Can someone plz help me I’m being timed!!!

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:

400 + 8m

Step-by-step explanation:

Starts with $400 in her account. Every day (we'll use the variable m for the number of days), she deposits $8.

400 + 8m

If you were to be asked how much money she has in her bank account after 10 days, you plug in 10 for m. Same for any other number of days.

difference is 33

Step-by-step explanation:

100 - 40% = 60 + 7% = 67 + 300 = 367

400 - 367  = 33

Answer: I might well as think the answer is 10.220

Answer: the length is 64

Step-by-step explanation: 2880 divided by 45 is 64

Answer:

64

Step-by-step explanation:

64

Answer:

1/18

Step-by-step explanation:

(1/6)/(3/1)

flip the 3 and the one and multiply

=(1/6)(1/3)

1(1)=1

6(3)=18

Answer:

1.11     2.40

Step-by-step explanation:

Answer:

1-  around 11

(Thats all i could answer)

Step-by-step explanation:

Subtract 406-278= 128 ÷ 12= approximately 11

Answer:

it should be 2.28

Step-by-step explanation:

srry if wrong

Answer:

A

Step-by-step explanation:

it's absolute value so it should be A

I can't see the picture, can you please explain the problem in the comment bar below this so can edit my answer to help?

Answer:

138 divited by 12. Then 11.50 X 5= 57.50

Step-by-step explanation:

Answer:

$88,000

Step-by-step explanation:

40,000*.12= 4,800

4,800*10= 48,000

40,000+48,000= 88,000

Answer:

5,491

step-step explanation:

multiply 646x8.5

Answer:

1 cm = 76 meters

Step-by-step explanation:

[tex]\frac{646m}{8.5cm} =\frac{x}{1cm}[/tex]

Find x.

x = 76m

1cm = 76meters

good luck, i hope this helps :)

Answer:

D

Step-by-step explanation:

there are data values from 17-26

so D

Answer:

2 times

Step-by-step explanation:

0.35×10×10=35

hope i am right?

Answer:

quadrant 3

Step-by-step explanation:

Cuz x and y are in the negative if they’re both less than 0

Answer:

Step-by-step explanation:

"<" means that it is less than "__" . X < 0 means the X value would be a negative . Y < 0 also means the same . This shows that the value of both X and Y are negatives . So the only place they belong is Quadrant 3 .

Answer:12/5 is correct.

Step-by-step explanation:

2 5ths is 10, add 2 it's 12. sorry for the bad explanation lol, btw nice pfp

Answer:

Step-by-step explanation:

Answer:

If you wash eight your friend would’ve washed 12 2:3 as 8:12

Step-by-step explanation:

The height of Miguel as an adult is 1.785 m.

The height of Ramona as an adult is 1.712 m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The adult height of a male is about 1.19 times his height at age 12.

The adult height of a female is about 1.07 times her height at age 12.

Now,

Miguel:

Height at the age of 12 = 1.5 m

The height when he is an adult.

= 1.19 x 1.5

= 1.785 m

Ramona:

Height at the age of 12 = 1.6 m

The height when she is an adult.

= 1.07 x 1.6

= 1.712 m

Thus,

The height of Miguel and Ramona as adults are 1.785 m and 1.712 m.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

Pheonix Lights, MIddle 3 for the 2nd question.

Step-by-step explanation:

Answer:

Step-by-step explanation:To answer your question, the first number 9/8 has the reciprocal 8/9.