Given the definitions of f(x) and g(x) below, find the value of (gof)(-2).
f(x) = 3x² – 3x – 7
-
g(x) = -3x - 10

The two related linear equations for |x – 2| = 5 are x - 2 = 5 and x - 2 = -5

From the question, we have the equation to be

|x - 2| = 5

This equation is an absolute value function

The general rule of an absolute value function is that:

An equation represented as y = |x| can be expressed as y = x or y = -x

Using the above guideline as a guide, we have the following representation of |x – 2| = 5

x - 2 = 5 and x - 2 = -5

Hence, the equations are x - 2 = 5 and x - 2 = -5

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Answer: -2 ==> A

Step-by-step explanation:

-23 - 12 - (-33) =

-23 - 12 + 33 = ==> subtracting by a negative number is basically adding by the positive number

-(23 + 12) + 33 =

-35 + 33 =

-(35 - 33)=-2 ==> A

Answer: -2

Step-by-step explanation:

The area of the rectangle is, 24 square centimeter.

What is area?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let, the perimeter of the rectangle is 20 centimeter.

The length is 6 centimeter.

Suppose the width of the rectangle is y.

So,

Perimeter = 2(6) + 2(y)

           20 = 12 + 2y

             8 = 2y

             y = 4

Hence, the width of the rectangle is 4 centimeter.

Since,

Area of rectangle = length x width

                          A =  6 x 4

                          A = 24

Therefore, the area of the rectangle is, 24 square centimeter.

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Answer:1/6.4, and there are 5.4 times as many pigs as cows.

Step-by-step explanation: In this scenario there are 64 animals, 54 pigs and ten cows. So the ration is 10/64, which can be simplified if you like to 1/6.4

There are 54 pigs for every 10 cows, which is the same as 5.4/1.

For every cow there is 5.4 pigs, so however many cows there are you can take that number and multiply it by 5.4 to get the number of pigs.

Answer:

5/32

5.4

Step-by-step explanation:

54:10 is the ratio of pigs to cows.

It could be assumed that there are 54 pigs and 10 cows.

Problem is asking for the ratio of cows to all animals. So,

Add up the pigs and cows to get 64 total animals.

Input the numbers to the ratio cows:all animals

10:64

Change to a fraction

5/32

How many times the number of cows is the number of pigs. This can be found by dividing the number of pigs by the number of cows.

54 / 10 = 5.4

The number of pigs is 5.4 times more than the number of cows.

The statement that "the sample is set of all people or objects whose properties ,  are to be described and analyzed by the data collector " is False .

In the question ,

it is given that ,

The sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector .

But we know that the Population is defined as "set of all people or objects whose properties are to be described and analyzed by the data collector"

and the Sample is the Subset or subgroup of the population .

Therefore , the given statement is False .

The given question is incomplete , the complete is

State whether the statement is True or false "a sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector " .

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Answer:

0.001? or -299.7

Step-by-step explanation:

so i don't have idea what do you meaning so

0,3:300=0.001 or 0,3-300=-299.7

so i think i help

The error occurs in Litas work is in step 3 and step 4.

An exponential function is a mathematical function of the following form:

f ( x ) = aˣ where x is a variable, and a is a constant called the base of the function.

The given expression is

25⁻⁴/(5⁻²)²

The given steps are

Step 1,

25⁻⁴/(5⁻²)²

Step 2,

(5²)⁻⁴/(5⁻²)²

Step 3,

(5²⁻⁴)/(5⁻²⁺²)

The step 3 is wrong because the exponents should be multiplied but not added.

The actual step should be

(5⁻⁸)/(5⁻⁴)

Hence the error occurs in Litas work is in step 3 and step 4.

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Answer:

I think it would be 12^1/4

Step-by-step explanation:

I hope this is what you were asking for :)

Answer:

x = 9

Step-by-step explanation:

Start by dividing both sides by the singular number, 3. We divide by 3 and not 21 because 21 is the result of the equation, not the coefficient.

[tex]\frac{3\left(x-2\right)}{3}=\frac{21}{3}[/tex]

We got 21 over 3 because you cannot divide 3 times an unknown number subtracted by 2 by 3. This is because we do not know the number. So that's where 21 comes in.

Next, simplify this equation by dividing whole numbers.

[tex]\frac{3}{3} = 1[/tex]

[tex]1\left(x-2\right) = \left(x-2\right)[/tex]

[tex]\frac{21}{3} = 7\\= x-2 = 7[/tex]

Lastly, add 2.

[tex]x - 2 + 2 = 7 + 2\\2 + 2 = 4\\7 + 2 = 9\\= x - 4 = 9\\x = 9[/tex]

Why x - 4 is 0: We assume x is always equal to 1, since 4 does not go into 1, the result would be 0. x - 0 = 0. Therefore, the problem became x = 9.

Hope this helps!

An equation for the trend line shown on the scatter plot is y = 5x + 15.

In order to determine a linear equation for the trend line (line of best fit) that models the data points described in the scatter plot above, we would have to calculate the slope of this line.

By critically observing the scatter plot, we can reasonably and logically deduce the following points through which the trend line passes through:

Points (x, y) = (2, 25)

Points (x, y) = (6, 45)

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (45 - 25)/(6 - 2)

Slope, m = 20/4

Slope, m = 5.

At point (2, 25), a linear equation for the trend line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the formula, we have;

y - y₁ = m(x - x₁)

y - 25 = 5(x - 2)

y - 25 = 5x - 10

y = 5x - 10 + 25

y = 5x + 15.

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Answer:

8 hours

Step-by-step explanation:

if it takes 2hrs to do 4 pages it takes an hour to do 2 pages

2*8=16

1*8=8

8 hours

hope it helps

Answer:

132

Step-by-step explanation:

240/5=48

48*2=96

240-15%=204

240-204=36

96+36=132

The number of pupils who came by bus is 108.

Total number of kids in school = 240

Fraction of pupils who came to school by car = 2/5

Number of pupils who came to school by car = [tex]\frac{2}{5}[/tex] × 240

                                                                           = 96

Percentage of pupils who came to school by walk = 15 %

Number of pupils who came to school by walk = [tex]\frac{15}{100}[/tex] × 240

                                                                              = 36

Number of people who came by bus  

                    =Total number of kids in school - number of pupils who         came by car - number of pupils who came by walk

                    = 240 - 96 - 36

                    = 108

Therefore, the number of pupils who came to school by bus = 108.

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Answer:

1700 - 700x

Step-by-step explanation:

assuming x is the number of weeks, the equation is 1700 - 700x equals the amount you are trying to solve for. You can say you are solving for y.

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{9}}(x-\stackrel{x_1}{9}) \\\\\\ y-1=\cfrac{1}{9}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{9}x \end{array}}[/tex]

Answer:

9/14 (9 over 14)

Step-by-step explanation:

Answer: $3.01

Step-by-step explanation:

1. You first have to find out how much she spent for ALL the jellybeans, you find this by multiplying the pounds by the cost per pound.

(7/2)*(2.58)

Kelsey spent $9.03 for the 3 1/2 pound bag of jellybeans

2. You now have to find out how much she spent for 1/3 if the bag. You do this by multiplying the total cost by 1/3.

(1/3)(9.03)

3.01

ANSWER: Kelsey spent $3.01 on the amount of jellybeans she gave away.

The absolute value equation representingnumbers all x whose distance from is 11 units is

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.

A number can never have a negative absolute value.

The equation is written in the form below

|1 - x| = 11

removing the absolute value sign

1 - x = ± 11

solving for x for positive value

1 - x = 11

1 - 11 = x

x = -10

solving for x for negative value

1 - x = -11

1 + 11 = x

12 = x

The absolute value equation as required is |1 - x| = 11 the values of is 12 or -10

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The values of x, y and z in the angles are as follows

When parallel lines are cut by a transversal line, angle relationship are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.

The parallel lines forms angles relationships.

Therefore,

x = 2y (alternate angles)

z = 2x + 90 (alternate angles)

Using substitution,

z = 2(2y) + 90

z = 4y + 90

x + 2x + 90 = 180 (sum of angles on a straight line)

3x  = 180 - 90

3x = 90

x = 90 / 3

x = 30°

Hence,

30 = 2(y)

y = 30 / 2

y = 15

z = 4(15)+ 90

z = 60 + 90

z = 150°

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We can easily see that two similar equation of under cube root of x.

So, the graph of cube root of x is identical.

The graph of under root x is positive half of parabola, consist of origin (0, 0). Its symmetric on the positive x-axis.

The graph of the  cube root function f(x) = ∛x.Take the numbers -8, -1, 0, 1, and 8 in the x column calculate the cube root of each of these numbers, and fill them in the column labeled y. Then we have 5. Just plot them and join them by a curve. As this curve is not complete, just extend it on both sides.

We can easily see that two similar equation of under cube root of x.

So, the graph of cube root of x is identical.

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Answer:

D F on edge

next one is A C D

Step-by-step explanation:

trust

Answer: 1.72

Step-by-step explanation:

Volume of the cone is 628 In^3

What is cone?

A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant.

Cones typically have pyramidal shapes with circular cross sections. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly determine the volume of a cone.

The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all the points on a base that is in a plane that does not contain the apex.

According to the question

The volume of a cone = (1/3) πr2h cubic units

r=10 inch

h=6 inch

π=3.14

Volume=0.33(3.14)(10)(10)(6)

volume=628 [tex]inch^3[/tex]

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Answer:

D

Step-by-step explanation:

500 user in a day that mean in 2 days you get 1000 user cause the double of 500 is 1000

In exponential relations, we can represents given values like this:

[tex]f(x)=a*c^x[/tex]

We're given:

⇒ Plug this information into [tex]f(x)=a*c^x[/tex]:

[tex]f(x)=27,100*(0.93)^x[/tex]

Why input 0.93 and not 0.07? Let's think of it this way: To calculate the new price of the car after one year, we find 93% of 27,100.

The dependent variable is the price (y) and the independent variable is the time in years (x).

Therefore, to find the value of the car after 6 years, we plug in 6 as x:

[tex]f(x)=27,100*(0.93)^6[/tex]

[tex]V=27,100*(0.93)^6[/tex]

Pressure = Force/Area

According to question, we have

18 = Force/4

force = 72 N

The value of m∠5 is 125°. option A is the correct answer

From the question, we have

m∠1=70°

As the sides are equal.

∠2=∠3=(180°-70°)/2

= 55°

∠5 = 180°-55°  (Linear pair)

= 125°

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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The expression that is equivalent to x is ∛4/s

In this question, the mathematical statement of the equation is given as

5x to the power of 7 times s = 20x to the power of 4

When the mathematical statement is represented as an equation, we have the following representation

5x⁷ * s = 20x⁴

Divide both sides by x⁴

So, we have the following representation

5x⁷/x⁴ * s = 20x⁴/x⁴

Evaluate the quotients

This gives

5x³ * s = 20

Divide both sides by 5

x³ * s = 4

So, we have

x³ = 4/s

Take the cube root of both sides

x = ∛4/s

Hence, the solution is x = ∛4/s

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The perimeter of the rectangle is 59.9 m.

The area of the rectangle is = 223.2 m²

the length(L) of the rectangle is = 16 m

we know that the area of the rectangle is given by

Area  = Length x Breadth

A =  LB

therefore ,

LB=  223.2

16 x B = 223.2

B = 223.2/ 16

B = 13.95 m

∴ breadth or the rectangle is 13.95 meter.

Now , we know that the perimeter of the rectangle is given by ,

(P) perimeter = 2( Length + Breadth )

P = 2(L + B)

P = 2( 16 + 13.95)

P = 2( 29.95)

P = 59.9 m

So the perimeter of the rectangle is 59.9 meter.

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Answer:

Step-by-step explanation:

The Cyclical Unemployment rate is 3%.

Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.

Actual Unemployment Rate = 8%

Natural Unemployment Rate = 5%

The Actual Unemployment rate will be:

= Cyclical Unemployment Rate + Natural Unemployment Rate

8% = 5% + C

C = 8% - 5%

C = 3%

C = Cyclical Unemployment rate

The unemployment is 3%.

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