MATHEMATICS
HIGH SCHOOL

Answer: Remember that

1) For functions and ,

2) For a function and a constant ,

Using these two properties of integrals, and the fact that , we can see that

1) For functions and ,

2) For a function and a constant ,

Using these two properties of integrals, and the fact that , we can see that

MIDDLE SCHOOL

Simplify.

(2x2 - 5x + 3) - (-x2 + 4x - 5)

Answer:

Simplify.

(2x2 - 5x + 3) - (-x2 + 4x - 5)

the answer is -7x +12

Step-by-step explanation:

the question can be solved using BODMAS law

from Simplify.

(2x2 - 5x + 3) - (-x2 + 4x - 5)

opening the bracket

4-5x + 3 + 2x - 4x + 5

collecting the like terms we have;

12-7x

therfore ; -7x + 12

HIGH SCHOOL

Write the expression as the sine, cosine, or tangent of an angle. sin 9x cos x - cos 9x sin x

Answer:

Step-by-step explanation:

Given : Expression

To write : The given expression as the sine, cosine, or tangent of an angle?

Solution :

The given expression is in the form

Using trigonometric identity,

Substituting, A=9x , B=x

Therefore, The given expression is in the sin form sin(8x).

Answer:

sin 8x

Step-by-step explanation:

MIDDLE SCHOOL

First question : Jill and Erika make 4 gallons if lemonade for their lemonade stand. How many quarts will they be able to sell? If they charge $2.50 per quart, how much money will they make if they sell it all?

second question :

Dairon needs 20 pieces of string 7/8 inch in length. He cut a 4 7/8 inch piece of string into pieces that are 7/8 of an inch long each. How many more pieces of string does he need?

40 and 10 plababs plbaba

HIGH SCHOOL

The length of a rectangle is 7 more than its width. The area of the rectangle is 120. Solve for the length and the width.

Length times width times height

L = w + 7

W = w

A = L * W

120 = w(w+7)

120 = w^2 + 7w

Subtract 120 from both sides.

w^2 + 7w - 120 = 0

Factor

(w + 15)(w - 8) = 0

Set each factor equal to zero.

w = -15, w= 8

Cannot be -15 so w = 8

Length = 15

Width = 8

W = w

A = L * W

120 = w(w+7)

120 = w^2 + 7w

Subtract 120 from both sides.

w^2 + 7w - 120 = 0

Factor

(w + 15)(w - 8) = 0

Set each factor equal to zero.

w = -15, w= 8

Cannot be -15 so w = 8

Length = 15

Width = 8