Drag a statement or reason to each box to complete this proof.

Remark

First of all you have to declare the meaning of g(f(x)) After you have done that, you have to make the correct substitution.

Givens

f(x) = 4x^2 + x + 1

g(x) = x^2 - 2

Discussion

What the given condition g(f(x)) means is that you begin with g(x). Write down g(x) = x^2 -  2

Wherever you see an x on either the left or right side of the equation, you put fix)

Then wherever you see f(x) on the right you put in what f(x) is equal to.

Solution

g(x) = x^2 - 2

g(f(x)) = (f(x))^2 - 2

g(f(x)) = [4x^2 + x + 1]^2 - 2

f(x)^2 =

4x^2 + x + 1

4x^2 + x + 1

16x^4 + 4x^3 + 4x^2

            4x^3  + x^2 +   x

                        4x^2 + x  + 1

16x^4 + 8x^3 + 9x^2 + 2x + 1

Answer

g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x + 1 - 2

g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x - 1

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Event A: You get a red car

and

[tex]P(A)=0.20[/tex]

Similarly,

Event B: You get a convertible

and

[tex]P(B)=0.40[/tex]

So, if A and B are independent , then they must satisfy,

[tex]P(A).P(B)=P(A\cap B)[/tex]

So,

[tex]P(A\cap B)=0.4\times 0.2=0.08[/tex]

Hence, Option 'D' is correct, which states that the probability of getting a red convertible is 0.08.

Answer:

D.The probability of getting a red convertible is 0.08

Step-by-step explanation:

ap3x

For this one, find out how many hour have passed per day with 6 pm Friday being where you start.  

6 pm Friday- 6 pm Saturday =24

6 pm Saturday - 6 pm Sunday= 24

6 pm Sunday - 6 am Monday = 12 hours

6 am Monday until 8 am Monday= 2 hours

Now just add the amount of hours together

24+24+12+2= 62 hours

Now convert that to minutes.

There are 60 minutes in 1 hour.  You multiply the amount of hours by 60 to get the minutes.

62 hours times 60 minutes in 1 hour

62*60= 3720.

So you will have a total of 3,720 minutes of tape to review.

Answer: 3,720

Step-by-step explanation:

If you borrowed $100, then your monthly payment is $2.44

If you borrowed $200, then your monthly payment is 2*2.44 = 4.88

etc etc

We can set up a proportion

2.44/100 = x/13300

to figure out the monthly payment x. Cross multiply and solve for x

2.44*13300 = 100*x

100x = 2.44*13300

100x = 32452

x = 32452/100

x = 324.52

So the monthly payment is $324.52

An alternative way to get this monthly payment is to apply 2.44% to 13300, which is another way to view the phrase  "monthly payment per $100 is 2.44"

------------------

There are 48 months in 4 years (start with 12 mon = 1 yr, then multiply both sides by 4) so we multiply 48 by the monthly payment to get the result 48*324.52 = 15,576.96. This is the total amount you have to pay back which is the principal plus interest.

Subtract off the principal (amount borrowed) to find the interest or finance charge: 15,576.96 - 13,300 = 2,276.96

Answer: Choice B

The finance charge on $13,300 financed at 7.9 percent for 4 years is $12,975.48.

To calculate the finance charge, we need to first find the total amount financed. We can do this by multiplying $13,300 by the monthly payment per $100, which is $2.44. $13,300 divided by 100 is 133, so we multiply 133 by 2.44 to get $324.52. Now, we can calculate the finance charge by subtracting the total amount financed from the original loan amount. $13,300 minus $324.52 is $12,975.48. Therefore, the finance charge is $12,975.48.

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m = [tex]\frac{5}{6}[/tex] , y - 7 = [tex]\frac{5}{6}[/tex] ( x - 12), y = [tex]\frac{5}{6}[/tex] x - 3

(a) calculate the slope using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂) = (12, 7)

m = [tex]\frac{7+8}{12+6}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]

(b) the equation of a line in point-slope form is

y - b = m(x - a )

where m is the slope and (a, b) a point on the line

using m = [tex]\frac{5}{6}[/tex] and (a , b) = (12, 7 )

y - 7 = [tex]\frac{5}{6}[/tex] (x - 12)

(c) the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange (b ) into this form

y - 7 = [tex]\frac{5}{6}[/tex] - 10

y = [tex]\frac{5}{6}[/tex] x - 3

If f(x) varies directly with  [tex]x^2[/tex]

If f(x) varies directly with x then we use equation f(x) = kx

where k is the constant of proportionality

So equation becomes [tex]f(x) = kx^2[/tex]

We use the information and find out k

f(x)= 10

[tex]f(x) = kx^2[/tex]

[tex]10= kx^2[/tex]

[tex]k = \frac{10}{x^2}[/tex]

now we use the value of k and find the value of f(x) when x=3

[tex]f(x) = \frac{10}{x^2}*x^2[/tex]

f(x) = 10

The value of f(x) = 10 when x= 3

The value of f(x) when x=3 is 90.

If f(x) varies directly with x2 and is given that f(x)=10 when x=1 (since 1 squared is 1), we can express the direct variation as f(x) = k × x2, where k is the constant of variation. To find the value of k, we use the information that f(1)=10. Thus, 10 = k × 12, which means k=10.

Now that we know k=10, we can find f(x) when x=3. We substitute x with 3 in the equation f(x) = 10 × x2, yielding f(3) = 10 × 32 = 10 × 9 = 90. Therefore, the value of f(x) when x=3 is 90.

Answer:

26% increase

Step-by-step explanation:

Answer:

26% increase

Step-by-step explanation:

You could buy 8 lemons for 60 cents.

Consider the parrent function [tex]y=\sqrt{x}.[/tex] The graph of this function you can  see in the attached diagram (red line).

1. Reflect this graph about the x-axis, then the function becomes [tex]y=-\sqrt{x}[/tex] (blue line).

2. Translate the reflected graph 2 units up, then the function becomes [tex]y=-\sqrt{x} +2[/tex] (green line).

Answer: correct choice is B.

Answer:

Because if you add the amount of Ys together it equals 3y

Step-by-step explanation:

The range = [0 , ∞)

We read from the y axis.  The graph exists from y = 0 to infinity.

f(x) + n - shift a graph n units up

f(x) - n - shift a graph n units down

f(x + n) - shift a graph n units left

f(x - n) - shift a graph n units right

-------------------------------------

We have:

[tex]y=\dfrac{1}{x}\to y=\dfrac{1}{x+4}\\\\f(x)=\dfrac{1}{x}\to f(x+4)=\dfrac{1}{x+4}[/tex]

Let us check the slope of y-intercepts of the given lines in the graph first.

The y-intercept of above line is 1 and slope of

Rise/run = 2/1 (Moving 2 units up and 1 unit right).

So, the equation should be

y=2x+1

Y-intercept of second line is -2 and slope is

Rise/run = -1/1 (Moving 1 unit down and 1 unit right).

So, the equation should be

y=-x-2.

Now, we need to check the shaded portion for inequality signs.

We have both lines dotted.

So, the inequality signs would be just < or >.

For y=2x+1 line : Shading is on the left side.

On the left side of the line y=2x+1, the y-values are greater than on right side.

Therefore, we got first inequality y>2x+1

For y=-x-2 line : Shading is on the down of the line.

On the down of the line y=-x-2, the y-values are less than up side of the line.

Therefore, second inequality would be

y<-x-2 or y+x<-2

Therfore, correct option is first option y>2x+1 and y+x<-2.

Answer:

A was the answer.

Step-by-step explanation:

i took the test.

Answer:

Step-by-step explanation:

The line in the graph has a rise of 1 for each run of 1, so its slope is 1/1 = 1. The slope (x-coefficient) of the function f(x) = -7x+1 is -7, so that is not the function shown in the graph.

The wording "the range ... is increasing as the domain increases" is a bit unusual. Usually "domain" and "range" refer to intervals or sets of values over which the function is defined. While it is true that extending the interval of definition (domain) of the function will extend the range of values it produces, we suspect this is supposed to suggest that the slope of the line is positive. (As you pick increasing elements from the domain, the function will map those values to increasing elements of the range.)

Answer:

c) to reveal how your own values may match certain career choices

Step-by-step explanation:

Let Maria = X

Andre = 3x ( 3 times as many as Maria)

Jane = 2(3x) = 6x ( 2 times as many as Andre)

All 3 need to equal 840 pounds:

X + 3x + 6X = 840

Combine like terms:

10X = 840

Divide both sides by 10:

X = 840 / 10

X = 84

Maria = X = 84 pounds

Andre = 3x = 3(84) = 252 pounds

Jane = 6x = 6(84) = 504 pounds

504 + 252 + 84 = 840 pounds.

Andre picked 252 pounds.

The answer is B.

Hi,

Jane, Andre, and Maria pick apples. Andre picks 3 times as many pounds as Maria. Jane picks 2 times as many pounds as Andre. The total weight of the apples is 840 pounds. How many pounds of apples does Andre.

Lets say andre picked 252!

Andre - 252

Maria - 252 / 3 = 84

Jane - 252 x 2 = 504

504 + 252 + 84 = 840

Answer:

B) 252 pounds

Solve for w by simplifying both sides of the equation, then isolating the variable.

The answer is A.

Answer with Explanation:

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

If a system has no solution, it is said to be inconsistent . Represent parallel lines.

1)   8x + y + 4 = 0  

       y = -8x - 4

If we solve equation 8x + y + 4 = 0  for y, we get

y = -8x -4

So, both equations are same. That means both lines are same. So infinite many solutions.

System is consistent

2) Both line slope are same and parallel to each other.

So,  no solution

System is  inconsistent.

3) Both equation represent the same line. So, infinite many solution.

System is consistent.

4)  Both lines are intersect at a point.

Intersection point is (7,0).

5) Both lines are parallel. So, no solution.

System is inconsistent.

if x can be 2-5 and y can be 1-6, c=3(5)+4(6)

which would turn out to be c=39

The maximum value of C will be equal to 39.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given constraints are:-

x  ≥   2

x  ≤   5

y  ≥   1

y  ≤  6

Here maximum value of x = 5 and for y = 6

Putting the maximum values of x and y to calculate the maximum value of C.

C  =  3x  +  4y

C  = ( 3 x 5 )  +  (  4  x  6 )

C  =  15  +  24

C   =  39

Therefore the maximum value of C will be equal to 39.

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Answer:  The correct option is  (C) [tex]2x+5y=-15.[/tex]

Step-by-step explanation:  Given that the equation of the line that passes through (-5, -1) and (10, -7) in point-slope form is given by

[tex]y+7=-\dfrac{2}{5}(x-10)~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the standard form of the equation for the above line.

We know that the STANDARD form of the equation of a line is given by

[tex]ax+by=c,~~~~~\textup{[a and b cannot be zero at the same time]}.[/tex]

From equation (i), we have

[tex]y+7=-\dfrac{2}{5}(x-10)\\\\\Rightarrow 5(y+7)=-2(x-10)\\\\\Rightarrow 5y+35=-2x+20\\\\\Rightarrow 2x+5y=20-35\\\\\Rightarrow 2x+5y=-15.[/tex]

Thus, the required standard form is [tex]2x+5y=-15.[/tex]

Option (C) is CORRECT.

In order to turn a ratio into a percentage, you have to turn the given fraction into an equivalent fraction with denominator 100. So, you have

[tex] \dfrac{3500}{5000}=\dfrac{x}{100} [/tex]

Solving for x, you get

[tex] x=\dfrac{3500\cdot 100}{5000} = \dfrac{3500}{50} = \dfrac{350}{5} = 70 [/tex]

So, they achieved the 70% of their goal.

The correlation coefficient of -0.93 suggests a strong negative association between the two variables. Thus, option D is the correct answer.

In the study, it was found that the correlation coefficient between two variables is -0.93, implying a strong relationship between the two variables. But because the coefficient value is negative, it means that there's a strong negative association between the variables. In other words, as one variable increases, the other decreases, and vice versa.

A correlation coefficient ranges from -1 to 1. The strength of the correlation is determined by the absolute value of the coefficient - the closer to 1 (or -1), the stronger the correlation. Positive values indicate a direct relationship, where both variables move in the same direction, while negative values indicate an inverse relationship, where the variables move in opposite directions.

Therefore, in your given options, the right choice is D. There is a strong negative association between the variables.

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ANSWER

The correct answer is D

EXPLANATION

The slope of the given line

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

The line perpendicular to it has slope

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

If the line passes through

[tex](1,27)[/tex]

Then the equation is given by

[tex]y-y_1=m(x-x_1)[/tex]

[tex]\Rightarrow y-27=3(x-1)[/tex]

[tex]\Rightarrow y=3x-3+27[/tex]

[tex]\Rightarrow y=3x+24[/tex]

Equation of the required line which is perpendicular to this line and passes through (1, 27) is y= 3x+24

The equation of the given line is y = -1/3x - 24

Comparing it with the standard form i.e y=mx+c

where 'm' is the slope of the line

and 'c' is the y-intercept of the line

we get 'm=-1/3' and 'c=-24'

Now if two lines are perpendicular the relation between their slopes  'm1' and 'm2' is given as

m1*m2=-1

Thus here m1=-1/3;

(-1/3)*m2=-1

m2=3

Therefore slope of any line perpendicular to  y = -1/3x - 24 would be m2=3

Also given that the line passes through the point  (1, 27)

Thus if a line having slope as 'm' and passing through the point (x1,y1) its equation is given as:

[tex]y-y_{1}=m(x-x_{1})[/tex]

here [tex](x1,y1)=(1,27)[/tex]

and [tex]m=3[/tex]

Thus required equation would be:

y-27 = 3*(x-1)

y-27 = 3x-3

y = 3x-3+27

y= 3x+24

Remark

Usually this is written in very simple terms. You could do it as a proportion, but it might be easier to see if you used Newton's formula twice.

Formula

F = m * a

m = mass, F = force, a = accelerationn

Givens

F1 = 70 N

a1 = 6.5 m/s^2

m = ?

F2 = ??

m = ?

a2 = 8 m/s^2

Step One

Solve for m

F1 = m * a1              Substitute the values

70 = m *  6.5           Divide by 6.5

70/6.5 = m

10.77 kg = m

Step Two

Solve for F2

m = 10.77 kg

a = 8

F2 = ??

F2 = m * a2

F2 = 10.77 * 8

F2 = 86.154

Answer: C rounded to the nearest 1/100