Question 1

To find the width of the rectangle, we divide the area by the length

÷

We use the method of long division to get the answer. The method is shown in the first diagram below

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

×= where

Question 7: (Question is not written well)

×

By performing long division we get an answer with remainder of 248

Question 8:

÷

×

×

Cancelling out we obtain

Question 9:

÷

×

Factorise all the quadratic expression gives

×

Cancelling out and gives a simplest form

Question 10:

Cancelling out the constants of each fraction

Question 11:

Cancelling gives us the simplified form

Question 12:

Factorising the numerator expression

Cancelling out gives the simplified form

Question 13:

Question 14:

Question 15:

Question 16:

Question 17:

Question 18

To find the width of the rectangle, we divide the area by the length

÷

We use the method of long division to get the answer. The method is shown in the first diagram below

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

×= where

Question 7: (Question is not written well)

×

By performing long division we get an answer with remainder of 248

Question 8:

÷

×

×

Cancelling out we obtain

Question 9:

÷

×

Factorise all the quadratic expression gives

×

Cancelling out and gives a simplest form

Question 10:

Cancelling out the constants of each fraction

Question 11:

Cancelling gives us the simplified form

Question 12:

Factorising the numerator expression

Cancelling out gives the simplified form

Question 13:

Question 14:

Question 15:

Question 16:

Question 17:

Question 18

carnival one f(x) = 0.5x - money per ticket

g(x) = 8x - tickets per hour

We replace g(x) with its value (8x).

f(g(x)) = f(8x)

We replace the x in f(x) with 8x.

f(8x) = 0,5 × 8x

f(8x) = 4x

⇒ f(g(x)) = 4x

Correct

a. f(g(x)) = 4x, which represents the money Aurora made in dollars per hour

Step-by-step explanation:

1. 4x⁶ + 6x⁵ + 8x⁴ is your answer, so b.

2. x^2 − 49 is your answer, so b.

3. 2x^2 + 6x-20 is your answer, so a.

4. (f • g)(2) = 12, the distance in miles the bicycle traveled, so b. ( not 100% sure tho)

5. 8x³-34x²+25x-3 is your answer, so c.

6. 30x^2 - 26x -12 is polynomial is the answer, so c.

7. not sure : (

8. not sure: (

9. not sure : (

10. x^2 − 14x + 49 is the answer, so a.

hope this ! : )

1) 10x⁵+38x⁴-23x³-101x²- 96x+50

-x+17

(7x²-x-29)=0

3x³ -13x²-4x + 67=0

3x³ -6x²-11x+19

5x²- 20x

Step-by-step explanation:

Spanish

Agregar los polinomios:

(4x + 9) + (5x - 8) (x2 - 4x + 7) + (2x2 + 6x - 8) (5x3 + 4x2 - 7x -8) + (2x3 - 3x2 + 4x - 3)

Primero multiplicaremos los polinomios con los corchetes

= 4x + 9 + (5x³- 20x² + 35x - 16x² + 32x-56) + (10x⁵ + 8x⁴- 14x³- 16x² + 30x⁴ + 24x³- 42x²- 48x- 40x³- 32x²- 56x + 64) + (2x³- 42x² + 4x -3)

Ahora simplificaremos dentro de los corchetes agregando primero los términos similares

= 4x + 9 + (5x³- 36x² + 67x-56) + (10x⁵ + 38x⁴- 30x³- 90x²-104x + 64) + (2x³- 42x² + 4x-3)

Ahora suma o resta todos los términos similares y distintos

= 10x⁵ + 38x⁴- 30x³ + 5x³ + 2x³- 90x²- 36x²- 42x² + 67x²-104x + 4x + 4x + 64 + 9-3

= 10x⁵ + 38x⁴-23x³-101x²- 96x + 50 Ans

Restando los polinomios

(4x + 9) - (5x - 8) = - x + 17

-5x +8 + 4x + 9 = -x + 17

-x + 17 = -x + 17

(x2 - 4x + 7) - (2x2 + 6x - 8) = -20x2-13x-72

x²-2x²-4x-6x + 7 + 8 = 20x2-13x-72

-x²-10x + 15-20x² + 13x + 72 = 0

-21x² + 3x + 87 = 0

-3 (7x²-x-29) = 0

(7x²-x-29) = 0

(5x3 + 4x2 - 7x -8) - (2x3 - 3x2 + 4x - 3) = 20x2 + 32x-45x-72

5x³-2x³ + 4x² + 3x²-7x-4x-8 + 3 = 20x2 -7x-72

3x³ + 7x²-11x-5-20x² + 7x + 72 = 0

3x³ -13x²-4x + 67 = 0

(7x3 - 10x2 - 11x + 9) - (4x3 - 4x2 - 10)

Los signos negativos cambian cuando restamos

= 3x³ -6x²-11x + 19

Ahora multiplicando

5x (x-4) = 5x²- 20x

English

Adding the polynomials :

(4x + 9) + (5x – 8) (x2 – 4x + 7) + (2x2 + 6x – 8) (5x3 + 4x2 – 7x -8) + (2x3 – 3x2 + 4x – 3)

First we will multiply the polynomials with the brackets

= 4x+9 + ( 5x³- 20x²+ 35x - 16x²+ 32x-56) + (10x⁵ + 8x⁴- 14x³- 16x²+30x⁴+ 24x³- 42x²- 48x- 40x³- 32x²- 56x+ 64) + ( 2x³- 42x²+ 4x-3)

Now we will simplify within the brackets first adding the like terms

= 4x+9 + (5x³- 36x²+67x-56) + (10x⁵ +38x⁴- 30x³- 90x²-104x+64) + ( 2x³- 42x²+ 4x-3)

Now add or subtract all the like and unlike terms

= 10x⁵+38x⁴- 30x³+5x³+2x³- 90x²- 36x²- 42x²+67x²-104x+4x+4x+64+9-3

= 10x⁵+38x⁴-23x³-101x²- 96x+50 Ans

Subtracting the Polynomials

(4x + 9) - (5x – 8)=-x+17

-5x +8 +4x+9 = -x+17

-x+17=-x+17

(x2 – 4x + 7) - (2x2 + 6x – 8)= -20x2-13x-72

x²-2x²-4x-6x+7+8=20x2-13x-72

-x²-10x+ 15-20x²+13x+72=0

-21x²+3x+87=0

-3(7x²-x-29)=0

(7x²-x-29)=0

(5x3 + 4x2 – 7x -8) - (2x3 – 3x2 + 4x – 3)= 20x2 +32x-45x-72

5x³-2x³+4x²+3x²-7x-4x-8+3= 20x2 -7x-72

3x³+7x²-11x-5-20x²+7x+72=0

3x³ -13x²-4x + 67=0

(7x3 – 10x2 – 11x + 9) - (4x3 – 4x2 – 10)

The negative signs are changed when we subtract

= 3x³ -6x²-11x+19

Now Multiplying

5x(x-4) = 5x²- 20x

** CORRECTIONS: Q1: It's 2x^3-29x+12; Q2,3,4,5,6: All conditions have ≠ symbol; Q7: it's (12x^2+32x+16); Q10: Option D should be divided by x^4; **

(1) Given:

Width = W = x+4

Area = A =

Length = L = ?

Since the pool is rectangular in shape:

area = width * length

A = W * L

Substitute:

The long division is attached with the answer (below in the picture). Hence the correct answer is (Option C)

(2) Given expression:

Where x ≠ 6. (Option B)

(3) Given :

Now simplify:

Where x ≠ -1/8 (Option A)

(4) Given:

Simplify:

Where x ≠ -1 (Option A)

(5) Given:

Simplify:

where x≠6 (Option C)

(6) Given:

Simplify:

Where a ≠ 0 (Option C)

(7) Mathematically:

Simplify:

(Option C)

(8) Simplify:

(Option A)

(9) Simplify:

(Option A)

(10) Given:

Simplify:

(Option D)

(11) Given:

Simplify:

(Option C)

(12) Simplify:

(Option A)

(13) Simplify:

(Option A)

(14) Simplify:

(Option B)

(15) Simplify:

(Option D)

(16) Given:

4/x + 5/x = -3

Simplify:

(4+5)/x = -3

-3x = 9

x = -3 (Option C)

(17) Simplify:

(Option D)

(18) Simplify:

(Option C)

(19) Dorothy's rate (alone) will be:

Rosanne's rate (alone) will be:

If both work together, add both the rates:

(in 1/hours)

To find the hours, flip the rate:

hours (Option B)

(20) As pressure (p) is inversely proportional with volume (v):

p = k/v (where k is constant of proportionality)

k = pv

Find constant using initial values:

k = (104)(108)

k = 11232

Now new pressure is:

p = k/v = 11232/432 = 26 Pa (Option A)

(21)

x: 1,3,5,10

y: 4,12,20,40

Direct variation is the value of y increases with x. So,

y = 4x

If x = 1,y=4(1)=4

If x = 3,y=4(3)=12

If x = 5,y=20

If x = 10,y=40 (Option A)

(22)

If x=-16,4(-16) + 64 = 0;denominator will become zero,which means that there will be discontinuity at x = -16. Hence, x=-16 (Option C) should be excluded.

x = -3 or +2

Step-by-step explanation:

Such an equation resolves into two equations. The argument of the absolute value function can be either positive or negative, so there is one equation for each case.

4x +2 = 10

4x = 8 . . . . subtract 2

x = 2 . . . . . divide by 4

4x +2 = -10

4x = -12 . . . subtract 2

x = -3 . . . . . divide by 4

The two solutions are x=-3 and x=2.

Remove the absolute value term. 4x+2=10 solve this, x=2

Set up the negative portion 4x+2= -10 solve this, x= -3

Set up the negative portion 4x+2= -10 solve this, x= -3

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