Find the area of the rectangle below by multiplying its length and width.



(7x-1) units

(3x-2) units

f(x) = 2x² - 4x - 3

g(x) = (x - 4)(x + 4)  = x² - 16

f(x) - g(x) = 2x² - 4x - 3 - (x² - 16)

              = 2x² - 4x - 3 - x² + 16

              = x² - 4x + 13

Answer: B

to test the points, substitute the x-coordinate into the equation and if the value of y equals the y-coordinate then the point lies on the graph

(0, [tex]\frac{1}{2}[/tex]) → y = 0 + [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{4}[/tex] ≠ [tex]\frac{1}{2}[/tex]

(0 , [tex]\frac{3}{4}[/tex]) → y = [tex]\frac{3}{4}[/tex] ← on graph

([tex]\frac{3}{4}[/tex], 0) → y = [tex]\frac{3}{8}[/tex] + [tex]\frac{3}{4}[/tex] ≠ 0

([tex]\frac{3}{4}[/tex],[tex]\frac{1}{2}[/tex] → y = [tex]\frac{3}{8}[/tex] + [tex]\frac{3}{4}[/tex] ≠ [tex]\frac{1}{2}[/tex]

([tex]\frac{1}{2}[/tex], 1) → y = [tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 1 ← on graph

the points (0, [tex]\frac{3}{4}[/tex]) and ([tex]\frac{1}{2}[/tex], 1) are on the graph

The points that are contained in the graph of the straight line y = (1/2)x + 3/4 are (0,3/4) and (1/2,1).

An equation describes that both sides of the variables and constants are in different forms but they are equal.

To determine if each given point is contained in the graph of the equation Y = (1/2)x + 3/4 we will put the values of x in the equation and determine the corresponding value of y.

When x = 0, y = (3/4).

When x = (3/4), y = 9/8.

When x = 1/2, y = 1.

So, the points that are contained in the graph Y = (1/2)x + 3/4 are (0,3/4), (1/2,1).

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The required integer is -100$.

It is required to find the integer.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

The given integer describes withdrawing $100 from your bank account.

According to given question we have,

-100$

negative one hundred

or

minus one hundred

Therefore, the required integer is -100$.

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The quickest way to do this is to plug the first b-value from each table into the equation to find p-value. Then compare your answer with the p-value from the table to find the one that is greater than your answer.

p = 3.25b  

                  Equation                    Table                   Table compared to Equation

Table A:  p = 3.25(1) = 3.25           p = 2.75                               <

Table B:  p = 3.25(1.5) = 4.875       p = 3.75                              <

Table C:  p = 3.25(2) = 6.50           p = 7.00                                 >

Table D:  p = 3.25(2.5) = 8.125       p = 10.00                               >

Table E:  p = 3.25(3) = 9.75             p = 11.25                               >

Table F:  p = 3.25(3.5) = 11.375       p = 10.50                          <

Answer: C, D, and E

To tell isf a table is proportional, divide y by x,

if all sets are the same it is proportional.

First table:

3 / -3 = -1

2 / -4 = -2

-1 and -2 are not the same

Table 2:

1/-1 = -1

3/-3 = -1

5/-5 = -1

These are all the same.

Table 2 is correct.

To find porportionality, you must note that: the x and y must have the same value throughout the table when multiplied.

For example:

x     |    y

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

1     |   2

2    |   4

etc.

In this case, it is multiplied by 2. Now let us look at the problem

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

Table 2 is your answer because, you are multiplying -1 each time

x(-1) = y   is your equation

To check, plug in the x, and see if the y is the same value

(-1)(-1) = 1 (True)

(-3)(-1) = 3 (True)

(-5)(-1) = 5 (True)

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

hope this helps

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

The answer is A.

ANSWER

The correct answer is A

EXPLANATION

To find the ink cost of each card coming from printer  B, we need to find the total cost from printer B and the total number of cards printed by Printer B.

The total hours of all the three printers over the three weeks

[tex]=40+45+55+50+50+30+45+40+60=415[/tex]

The total hours of printer B only

[tex]=50+50+30=130[/tex]

Total number of cards produced over the three weeks

[tex]=7950+7800+9600=25350[/tex]

We can use ratio and proportion to determine the total cards produce by printer B only.

[tex]415:25350[/tex]

[tex]130:x[/tex]

If less, more divides

[tex]x=\frac{130\times 25350}{415} \approx7941[/tex]

Total cost of Printer B in 130 hours

$[tex]=130 \times 15=1950[/tex]

The ink cost

[tex]=\frac{1950}{7941}[/tex]

[tex]=0.2456[/tex]

$[tex]\approx 0.30[/tex]

to 2 decimal places

we know that

[tex]I=Prt[/tex]

where

I is the amount in interest

P is the investment

r is the interest rate

t is the time in years

Solve for t

[tex]t=I/(Pr)[/tex]

we have

[tex]I=\$1,400\\ P=\$27,000\\ r=4.2\%=0.042[/tex]

substitute

[tex]t=1,400/(27,000*0.042)=1.23\ years[/tex]

therefore

the answer is

[tex]1.23\ years[/tex]

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:

Answer:

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

Step-by-step explanation:

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:

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

Step-by-step explanation:

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.

The range = [0 , ∞)

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

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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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

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

Hey there!!

Co-ordinates for midpoint when two endpoints are given :

... [tex]\frac{x2+x1}{2} , \frac{y2+y1}{2}[/tex]

Given endpoints :-

... ( -1, 7 ) ( 3, -3 )

... [tex]\frac{3-1}{2},\frac{-3+7}{2}[/tex]

... [tex]\frac{2}{2},\frac{4}{2}[/tex]

... [tex]1,2[/tex]

Hence, the midpoint is ( 1,2 )

Hope my answer helps!

The midpoint of the line segment with endpoints (-1,7) and (3,-3) would be (1, 2).

Suppose we've two endpoints of a line segment:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}\\and \\y = \dfrac{q+n}{2}[/tex]

Given endpoints ; ( -1, 7 ) ( 3, -3 )

[tex]x = \dfrac{-1+3}{2}\\\\\\x = 1\\y = \dfrac{7-3}{2}\\\\ y = 2[/tex]

Hence, the midpoint is ( 1,2 ).

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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.)

chicken: ($2.99) c

steak: ($5.79) s

chicken + steak = total

2.99c + 5.79s = 50

Answer: D

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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