MATHEMATICS HIGH SCHOOL

1. Which of the following is the factored form of the expression: 3x2 – 4x? A. x(3x - 4)
B. x(3 – 4x)
C. (3x -1) (x -1)
D. (3x +1)(x -1)

2. Which is a completely factored form of the expression: x2 + 21x +20 ?

A. (x + 5)(x + 4)
B. (x + 10)(x + 2)
C. (x + 20)(x + 1)
D. (x + 21)(x - 1)

3. Which expression is factored form of 4x2 -9?

A. 2(x - 3)2
B. (x - 3)2
C. 2(x + 3)(x - 3)
D. (2x + 3)(2x - 3)

4. Below are factored forms of the expression: 12x3 – 36x2 . Which expression has the greatest common factor as the first term?

A. 3x (4x2 – 12x)
B. 4x2(3x -9
C. 12x2(x – 3)
D. 12x(x2 - 3x)
5. Adele’s lawn has an area of (x2 -5x -6) square feet and a length of (x + 1) feet. What is the width of the lawn in feet?

A. (x -6)
B. (x +6)
C. (x2 -4x -5)
D. (x2 -6x -7)

6. The expression below represents the area, in square meters, of a rectangle:
X2 + 5x -24
Which of the following pairs of expressions could represent the length and width, in meters, of the rectangle?

A. (x – 3) and (x + 8)
B. (x – 4) and (x + 6)
C. (x – 6) and (x + 4)
D. (x – 8) and (x + 3)

7. What is the complete factorization of 32 – 8z2?

A. -8(2 + z)(2 –z)
B. 8(2 + z)(2 – z)
C. -8(2 + z)2
D. 8(2 – z)2

8. What is the greatest common factor of: 12x2 , 24x2y2 , and 46xy?

A. 4x
B. 3x
C. 6x
D. 2x
9. Which expression is equivalent to: 2x2 -3x -35?

A. (2x + 7)(x - 5)
B. (2x - 7) (x + 5)
C. (2x - 5)(x + 7)
D. (2x + 5)(x - 7)

10. What are the factors of 81x2 + 36x + 4?

A. (9x + 2)(x +2)
B. (9x +2)(9x +2)
C. (9x -2)(9x -2)
D. (9x +2)(9x -2)

11. The top of a rectangular table has an area of: 18x2+ 69x +60.
The width of the table is 3x + 4. What is the length of the table?
(Show proof by multiplying – show your work)

12. Simplify: (x2 +2x)(5x -3)
A. 11x2 -3
B. 6x3 -6x
C. 5x3 + 7x2 – 6x
D. 5x3 – 13x2 -6x

13. Factor by grouping: 30g5 +24g3h – 35g2h2 - 28h3 Show your work!

14. Which is the correct way to factor the polynomial : x2 -16?

A. (x -4)(x -4)
B. (x -4)(x +4)
C. (x +4)(x -2)(x +2)
D. Not factorable

15. The area of a square painting is: 81p2 + 90p +25. What is the length of one side? Prove by multiplication – show your work.

Answers

Answer 1

Answer:

1. $3x^2-4x=x(3x-4)$ - A.

2. $x^2 + 21x +20=(x-x_1)(x-x_2)$

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ √(D)=19,\n \nx_1=(-21-19)/(2)=-20, \ x_2=(-21+19)/(2)=-1$ ,

then

$x^2 + 21x +20=(x+20)(x+1)$ - C.

3. $4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3)$ - D.

4. $12x^3-36x^2=12x^2(x-3)$ - C.

5. $x^2 -5x -6=(x-x_1)(x-x_2)$

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ √(D)=7,\n \nx_1=(5-7)/(2)=-1, \ x_2=(5+7)/(2)=6$ ,

then

$x^2 -5x -6=(x-6)(x+1)$ and the width of the lawn is x-6 - A.

6. Since $x^2 + 5x -24=(x+8)(x-3)$ the length and width are x+8 and x-3 - A.

7. $32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z)$ - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \n24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \n 46xy=2\cdot 23\cdot x\cdot y$ .

So the greatest common divisor is $2\cdot x=2x$ - D.

9. $2x^2 -3x -35=2(x-x_1)(x-x_2)$

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ √(D)=17,\n \nx_1=(3-17)/(2\cdot 2)=-(7)/(2), \ x_2=(3+17)/(2\cdot 2)=5$ ,

then

$2x^2 -3x -35=2(x+(7)/(2))(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+(5)/(2))(x+(4)/(3))=(6x+15)(3x+4)$ , the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. $30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2)$ .

14. $x^2 -16=(x-4)(x+4)$ - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$ , the length of one side is 9p+5.

Answer 2

Answer:

Answer:

yes that is right

Step-by-step explanation:

usa test prep

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You are working in a hospital supply room and make $13.65 an hour. The union negotiates a new contract giving each employee a 4.3% cost of living raise. What is your new hourly rate?

Answers

The new hourly rate will be $14.196 per hour.

What is a mathematical function, equation and expression?

function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

equation : A mathematical equation is used to equate two expressions.

Given is that you are working in a hospital supply room and make $13.65 an hour. The union negotiates a new contract giving each employee a 4.3% cost of living raise

Assume that the new hourly rate be $[x]. Then, we can write -

[x] = 13.65 + {4% pf 13.65}

[x] = 13.65 + {4/100 x 13.65}

[x] = 13.65 + 0.546

[x] = 14.196

Therefore, the new hourly rate will be $14.196 per hour.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

Find the amount of the raise by multiplying 13.65 x 4.3%...

13.65 x .043 = .58695

Round to the nearest cent

.59

So the raise is .59 (59 cents)

Add it to the original salary

13.65 + .59 = 14.24

New hourly wage... $14.24

What percent of 200 is 6?

Answers

Answer=3%

6 x
____=____
200 100

cross multiply
200x=600
divide both sides by 200
x=3

3% because 1% is 2, 2x3 equals 6《 i messed up on this im just fixing it》

What is the perimeter of a triangle that has two sides measuring 7 centimeters and a third side measuring 9 centimeters?

Answers

The answer is 23cm just add the sides

The perimeter is the sum of all of the lengths of the sides. To find the perimeter, add together the length of each side.

For this triangle, our side lengths are 7, 7, and 9.

7 + 7 = 14

14 + 9 = 23

The perimeter of a triangle that has two sides measuring 7 centimeters and a third side measuring 9 centimeters is 23 centimeters.

Hope this helps!! :)

Apple + Orange = $20Apple is twice the price of the orange
How much does the apple cost?

Answers

It costs 40 dollars bcz twhce the number of 20 is 40 its like multiple by 2

Two urns each contain green balls and blue balls. Urn I contains 4 green balls and 6 blue balls, and Urn II contains 6 green balls and 2 blue balls. A ball is drawn at random from each urn. What is the probability that both balls are blue?A. 2/51
B. 3/20
C.1/10
D.4/153

Answers

b- 3/20. first, add up the number of balls in each urn.
urn 1- 10
urn 2- 8
then, make a fraction where the numerator is the number of blue balls in the urn and the denominator is the total number of balls
urn 1- 6/10 (simplified to 3/5)
urn 2- 2/8 (simplified to 1/4)
finally, multiply your two probabilities and simplify
1/4*3/5=3/20

What is the volume of the a cube with a side of length 11 unitsA. 33 units
B. 121 units
C. 1331 units
D. 14641 units

Answers

The volume of a cube is

(length of a side) x (length of a side) x (length of a side)

usually written as (length of a side)³ or (length of a side) cubed.

If the length of a side is 11 units, then the volume is

(11 units) x (11 units) x (11 units) = 1,331 units-cubed.

None of the choices on the list is correct. The nearest one is 'C'.
It has the correct number but the wrong units.

Volume of a cube is
Volume=length×width×height

Substitute in the value
Volume=11×11×11

Volume=1331

The answer to your question is C. The volume of a cube with a side length 11 is 1331.

I hope this has helped.

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