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2 years ago

Please factor completely: 20x^2 - 102x + 54

Mathematics

1 answer:

Temka [501]2 years ago

5 0

Answer:

The answer to your question is 2(x - 9/2)(x - 3/5)

Step-by-step explanation:

Polynomial 20x² - 102x + 54

Process

1.- Find the Greatest Common Factor

20 102 54 2

10 51 27 2

5 51 27 3

5 17 9 3

5 17 3 3

5 17 1 5

1 17 17

GCF = 2

2.- Factor 2

2(10x² - 51x + 27)

3.- Factor 10x² - 51x + 27

Use the general formula to solve this equation

x = $\frac{-b +- \sqrt{b^{2} - 4ac}}{2a}$

a = 10 b = -51 c = 27

x = $\frac{51 +- \sqrt{51^{2} -4(10)(27)}}{2(10)}$

-Simplification

x = $\frac{51 +- 39}{20}$

-Result

x₁ = 9/2 x₂ = 3/5

(x - 9/2) (x - 3/5)

4.- Answer

2(x - 9/2)(x - 3/5)

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The expression that can be used to determine how fast an elephant runs in miles per hour is 100 miles per hour

Solution:

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2 years ago

Four times the sum of a number and 15 is at least 120. Find all possible solutions for x

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First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.

"Four times..." means we're multiplying something by 4.

"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.

"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.

So, the resulting inequality is 4(x + 15) ≤ 120.

Simplify the inequality.

4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4

Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.

In interval notation it would look something like this:

[15, ∞)

In set builder notation it would look something like this:

{x | x ∈ R, x ≤ 15}

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Answer:

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