Determine if triangle EFG and triangle HIJ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)

To calculate (f g)(-1), we use the definition:

This is true if x is defined for f and g. Now, for our problem:

Answer: Infinite Solution

Step-by-step explanation:

3x+12-4=2x+8+x

3x+8=3x+8

Answer:

All real numbers

The answer to this equation is 0=0

Step-by-step explanation:

3(x+4)-4= 2(x+4)+x

3x+12-4= 2x+8+x    

3x+8=3x+8              

3x-3x=8-8

0=0 Answer

We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given Data

We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.

Series of transformation Matt can perform:

Reflection (Flip)

Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.

Rotations as a Transformation of Congruence

A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.

Congruence transformation through translation

When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.

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Area of shaded region = 168.56  [tex]m^2[/tex]

What is area of square and semicircle?

Area of square is the total space taken by the square.

If the side of square is a units, then area of square is calculated by

Area of square = [tex]a \times a[/tex] sq units

Area of semicircle is the total space taken by the semicircle

If the radius of semicircle is r units, then area of semicircle is calculated by

Area of semicircle = [tex]\frac{1}{2}\times \pi \times r^2[/tex] sq units

Here,

Side of square = 28 m

Area of square = [tex]28 \times 28 = 784 m^2[/tex]

Radius of circle = [tex]\frac{28}{2} = 14 m[/tex]

Area of two semicircles =

                                         [tex]2 \times \pi \times r^2 \times \frac{1}{2}\\3.14 \times 14 \times 14\\615.44 m^2[/tex]

Area of shaded region = [tex](784 - 615.44) m^2[/tex]

                                      = 168.56 [tex]m^2[/tex]

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Complete Question

The figure has been attached here.

The solution for the given equation is x = -5 and x = 3.

How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.

Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.

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Using Pythagoras's theorem, the length of the third side of the right triangle is 3 units.

The length of the third side of the right triangle can be found using Pythagoras's theorem.

The Pythagoras's theorem can be represented as follows:

c² = a² + b²

where

Therefore, the missing side of the right triangle is the other legs.

b²  = (3√5)² - 6²

b² = 45 - 36

b = √9

b = 3

Therefore,

third side of the right triangle = 3 units

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By using Pythagoras' theorem the length of the third side is 3 units

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, the hypotenuse is 3√5 units and one of the legs is 6 units and assuming the length is x units.

∴ x² = (3√5)² - 6².

x² = 9×5 - 36.

x² = 45 - 36.

x² = 9.

x = ± 3.

As length can not be negative the appropriate value for x is + 3.

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Answer:

b. $0.21

Step-by-step explanation:

(7·49.95 + 162.38)/2465 = 0.2077

Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3

and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%

so the answer is 1 whole batch and 81% of another

or 1 9/3

Step-by-step explanation:

You have found a used car and your parents have agreed to pay the first $750 for you. You have a summer job mowing yards for $25 per yard. Write and inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.

25y + 750 = C

If the car cost a total of $4500 how many yards will you have to mow?

25y + 750 = 4,500

subtract 750 from both sides:

25y + 750 - 750 = 4,500 - 750

25y = 3,750

divide both sides by 25:

25y/25 = 3,750/25

y = 150

Must mow 150 yards.

check:

25(150) + 750 = 4,500

3,750 + 750 = 4,500

4,500 = 4,500

The average rate of change of the function f(x) = x² + 8x from x₁ = 1 to x₂ = 2. is 16

The average rate of change expresses how frequently one quantity changes in relation to another. It provides an idea of the amount the function changed per unit throughout the specified time period. In order to calculate the rate of change, one simply divides the amount of change in one thing by the comparable amount of change in another.

The average rate of change of a continuous function,

f(x) , on a closed interval [a,b] is given by

F(x)=[tex]\frac{F(b)-F(a)}{b-a}[/tex]

[tex]\frac{25 -9}{1}\\ \frac{16}{1}\\ =16[/tex]

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Given the functions:

1. (h/g)(x)

We substitute the functions and solve:

Factor the common term 8:

And we have:

1. Store A's unit price = $4 per pound

2. Store B's unit price = $2 per pound.

3. Store C's unit price = $3 per pound.

4. Store B's unit price is the lowest.

The unit rate of the relationship between variables x and y, is given as:

Unit rate, m = y/x.

In a given equation, y = mx, the value of m represents the unit rate of the relationship.

In the scenario given, y represents cost in dollars while x represents the  number of pounds of apples.

1. The unit rate = unit price of apples. For store A, we are given 3 pounds of apples will cost $12, therefore:

Unit price = y/x = 12/3

Unit price = $4 per pound

2. For store B, the "2" in the equation, y = 2x, represents the unit price.

Unit price for store B = $2 per pound.

3. Using one point on the graph for Store C, say, (2, 6):

Unit price = y/x = 6/2

Unit price = $3 per pound.

4. The lowest unit price is $2 per pound, therefore, Store B has the lowest unit price for apples.

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The personal trainer took 11 plan A and 7 plan B classes.

Let the number of sessions of plan A be x. So, the number of sessions of plan B be (18 - x). Now forming the equation as per the mentioned information.

25×x + 50 (18 - x) = 625

Performing multiplication on Left Hand Side of the equation

25x + 900 - 50x = 625

Rearranging the equation

900 - 625 = 50x - 25x

Performing subtraction on both the sides of the equation

275 = 25x

Shifting 25 to other side of equation

x = 275/25

Performing division to find the value of x

x = 11

Number of plan A classes = 11

Number of plan B classes = 18 - 11

Number of plan B classes = 7

Thus, the number of plan A classes is 11 and plan B classes is 7.

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The value of the length of the segment SR is; 12 units.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

According to the diagram at point it makes the angle of 90° with both triangles, thus;

SR = SQ

2x + 8 = 8x - 4

And to find the value of x, we will find the value of  line segment SR

8x -2x = 8+4

6x = 12

x = 12/6

x = 2

Then we will put the value of x in SR ;

SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12

SR = 12

Hence, The value of the length of the segment SR is; 12 units.

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Given the expression:

The answer = 3

The word problem for the given expression will be:

What is the 18 divided by 6?

Answer:  72.4

Step-by-step explanation:

soh-cah-toa

cos(25)= adjacent/hypotenuse

cos(25)= adjacent/48

adjacent= 48 * cos(25)

tan(59) = opposite/adjacent

tan(59) = x / 48 * cos(25)

x = 72.4

The total dollar amount of her commission last year equals to $19,200.

This refers to the percentage of the value of a sale that a sales associate or representative may earn.

To start, we must analyze the data we have. Given that Alexandria's total sales were $ 480000, and the commission received is 1/25 of that sales.

The commission earned from the sales:

= 1/25 * $480000

= $19,200

Therefore, the total dollar amount of her commission last year equals to $19,200.

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The probability is 0.9204 that exactly 3 of them say job applicants should follow up within two weeks.

Binomial probability distribution

P(X = x) = [tex]C_{n,x}[/tex] . [tex]p^{x}[/tex] .[tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex]= n!/ x!(n - x)!

The parameters are:

n is the number of trails.

x is the number of successes.

p is the probability of success on a single trial.

In this problem:

43% say job applicants should follow up within two weeks, thus p = 0.43

6 managers are selected, thus n= 6.

The probability that at least 3 of them say job applicants should follow up within two weeks is P(X≥ 3), which is given by:

P(X ≥3) = 1 -P(X < 3)

In which:

P(X < 3 ) = P(X = 0) + P(X = 1) + P(X = 2)

Then:

P(X = x) = [tex]C_{n,x}[/tex]. [tex]p^{x}[/tex]. [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{6,0}[/tex] [tex](0.43)^{0}[/tex]. [tex](0.57)^{6}[/tex] = 0.0342

P(X = 1) = [tex]C_{6,1}[/tex](0.43) . [tex](0.57)^{5}[/tex] = 0.0259

P(X = 2) = [tex]C_{6,2}[/tex](0.43)² [tex](0.57)^{4}[/tex] =0.0195

P(X<3) = P(X = 0) + P(X = 1) + P(X =2) = 0.0342 + 0.0259 + 0.0195

                                                             = 0.0796

P(X≥3) = 1 - P(X<3) = 1- 0.0796 = 0.9204

0.9204 is the probability that at least 3 of them say job applications should follow up within two weeks.

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The only way to check which one is the correct answer is to perform each set of transformations and check which one is the correct one. First, note that the initial position of the smiley face is the third quadrant. So, we will first apply vaguely the transformations to check to which one is the smiley face located in the first quadrant once we are done with the transformations.

So, let us analyze each set of transformations separately.

Option A

After reflexing over the x axis, the smiley face position would be

so, once rotated 270° counterclockwise, the position of the smiley face would be

so option A is not the correct answer

Option B

if we rotate 270° counterclockwise, the smiley face's position would be

and by translating 8 units to the right, it would be

so option B is the correct answer

Solution

Houe Call = $55

Workdone call per hour = $40

Let h denotes the number of hours used

Total charges on the call

The client can spend no more than $250 for the call to the mechanic

The inequality is

There is a mound of 2000 pounds of gravel in a quarry

Quantity of gravel added in the mound throughout the day = 400 pounds

Quantity of orders sold from the mound = 600*2 = 1200 pounds

Quantity of gravel left in the mound at the end of the day = 1200 pounds

Let g represent the pounds of gravel in the quarry

Formulating the equation we get the following:

Mounds of gravel in the quarry + Gravel added in the mound - Gravel sold from the mound = Gravel left at the end of the day

g + 400 - 600(2) = 1200

g + 400 - 1200 = 1200

g = 2000

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If the length of a side of cube is "s", then total edge length (E = 12s), total surface area (A = 6s²) and Volume (V = s³).

As per the question statement, the length of a side of cube is "s".

We are required to write down the equations for total edge length "E", total surface area "A" and Volume "V" of the cube with respect to "s".

To solve this question, we need to know a couple of basic structural properties of a cube, that is,

There are 12 edges in a cube, all of equal length,

And, there are 6 faces in a cube, all of equal surface area.

[A reference image is attached hereby for better understanding;

The 12 edges of the cube are: AB, BC, CD, AD, CG, DH, BF, AE, EF, FG, GH and EH,

And, the 6 Faces of the cube are: ABCD, ABEF, CDGH, BCFG, ADEH and EFGH]

Therefore, total edge length (E) = (12 * s) = 12s,

Or, (E = 12s)

Total surface area (A) = [6 * (s)²] = 6s²,

Or, (A = 6s²)

[Since, area of a square of edge length "s" = s², and every face of a cube is a square]

Finally, Volume (V) of the cube = [s * s * s] = s³,

Or, (V = s³).

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We know that

• The dimensions of the pool are 26 meters by 12 meters.

• The uniform surrounding path has a width of ,x, meters.

To find a function of x to express the whole area, we have to define the width and length including the path.

The width would be-

The length is

The total area is

We use the distributive property to show the function in the simplest form.

Then, we reduce like terms. So, the function is

Answer: [tex]y=-2x+3[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocal slopes, so the slope of the line we want to find is -2.

The y-intercept is given to be 3, so the equation is [tex]y=-2x+3[/tex].

If a bicycle has a listed price of $522.95  before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47

The listed price of bicycle = $522.95

The sales tax percentage = 7.75%

We know

C = p(t×p)

Where C is the total cost

p is the listed price

t is the sales tax percentage

Substitute the values in the equation

C = 522.95+((7.75/100)×522.95)
= 522.95+40.53

= $563.47

Hence, if a bicycle has a listed price of $522.95  before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47

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a)36 is 75 % of 48

b)18 is 25% of 72

Explanation

when we have the percentage and the number , the easiest way to find the value is by applying this formula:

hence

Step 1

a)

what percet of 72 is 18?

let

100 % = 72, ( the number)

x %, = 18

so

replace

therefeore,

18 is 25% of 72

Step 2

b) 36 is 75 % of what,so

let

100%= x=original value

75%=36

so

therefore, 36 is 75 % of 48

I hope this helps you

ANSWER

EXPLANATION

To find the two numbers that are located 5/8 of a unit from 1/6 on the number line, we have to first understand that for a number on a number line, there are numbers both ahead and behind the number.

So, the numbers that are 5/8 from 1/6 on the number line will be:

=> one number that is +5/8 from 1/6

=> one number that is -5/8 from 1/6

Therefore, the two numbers are:

Those are the two numbers.

Answer:

  (c)  corresponding angles

Step-by-step explanation:

You want to know the description of the marked angles in the given diagram.

Interior angles are between the "parallel" lines. Angle 5 is interior, but angle 1 is not, so they cannot be described as interior angles.

Exterior angles are both outside the "parallel" lines. Angle 1 is exterior, but angle 5 is not, so they cannot be described as exterior angles.

Corresponding angles are both in the same direction from the point of intersection of the "parallel" lines with the transversal. Here, both angles 1 and 5 are "northwest" of the intersection point, so are corresponding angles.

Alternate angles are on opposite sides of the transversal. Consecutive, or same-side, angles are on the same side of the transversal. Angles 1 and 5 are not alternate angles, as they are both on the same side of the transversal.

Answer:

Step-by-step explanation:

point of intersection of the equations: (4,6)

The line parallel to the given line would be y = -x + k

the line passes through (4,6)

putting the values, we get, 6 = -4 + k ⇒ k = 10

Required equation⇒ y = -x + 10