MATHEMATICS
HIGH SCHOOL

Answer:

Answer:

$57.62

Step-by-step explanation:

$53.98 x 6.75% = $3.64

$53.98 + $3.64 = $57.62

MIDDLE SCHOOL

Function f is represented by the equation given below. Function g has a vertex at (2,4) and the parabola opens downwards.

Which of the following statements is true? f(x)=x^2-5x+6

A.

The minimum of function f is at (-5,6).

B.

The minimum of function g is at (2,4).

C.

The y-intercept of function f is less than the y-intercept of function g.

D.

The y-intercept of function f is greater than the y-intercept of function g.

Answer:

Step-by-step explanation:

Unfortunately, you have not shared function g(x). But I can focus on questions involving function f(x) alone:

A: We can find the x-coordinate of the minimum of f by calculating x = -b/(2a). Here that comes out to x = 5/2*1) = 5/2. This does not agree with A. A is FALSE.

B: Function g(x) unknown; cannot answer this.

C: The y-intercept of function f(x) is 6. That of g(x) is unknown.

D: The y-intercept of function f(x) is 6. That of g(x) is unknown

HIGH SCHOOL

A video game sets the points needed to reach the next level based on the function g(x) = 12(2)x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 3x. How many points will a player need on the hardest setting of level 6?

g(x) = 12(2)x - 1

h(x) = 3x

We are looking for this :

g(6) * h(6) ....so we have....

12(2)6-1 * 36 =

12(2)5 * 729 =

12*32 * 729 = 279,936 points

MIDDLE SCHOOL

Dominic uses 1/2 tablespoon of almond butter to make a sandwich. He needs to make 5 sandwiches. How many tablespoons of almond butter does he need to make the sandwiches?

2 and a half tablespoons of almond butter

HIGH SCHOOL

Your gross pay is $2,759.00. Your involuntary deductions are FICA (7.65%), federal withholding (12%), and state withholding (7%). How much are you allowed for housing and fixed expenses?

Answer:

$2,023.73

Step-by-step explanation:

First step

Add up all tax percentage

7.65

12

7

26.65% total tax deductions

Second Step

Find total taxes

Gross Pay $2,759 × 26.65% or .2665=$735.27 total taxes

Third Step

Find net pay (gross pay minus taxes)

Gross Pay $2,759 - $735.21=$2,023.73 the amount left to spend on housing and fixed expenses.

MIDDLE SCHOOL

Consider the following pair of equations: y = 3x + 3

y = x − 1

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Y = 3x + 3 this is equation 1

y = x -1 this is equation 2

since equation 1 and 2 already defined y in terms of x, we're just gonna substitute y into the other equation. as 2 is shorter I'm going with that today

x - 1 = 3x +3

-1 - 3 = 3x - x

-4 = 2x

x = -2

now we've got x just sub it in equation 2

y = -2 -1

y = -3

so the answer is (-2,-3)

y = x -1 this is equation 2

since equation 1 and 2 already defined y in terms of x, we're just gonna substitute y into the other equation. as 2 is shorter I'm going with that today

x - 1 = 3x +3

-1 - 3 = 3x - x

-4 = 2x

x = -2

now we've got x just sub it in equation 2

y = -2 -1

y = -3

so the answer is (-2,-3)

MIDDLE SCHOOL

Which ordered pair is a solution to the linear inequality? y - 4 x ≤ - 6

A. (-2, 4)

B. (1, -2)

C. (1, 3)

D. (2, 3)

Thank you everyone!

Answer:

b

Step-by-step explanation:

HIGH SCHOOL

Lukas graphed the system of equations shown. 2x + 3y = 2 y = x + 3 What is the solution to the system of equations?

Rewrite the first equation to be in y=... form:

2x+3y=2

3y = 2-2x

y = (2-2x)/3

Now you can equate it to the second (the y drops out):

(2-2x)/3 = x+3

2/3 - 2/3x = x + 3

-5/3x = 7/3

x = - 7/5

so y = x+3 = -7/5 + 3 = 8/5

The intercept is at (-7/5, 8/5)

2x+3y=2

3y = 2-2x

y = (2-2x)/3

Now you can equate it to the second (the y drops out):

(2-2x)/3 = x+3

2/3 - 2/3x = x + 3

-5/3x = 7/3

x = - 7/5

so y = x+3 = -7/5 + 3 = 8/5

The intercept is at (-7/5, 8/5)

Answer: its (-2,2)

yeah its (-2,2)

MIDDLE SCHOOL

Given the functions below, find f(x) · g(x)

f(x) = 2x + 5

g(x) = x2 – 3x + 1

Answer: 2x3 - x2 -13x + 5

Step-by-step explanation:

(2x2 + 5) (x2 -3x + 1)

(2x3 - 6x2 + 2x + 5x2 -15x +5)

= 2x3 - x2 - 13x + 5

HIGH SCHOOL

The cool company determines that the supply function for its basic air-conditioning unit is S(p) = 10 + 0.002p^3 and that its demand function is D(p) = 50 - 0.04p^2 , where P is the price. Determine the price for which the supply equals the demand.

D(p) = 50 - 0.04p^S(p) = 10 + 0