Question 5 : CONSUMER MATH

Answer:

A, B, and C

Step-by-step explanation:

We can substitute each number into each equation

2 < -1 + 5 true

2 > 1 true

1 > 0 true

A is correct

4 < -1 + 5 true

4 > 1 true

1 > 0 true

B is correct

3 < -0 + 5 true

3 > 0 true

0 > 0 true

C is correct

5 < -2 + 5 false

D is incorrect

Answer:

F

Step-by-step explanation:

There's no Q in APOR or AXYZ

Answer:

The y intercept is (0, 8). The equation of the function is f(x) = 10x + 8

Step-by-step explanation:

Given that after 1 hour of work, Jack will make 18 dollars and the slope is 10, subtract 10 dollars from 18 dollars to find his set amount, or y-intercept.

18 - 10 = 8 dollars.

Now that we have the m and b values, we can create our equation.

The equation in standard form is f(x) = mx +b, where m = the slope and b = the y-intercept. Plug our values in and the equation will be f(x) = 10x + 8. You can test if this is correct by plugging in x values from the table and seeing if your calculated value correctly corresponds to the given y value in the table.

Answer:

Step-by-step explanation:

3(4x-5)-3x+2 work the ()

12x-15-3x+2 combine like terms

9x-13

Answer:

59/6

Step-by-step explanation:

9x6=54

54+5= 59

put the denominator of the fraction to the denominator to the new fraction. I hope this helps.

Answer:

Step-by-step explanation:

1. use the slope formula --> (y2-y1)/(x2-x1)

2. (8 - 4)/(13 -(-3))

3. 4/16

4. m = 1/4

Answer:

r = 5y/8

Step-by-step explanation:

isolate the variable by dividing each side by factors that contain the variable.

Answer:           0.875

Step-by-step explanation:

Answer:

The solution is too long. So, I included them in the explanation

Step-by-step explanation:

This question has missing details. However, I've corrected each question before solving them

Required: Determine the inverse

1:

[tex]f(x) = 25x - 18[/tex]

Replace f(x) with y

[tex]y = 25x - 18[/tex]

Swap y & x

[tex]x = 25y - 18[/tex]

[tex]x + 18 = 25y - 18 + 18[/tex]

[tex]x + 18 = 25y[/tex]

Divide through by 25

[tex]\frac{x + 18}{25} = y[/tex]

[tex]y = \frac{x + 18}{25}[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{x + 18}{25}[/tex]

2. [tex]g(x) = \frac{12x - 1}{7}[/tex]

Replace g(x) with y

[tex]y = \frac{12x - 1}{7}[/tex]

Swap y & x

[tex]x = \frac{12y - 1}{7}[/tex]

[tex]7x = 12y - 1[/tex]

Add 1 to both sides

[tex]7x +1 = 12y - 1 + 1[/tex]

[tex]7x +1 = 12y[/tex]

Make y the subject

[tex]y = \frac{7x + 1}{12}[/tex]

[tex]g'(x) = \frac{7x + 1}{12}[/tex]

3: [tex]h(x) = -\frac{9x}{4} - \frac{1}{3}[/tex]

Replace h(x) with y

[tex]y = -\frac{9x}{4} - \frac{1}{3}[/tex]

Swap y & x

[tex]x = -\frac{9y}{4} - \frac{1}{3}[/tex]

Add [tex]\frac{1}{3}[/tex] to both sides

[tex]x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}[/tex]

[tex]x + \frac{1}{3}= -\frac{9y}{4}[/tex]

Multiply through by -4

[tex]-4(x + \frac{1}{3})= -4(-\frac{9y}{4})[/tex]

[tex]-4x - \frac{4}{3}= 9y[/tex]

Divide through by 9

[tex](-4x - \frac{4}{3})/9= y[/tex]

[tex]-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y[/tex]

[tex]\frac{-4x}{9} - \frac{4}{27}= y[/tex]

[tex]y = \frac{-4x}{9} - \frac{4}{27}[/tex]

[tex]h'(x) = \frac{-4x}{9} - \frac{4}{27}[/tex]

4:

[tex]f(x) = x^9[/tex]

Replace f(x) with y

[tex]y = x^9[/tex]

Swap y with x

[tex]x = y^9[/tex]

Take 9th root

[tex]x^{\frac{1}{9}} = y[/tex]

[tex]y = x^{\frac{1}{9}}[/tex]

Replace y with f'(x)

[tex]f'(x) = x^{\frac{1}{9}}[/tex]

5:

[tex]f(a) = a^3 + 8[/tex]

Replace f(a) with y

[tex]y = a^3 + 8[/tex]

Swap a with y

[tex]a = y^3 + 8[/tex]

Subtract 8

[tex]a - 8 = y^3 + 8 - 8[/tex]

[tex]a - 8 = y^3[/tex]

Take cube root

[tex]\sqrt[3]{a-8} = y[/tex]

[tex]y = \sqrt[3]{a-8}[/tex]

Replace y with f'(a)

[tex]f'(a) = \sqrt[3]{a-8}[/tex]

6:

[tex]g(a) = a^2 + 8a- 7[/tex]

Replace g(a) with y

[tex]y = a^2 + 8a - 7[/tex]

Swap positions of y and a

[tex]a = y^2 + 8y - 7[/tex]

[tex]y^2 + 8y - 7 - a = 0[/tex]

Solve using quadratic formula:

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]a = 1[/tex] ; [tex]b = 8[/tex]; [tex]c = -7 - a[/tex]

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes

[tex]y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 }[/tex]

Factorize

[tex]y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }[/tex]

[tex]y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }[/tex]

[tex]y = -4 \±\sqrt{(23 + a)}[/tex]

[tex]g'(a) = -4 \±\sqrt{(23 + a)}[/tex]

7:

[tex]f(b) = (b + 6)(b - 2)[/tex]

Replace f(b) with y

[tex]y = (b + 6)(b - 2)[/tex]

Swap y and b

[tex]b = (y + 6)(y - 2)[/tex]

Open Brackets

[tex]b = y^2 + 6y - 2y - 12[/tex]

[tex]b = y^2 + 4y - 12[/tex]

[tex]y^2 + 4y - 12 - b = 0[/tex]

Solve using quadratic formula:

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]a = 1[/tex] ; [tex]b = 4[/tex]; [tex]c = -12 - b[/tex]

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes

[tex]y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}[/tex]

[tex]y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}[/tex]

Factorize:

[tex]y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{16+b}}{2}[/tex]

[tex]y = -2\±\sqrt{16+b}[/tex]

Replace y with f'(b)

[tex]f'(b) = -2\±\sqrt{16+b}[/tex]

8:

[tex]h(x) = \frac{2x+17}{3x+1}[/tex]

Replace h(x) with y

[tex]y = \frac{2x+17}{3x+1}[/tex]

Swap x and y

[tex]x = \frac{2y+17}{3y+1}[/tex]

Cross Multiply

[tex](3y + 1)x = 2y + 17[/tex]

[tex]3yx + x = 2y + 17[/tex]

Subtract x from both sides:

[tex]3yx + x -x= 2y + 17-x[/tex]

[tex]3yx = 2y + 17-x[/tex]

Subtract 2y from both sides

[tex]3yx-2y =17-x[/tex]

Factorize:

[tex]y(3x-2) =17-x[/tex]

Make y the subject

[tex]y = \frac{17 - x}{3x - 2}[/tex]

Replace y with h'(x)

[tex]h'(x) = \frac{17 - x}{3x - 2}[/tex]

9:

[tex]h(c) = \sqrt{2c + 2}[/tex]

Replace h(c) with y

[tex]y = \sqrt{2c + 2}[/tex]

Swap positions of y and c

[tex]c = \sqrt{2y + 2}[/tex]

Square both sides

[tex]c^2 = 2y + 2[/tex]

Subtract 2 from both sides

[tex]c^2 - 2= 2y[/tex]

Make y the subject

[tex]y = \frac{c^2 - 2}{2}[/tex]

[tex]h'(c) = \frac{c^2 - 2}{2}[/tex]

10:

[tex]f(x) = \frac{x + 10}{9x - 1}[/tex]

Replace f(x) with y

[tex]y = \frac{x + 10}{9x - 1}[/tex]

Swap positions of x and y

[tex]x = \frac{y + 10}{9y - 1}[/tex]

Cross Multiply

[tex]x(9y - 1) = y + 10[/tex]

[tex]9xy - x = y + 10[/tex]

Subtract y from both sides

[tex]9xy - y - x = y - y+ 10[/tex]

[tex]9xy - y - x = 10[/tex]

Add x to both sides

[tex]9xy - y - x + x= 10 + x[/tex]

[tex]9xy - y = 10 + x[/tex]

Factorize

[tex]y(9x - 1) = 10 + x[/tex]

Make y the subject

[tex]y = \frac{10 + x}{9x - 1}[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{10 + x}{9x -1}[/tex]

Answer:

a= (Z + 2b)/24

Step-by-step explanation:

given:

Z = 24a - 2b

to solve for a, we will try to move "a" to one side of the equation and all other terms to the other side:

Z = 24a - 2b    (add 2b to both sides)

Z + 2b = 24a -2b +2b

Z + 2b = 24a  (switch sides)

24a = Z + 2b (divide both sides by 24)

a/24 = (Z + 2b)/24

a= (Z + 2b)/24

Answer:

5/8

Step-by-step explanation:

1/4=2/8

7/8-2/8=5/8

Answer:

x=19/4

Step-by-step explanation:

The product of 5 and a number x is 1/4

Answer:

Step-by-step explanation:

Rule for the dilation of a point by a scale factor 'k',

(x, y) → (kx, ky)

If we impose this rule in this problem,

k = [tex]\frac{\text{Distance of A' from P}}{\text{Distance of A from P}}[/tex]

1). If k = 3

   Therefore, Distance of A' from P = 3(Distance of A from P)

   And point A' will be on the third circle.

2). If k = 2

   Distance of B' from P = 2(Distance of B from P)

   Since, B is on circle 2, B' will be on circle 4.

Now we can plot these points A' and B' on the graph.

After the dilation point A becomes A' and it is at a distance of 3 units from point P and after the dilation point B becomes B' and it is at a distance of 2 units from point P.

1)

Given :

Dilate A using P as the center of dilation and a scale factor of 3.

Let the coordinates of point A be (x,y) then after dilation point A becomes A'(3x , 3y). So, the distance of the point A' from the point P is 3 units

2)

Given :

Dilate Busing P as the center of dilation and a scale factor of 2.

Let the coordinates of point B be (x',y') then after dilation point B becomes B'(2x' , 2y'). So, the distance of the point B' from the point P is 2 units

For more information, refer to the link given below:

https://brainly.com/question/2856466

Answer:

8 pounds

Step-by-step explanation:

Shipping Company A = 14 + 2.25p

Shipping Company B = 20 + 1.50p

Where,

p = the number of pounds.

For what weight is the charge the same for the two companies

Equate the charges of the two companies

14 + 2.25p = 20 + 1.50p

14 - 20 = 1.50p - 2.25p

-6 = -0.75p

Divide both sides by -0.75

p = -6 / -0.75

= 8

p = 8 pounds

Answer:

For statement 1 :

INPUT UNIT OF ITEM : Time of the year on Serengeti Desert

OUTPUT UNIT OF ITEM : Simba washes his clothes

For statement 2

INPUT UNIT OF ITEM : 1 capful of detergent

OUTPUT UNIT OF ITEM : each load of wash

Step-by-step explanation:

For statement 1 :

INPUT UNIT OF ITEM : Time of the year on Serengeti Desert

OUTPUT UNIT OF ITEM : Simba washes his clothes

For statement 2

INPUT UNIT OF ITEM : 1 capful of detergent

OUTPUT UNIT OF ITEM : each load of wash

From answers provided above the basis for the answers is that an input unit of item will have to result to a reaction which is an output unit of item hence the answers above

Answer:

Required equations in standard form are:

1. 3x+4y=12

2. -5x+2y = 10

Step-by-step explanation:

Standard form of equation is given as:

[tex]Ax+By = C[/tex]

1. x – intercept is 4 and y – intercept is 3.

The points will be:

(4,0) and (0,3)

Slope: m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{3-0}{0-4}\\m = -\frac{3}{4}[/tex]

Slope intercept form of line is:

[tex]y = mx+b[/tex]

Putting the values of m and b(y-intercept)

[tex]y = -\frac{3}{4}x+3[/tex]

Multiplying whole equation by 4

[tex]4y = -3x+12\\3x+4y = 12[/tex]

2. x – intercept is -2 and y – intercept is 5

The points will be:

(-2,0) and (0,5)

Now

[tex]m = \frac{5-0}{0+2}\\m = \frac{5}{2}[/tex]

Putting the values of m and b in slope intercept form

[tex]y = \frac{5}{2}x+5[/tex]

Multiplying the equation by 2

[tex]2y = 5x+10[/tex]

[tex]-5x+2y=10[/tex]

Hence,

Required equations in standard form are:

1. 3x+4y=12

2. -5x+2y = 10

Answer:

1,880 people will fit in 94 ft by 50 ft

Step-by-step explanation:

We can estimate this using the area

For 5 ft by 5ft ; 10 people can fit in an area of 5 * 5 = 25 ft^2

In an area of 94 ft by 50 ft, the number of people that can fit will be;

let’s start with the area

Area = 94 * 50 = 4,700 square feet

10 people will fit in 25 square feet

x people in 4,700 square feet

25 * x = 10 * 4700

25x = 47,000

x = 47000/25

x = 1,880 people

Answer:My suggestion is practice what you learned after each class for like 10-20 min and pay close attention in class. Wish you the best of luck.

Step-by-step explanation:

Answer:

niwebfasfbjsdfb

Step-by-step explanation:

jsdfhsdbfjhadsjbdsfhb

Answer:

Scatter plots

Pie graph

graph

in words

Step-by-step explanation:

the regular form of r=8

Answer:

5/2

Step-by-step explanation:

25 and 10 so 25/10 or 5/2 or 2 1/2

Answer:

It's 576 if you mean 64 times 9!

Step-by-step explanation:

Answer:

d=25 or d=2

Step-by-step explanation:

hope that helps!

Answer:

d=2/5 or d=2

Step-by-step explanation:

Step 1: Subtract -6d^2 from both sides.

−d2−12d+4−−6d2=−6d2−−6d2

5d2−12d+4=0

Step 2: Factor left side of equation.

(5d−2)(d−2)=0

Step 3: Set factors equal to 0.

5d−2=0 or d−2=0

d= 2/5 or d=2

Answer:

Ich weiß nicht =13

die Antwort -2 -4 (6p-5)

Step-by-step explanation:

Answer:

0.0425

Step-by-step explanation:

Answer:

0.0425

Step-by-step explanation:

hope this helped ^^