpendicular-bisector of A F. Thus;

AJ = FJ and AL = FL

Thus;

FL = AL gives;

3m = 42

m = 42/3

m = 14

Similarly;

2m + 3n = 34

2(14) + 3n = 34

28 + 3n = 34

3n = 6

n = 2

m + n = 14 + 2 = 16

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So, let's think about what it's asking

it next to the parentheses means to distribute, or multiply into.

Multiply 9 * -2

A negative times a positive is a negative.

9 * 2 = 9 + 9 = 18

Make the final answer negative because its a positive and a negative multiplied.  A positive and a positive multiplied gives you a positive.  A negative and a negative multiplied gives you a positive too.

-18

The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

H(t) = 50 - t / 5

At t = 35, the value of the function will be given as,

H(35) = 50 - 35 / 5

H(35) = 50 - 7

H(35) = 43

The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.

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The least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month, so option A is correct.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

Pedro has a balance of $5810 on a credit card with an APR of 16.2%,

Calculate the simple interest for one month as shown below,

[tex]SI = P \times r \times t / 100[/tex]

SI = 5810 × 16. 2 × 1 / (12 ×100)   [time in year = 1 / 12]

SI = $78.345

SI =  5810 × 16. 2 × 2 / (12 ×100)   [For 2 months]

SI = $156.87

Therefore, the least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month.

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The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.

Please also notice that the sign for inches is the double prime ("), not the double quotation mark, the straight quotation mark, or even (gasp!) the two consecutive single quotation marks (").

The inch was defined as "three dry, spherical grains of barley set end to end lengthwise" during the early 14th century under King Edward II. The lengths of 12 poppy seeds together have also been used at various periods to define one inch. Since 1959, 2.54 cm has been the official definition of an inch.

From the above definition, we get that

The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.

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y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

After 10 mins your phone is at 30%.

If your phone is charging at a rate of 5% every 2 minutes,

4 minutes=10%

6 minutes=15%

8 minutes=20%

10 minutes=25 %

The equation of point slope form.

y-5=3(x-2)

Hence, y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.

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To split a sentence into two simple sentences, first, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.

In the given question we have to explain how we split a sentence into two simple sentences.

As we know that;

A basic sentence typically consists of a subject, a verb, and maybe an object and modifiers. It only has one independent clause, though. Here are a few illustrations: She composed.

First, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.

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Answer:

0.309

Step-by-step explanation:

To calculate the expected risk premium on a stock, one must subtract the Inflation rate from the stock’s expected return.

From the question, we have the following parameters that can be used in our computation:

Mathematically, the relationship between the expected risk premium and the stock's expected return is represented as follows

Expected risk premium = Stock's expected return - Inflation rate

This means that the Inflation rate must be subtracted from the stock’s expected return to calculate the expected risk premium

Hence, the statement that completes the blank is Inflation rate.

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Answer: 4 days, more below

Step-by-step explanation:

40.50x + 0.15y < 210

(0.15)(125)=18.75

40.50x + 18.75 < 210

40.50x < 191.25

x < 4.7222222...

She can afford to rent the car for 4 days if she drives 125 miles and has 210$ to spend.

x= -9 and y= -3

What is equation?

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

A)  rearranging equation (2) to make x the subject

[tex]x-3=4y\\x-4y=3[/tex]

Also,

[tex]4y=x-3\\y=(x-3)/4[/tex]

by subtitution method

putting this value of y in equation 1)

[tex]x-2((x-3)/4)=15\\\\x-2x+6=15\\x=-9\\y=(-9-3)/4\\y=-3[/tex]

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The largest figure that Ash can built with 61 toothpicks is of:

A composition of 12 hexagons.

The number of toothpicks needed is modeled with a linear function, defined as follows:

y = mx + b.

The coefficients of the function are given as follows:

The number of toothpicks in each figure is represented by the following sequence:

(6, 11, 16, ...).

Hence the parameters are given as follows:

m = 5, b = 6.

Thus the definition of the function is of:

T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).

T(n) = 5n + 1.

Then the number of hexagons with 61 toothpicks is obtained as follows:

5n + 1 = 61

5n = 60

n = 60/5

n = 12 hexagons.

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The measure of one of the central angles of a regular pentagon is 72° .

In the question ,

a regular pentagon is given ,

we have to find the measure of one of central angle ,

we know that a pentagon has 5 equal sides .

and the sum of the central angles is 360° .

it is given that the pentagon is regular , So , all the central angles are equal in measure .

The central angle can be calculated using the formula ,

central angle = 360°/n , where n is number of sides .

substituting the value of number of sides as = 5 ,

we get ,

central angle = 360°/5 = 72° .

Therefore , the central angle is = 72°  .

The given question is incomplete , the complete question is

What is the measure of one of the central angles in the regular Pentagon ?

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Answer:

used formula

Step-by-step explanation:

y-y1=m(x-x1)

The earth is 21.24 x 10¹⁴ miles far from the star.

What are the light years?

A light-year is a significant length measure that is used to express astronomical distances. It is around 9.46 trillion kilometers, or 5.88 trillion miles, in length.

We have given,

1 light year = 5.9 x 10¹² miles

Distance of the star =  3.6 x 10² light years

To get this we just convert the distance of the star in light years into miles.

3.6 x 10² light years x( 5.9 x 10¹² miles/1 light years)

We cancel out the lightyears and then we are left with:

3.6 x 10² light years x 5.9 x 10¹² miles

In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.

Coefficients:

3.6 x 5.9 = 21.24

Exponents of 10:

10² x 10¹² = 10⁽²⁺¹²⁾ = 10¹⁴

Then we combine them again to form:

21.24 x 10¹⁴ miles

Hence, the earth is 21.24 x 10¹⁴ miles far from the star.

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Answer: 1/10th

Step-by-step explanation:

20 different lengths, 2 are 21.5 = 2/20 reduce to 1/10 so 10%

By algebra properties, the quadratic function x² - x - 20 = 0 is equivalent to the quadratic function (x + 1 / 2)² - 81 / 4 = 0.

In this problem we have a quadratic function whose form does not correspond with a perfect square trinomial, that is, a polynomial of the form (x + a)² = x² + 2 · a · x + a². Herein we can modify part of the function by means of completing the square, an application of algebra properties.

First, write the quadratic function described in the statement:

x² - x - 20 = 0

Second, use algebra properties until the square is complete:

x² - x - 20 = 0

x² - x = 20

x² - x + 1 / 4 = 20 + 1 / 4

(x + 1 / 2)² = 81 / 4

(x + 1 / 2)² - 81 / 4 = 0

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The Equation represent the line that passes through the points  (2, -8) and (-3, 2) is 2x + y + 4 = 0

Two point form is one of the important forms used to represent a straight line algebraically. The equation of a line represents each and every point on the line, i.e., it is satisfied by each point on the line.

The two point formula is used to represent a line algebraically using the coordinates of two points that lie on that line. The formula for two point form can be given as:

(y - y1) = m(x-x1) -----------(1)

where , m is slope of line given by => y2-y1/ x2 - x1

(x, y) is an arbitrary point on the line.

(x1, y1) and (x2 , y2) are coordinates of points lying on the line.

According to the question,

The required line passes through (2,-8) and (-3,2)

Slope : m = 2 - (-8) / -3 -2

=> m = 2+8/-5

=> m = 10/-5

=> m = -2

Substituting the values in equation (1)

(y - (-8)) = -2(x-2)

Solving,

=> y + 8 = -2x + 4

=> 2x + y + 4 = 0 is required equation of line

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The shorted distance from Asheboro to Fort Jennings is, 20.4 miles.

What is Pythagorean theorem?

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

In this problem we have to find the shortest  route from Asheboro to Fort Jennings using the roads shown.

From the given route the shorted distance from Asheboro to Fort Jennings is,

= 3 mi + 8 mi + (distance from North lean to Fort Jennings)

Let distance from North lean to Fort Jennings is x.

To find the value of x using Pythagorean theorem.

x^2 = 8^2 + 5^2

x^2 = 64 + 25

x^2 = 89

x = 9.433

x = 9.4

So, the total distance is, 3 mi + 8 mi + 9.4 mi =20.4 miles.

Hence, the shorted distance from Asheboro to Fort Jennings is, 20.4 miles.

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Complete question:

Complete question is attached below.

The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.

A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.

While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.

Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.

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Answer:

A,B,C,

Step-by-step explanation:

PLATO

The quadratic formula x = [-b (b2 - 4ac)] / 2a] provides the solutions to the quadratic equation ax2 + bx + c = 0. (2a).

Given,

Equation with two answers are quadratic equations.

Quadratic equation;

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

The solution for quadratic equation;

The quadratic formula x = [-b (b2 - 4ac)] / 2a]gives the solutions to the quadratic equation ax2 + bx + c = 0. (2a). Get the problem into standard form, ax2 + bx + c = 0, and then use the quadratic formula to solve the quadratic equation.

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Derivatives is used to calculate the maximum value of a function.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

Derivatives

The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

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Answer: 4z

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

So we are going to find c(2)

c(2)=c(1)+10

c(2)=-20+10

c(2)=-10