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3 years ago

Factor the following expression: 16z+20

Mathematics

2 answers:

ale4655 [162]3 years ago

5 0

Answer:

4(4z + 5)

Step-by-step explanation:

Given

16z + 20 ← factor out 4 from each term

= 4(4z + 5) ← in factored form

Evgen [1.6K]3 years ago

3 0

Answer:

4z + 5

Step-by-step explanation:

16 and 20 are both dividable by 4, so you divide them both by four and then you have your answer

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How to do this problem

Vera_Pavlovna [14]

X(x-1)(x^2+4)=(x^2-x)(x^2+4)=(x^4)+(4x^2)-(x^3)-(4x)=(x^4)-x(x^2+4)+(4x^2)

6 0

3 years ago

Is -8-2(3+2n)+7n equivalent to -30-13n. Explain why or why not.

seropon [69]

No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n

Step-by-step explanation:

Let us revise the operation of the negative and positive numbers

(-) + (-) = (-)
(-) × (-) = (+)
(-) + (+) = the sign of greatest [(-) if the greatest is (-) or (+) if the greatest is (+)]
(-) × (+) = (-)
(-) - (+) = (-)
(+) - (-) = (+)

∵ The expression is -8 - 2(3 + 2n) + 7n

- Simplify it

∵ 2(3 + 2n) = 2(3) + 2(2n) = 6 + 4n

∴ -8 - 2(3 + 2n) + 7n = -8 - (6 + 4n) + 7n

- Multiply the bracket by (-)

∴ -8 - (6 + 4n) + 7n = -8 - 6 - 4n + 7n

- Add the like terms

∴ -8 - (6 + 4n) + 7n = (-8 - 6) - 4n + 7n

∴ -8 - (6 + 4n) + 7n = -14 + 3n

∴ -8 - 2(3 + 2n) + 7n is equivalent to -14 + 3n

∵ -14 + 3n ≠ -30 - 13n

∴ -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n

No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n

Learn more:

You can learn more about the directed numbers in brainly.com/question/10364988

#LearnwithBrainly

8 0

3 years ago

Find the value of Q in the following system so that the solution to the system

lisabon 2012 [21]

Answer:

Step-by-step explanation:

If the solution of the system of equations is {(x, y): x - y = 4} - infinitely many solutions, then this system is consistent and dependent.

x - 3y = 4 <em>multiply both sides by 2</em>

2x - 6y = 8

Therefore Q = -6

8 0

4 years ago

A farmer has a 100 ft by 200 ft rectangular field that he wants to increase by 15.5% by cultivating a strip of uniform width aro

Advocard [28]

Answer:

(a) The strip should be 5ft wide

(b) The strip around the outside field is 10ft wide.

Step-by-step explanation:

Given:

Length of the rectangular field, L= 200 ft

width of the rectangular field, w = 100 ft

Area of the rectangular field, A = 200ft x 100ft = 20000 ft^2

let the width of the strip = x

The strip around the outside field = 2x

If the field is increased by 15.5%

New area of the field = 1.155 x 20000 = 23,100 ft^2

The increase in area of the field = 3,100 ft

3,100 = New area of field - old area of the field

3100 = (200 + 2x)(100 + 2x) - 20000

3100 = 20000 + 400x 200x + 4x^2 - 20000

3100 = 600x + 4x^2

Divide through by 4

775 = 150x + x^2

x^2 + 150x - 775 = 0

Factorize

(x + 155)(x-5) = 0

x = 5 ft

The strip should be 5ft wide.

The strip around the outside field = 2 x 5 ft = 10 ft

Thus, the strip around the outside field is 10ft wide.

3 0

3 years ago

a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is t

frez [133]

Answer:

1.5 seconds

Step-by-step explanation:

Since f(x) represents the distance from the ground to the rock (in feet), we just need to find the values of x for which f(x) = 340. Substituting f(x) = 340 into f(x) = -16x² - 4x + 382 gives us:

340 = -16x² - 4x + 382

0 = -16x² - 4x + 42 (Subtract 340 from both sides)

16x² + 4x - 42 = 0 (Multiply entire equation by -1, "flip" equation)

8x² + 2x - 21 = 0 (Divide entire equation by 2)

(4x + 7)(2x - 3) = 0 (Factor LHS)

4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)

4x = -7 or 2x = 3 (Subtract -7 and add 3 from/to both sides, respectively)

$x = -\frac{7}{4} = -1.75$ or $x =\frac{3}{2} = 1.5$

x = -1.75 is an extraneous solution because in the context of the question, you can't have negative seconds so therefore, the final answer is 1.5 seconds.

Hope this helps!

3 0

3 years ago