7(x+6)
Distributive Property
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Answer:

[tex]f(x) = 3^x[/tex] --- Function A

[tex]f(x) = x^2 - 5[/tex] --- Function B

[tex]f(x) = 18x -6[/tex] --- Function C

Step-by-step explanation:

Solving (a): Equation of Function A

An exponential equation is represented as:

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

From the graph of function A,

[tex]x = 0\ when\ y = 1[/tex]

[tex]x = 1\ when\ y = 3[/tex]

For: [tex]x = 0\ when\ y = 1[/tex]

[tex]y = ab^x[/tex] becomes

[tex]1 = ab^0[/tex]

[tex]1 = a[/tex]

[tex]a =1[/tex]

For: [tex]x = 1\ when\ y = 3[/tex]

[tex]y = ab^x[/tex] becomes

[tex]3 = a*b^1[/tex]

[tex]3 = a*b[/tex]

Substitute 1 for a

[tex]3 = 1*b[/tex]

[tex]3 = b[/tex]

[tex]b = 3[/tex]

[tex]y = ab^x[/tex] becomes

[tex]y = 1*3^x[/tex]

[tex]y = 3^x[/tex]

Replace y with f(x)

[tex]f(x) = 3^x[/tex]

Solving (b): Equation of Function B

A quadratic equation is represented as:

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

From the table of function B,

[tex]x = 3\ when\ y =4[/tex]

[tex]x = 5\ when\ y =20[/tex]

[tex]x = 6\ when\ y =31[/tex]

For: [tex]x = 3\ when\ y =4[/tex]

[tex]y = ax^2 + bx + c[/tex] becomes

[tex]4 = a*3^2 + b*3 + c[/tex]

[tex]4 = a*9 + 3b + c[/tex]

[tex]4 = 9a + 3b + c[/tex]

For [tex]x = 5\ when\ y =20[/tex]

[tex]y = ax^2 + bx + c[/tex] becomes

[tex]20 = a*5^2 + b*5 + c[/tex]

[tex]20 = a*25 + b*5 + c[/tex]

[tex]20 = 25a + 5b + c[/tex]

For [tex]x = 6\ when\ y =31[/tex]

[tex]y = ax^2 + bx + c[/tex] becomes

[tex]31 = a*6^2 + b*6 + c[/tex]

[tex]31 = a*36 + b*6 + c[/tex]

[tex]31 = 36a + 6b + c[/tex]

So, we solve for a, b and c in:

[tex]4 = 9a + 3b + c[/tex]

[tex]20 = 25a + 5b + c[/tex]

[tex]31 = 36a + 6b + c[/tex]

Make c the subject in [tex]4 = 9a + 3b + c[/tex]

[tex]c = 4 - 9a - 3b[/tex]

Substitute [tex]c = 4 - 9a - 3b[/tex] in [tex]20 = 25a + 5b + c[/tex] and [tex]31 = 36a + 6b + c[/tex]

[tex]20 = 25a + 5b + c[/tex] becomes

[tex]20 = 25a + 5b + 4-9a-3b[/tex]

Collect Like Terms

[tex]-4+20 = 25a -9a+ 5b -3b[/tex]

[tex]16 = 16a+ 2b[/tex]

Divide through by 2

[tex]8 = 8a + b[/tex]

[tex]c = 4 - 9a - 3b[/tex]

[tex]31 = 36a + 6b + c[/tex] becomes

[tex]31 = 36a + 6b + 4 - 9a - 3b[/tex]

Collect Like Terms

[tex]-4+31 = 36a - 9a+ 6b - 3b[/tex]

[tex]27 = 27a+ 3b[/tex]

Divide through by 3

[tex]9 = 9a + b[/tex]

Solve for a and b in: [tex]8 = 8a + b[/tex] and [tex]9 = 9a + b[/tex]

Subtract both equations:

[tex]8 - 9 = 8a - 9a + b - b[/tex]

[tex]8 - 9 = 8a - 9a[/tex]

[tex]-1 = -a[/tex]

Divide both sides by -1

[tex]1 = a[/tex]

[tex]a = 1[/tex]

Substitute 1 for a in [tex]9 = 9a + b[/tex]

[tex]9 = 9*1 + b[/tex]

[tex]9 = 9 +b[/tex]

Subtract 9 from both sides

[tex]9-9=9-9+b[/tex]

[tex]0=b[/tex]

[tex]b = 0[/tex]

Substitute [tex]b = 0[/tex] and [tex]a = 1[/tex] in [tex]c = 4 - 9a - 3b[/tex]

[tex]c = 4 - 9*1-3*0[/tex]

[tex]c = 4 - 9-0[/tex]

[tex]c = -5[/tex]

So, the equation is:

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

[tex]y=1*x^2 +0*x-5[/tex]

[tex]y=x^2 -5[/tex]

Replace y with f(x)

[tex]f(x) = x^2 - 5[/tex]

Solving (c): Equation of Function C

This is calculated using:

[tex]f(x) =a + (x -1)d[/tex]

Where

[tex]a = 12[/tex] -- the first term

d = the difference between successive terms

[tex]d = 30 -12 = 48-30 = 66 -48[/tex]

[tex]d =18[/tex]

So, we have:

[tex]f(x) =a + (x -1)d[/tex]

[tex]f(x) = 12 + (x - 1)*18[/tex]

Open bracket

[tex]f(x) = 12 + 18x - 18[/tex]

Collect Like Terms

[tex]f(x) = 18x - 18+12[/tex]

[tex]f(x) = 18x -6[/tex]

Answer:

W

Step-by-step explanation:

quadrant 4 is the bottom right one

W: 4;5

V: 4;2

Y: -1;2

X: -5;-1

Answer:

351 Students

Step-by-step explanation:

First Find 57% of 817

817 x .57 = 465.69

Then subract that from how many students attend the school now(817)

817- 465.69= 351. 31

Answer = 351 Students

Answer:

i dont see a x-

Step-by-step explanation:

Step-by-step explanation:

Answer: -40

Step-by-step explanation:

1/26

Because there are 26 letter in the Alphabet

Answer: 1/26

Step-by-step explanation:

Answer:

Step-by-step explanation:

The above list is for the figures numbered 1-3 (left to right) on the top row, and 4-5 (left to right) on the bottom row.

__

"Alternate" angles are on opposite sides of the transversal. If the angles are between the parallel lines, they are "interior" (fig 4). If they are outside the parallel lines, they are "exterior" (fig 1).

"Corresponding" angles are found in the same direction from the point of intersection. Upper-left corresponding angles are seen in fig. 3; lower-right corresponding angles are seen in fig. 5.

The angles marked in figure 2 are "consecutive exterior" angles, also called "same-side exterior" angles. The applicable descriptive choice in this problem is "none of these".

Answer:

Hello

Step-by-step explanation:

Answer:

1,728 yd²

Step-by-step explanation:

Area = b × h

36 yd will be the replacement for b

48 yd will be the replacement for h

Now we multiply 36 by 48

36 × 48 = 1,728 yd²

Answer:

1728

Step-by-step explanation:

Answer:

35 squared plus x squared equals 78 Squared

which makes your answer

69.7

Step-by-step explanation:

Answer:

35 square + x square 78 square

= 69.7

Step-by-step explanation:

Answer:

23/6

Step-by-step explanation:

3/56

Based on the model, we find the dimensions of the cube. The length of the model building is 2/3 centimeter. The width of the model building is 1/3 centimeter. The height of the model building is 1/2 centimeter. The volume of the model building is 1/9 cubic centimeter.

A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices in geometry. Each face of a cube is a square. In 3 – dimension, the cube’s sides are; the length, width, and height. Sides of a cube are all equal i.e. Length = Width = Height = a.

The length = breadth = height (of one cube) = 1/6 cm

The length of the model consist of 4 cubes.

Length of model building = 4 * 1/6 cm = 2/3 cm

The width of the model consist of 2 cubes.

Width of model building = 2 * 1/6 cm = 1/3 cm

The height of the model consist of 3 cubes.

Height of model building = 3 * 1/6 cm = 1/2 cm

Volume of the model (cuboid) =

= Length * breadth * height

= [tex]\frac{2}{3} * \frac{1}{3}*\frac{1}{2} = \frac{1}{9}[/tex]

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Answer:

x+40 or 40+x

Step-by-step explanation:

It doesn't tell you the amount of money she's saved before so you make it a variable. I used x.

After mowing she got $40 and decided to add that to her savings.

You already know her savings before, x, and now you have $40.

So you end up writing the expression x+40 or 40+x.

Answer:

-x

Step-by-step explanation:

From the values in the statistical data we have;

The possible given data in question, are as follows;

[tex]\begin{array}{cccc}1\frac{3}{4} &2\frac{1}{2} &2&2\frac{3}{4} \\\\1&1\frac{3}{4} &1\frac{1}{4} &3\\\\3\frac{1}{4} &3\frac{3}{4} &2&2\end{array}\right][/tex]

From the data, we have;

The most amount of time spent = [tex]3\frac{3}{4}[/tex]

The least amount of time spent = 1

Therefore;

The most amount of time is [tex]3\frac{3}{4} \times 1[/tex] = [tex]3\frac{3}{4}[/tex] times the least amount of time

Second part;

The number of students that spent less than [tex]2\frac{1}{2}[/tex] = 7

The number of students that spent [tex]2\frac{1}{2}[/tex] or more = 5

The number of students in the survey = 12

Therefore, more than half the students spent less than [tex]\mathbf{2\frac{1}{2}}[/tex] hours on homework

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Answer:

9 hours with no stops

Step-by-step explanation:

540 mile drive  

60 MPH

distance divided by rate is 540 divided by 60 = 9

Answer:

Rip i saw you said times up :/

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

there are data values from 17-26

so D

Answer:

1 - 155 +27n

2- 2x+15=33

Step-by-step explanation:

hope this helps

Answer:

I'm sorry but I was doing it in my notebook and no and it came out a proper answer and well I'm not going to answer something that this bad I don't like to look bad the truth I thought was going to be easier but I couldn't do it I hope that another volunteer arrives and helps you and give you a better answer I will tell you what was my answer I think is not going to be bad 45.90

Step-by-step explanation:

Look up "Everything You Need To Know About Math In One Big Fat Notebook pdf." It's the best thing I've ever been given, I have it with me in math class all the time and I've aced every test. I have it with me right now and it has everything I've ever been taught about math in it so it might help you.

Answer:

C

Step-by-step explanation: