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nadezda [96]
3 years ago
13

Find the solutions to the equation below. check all that apply

Mathematics
1 answer:
BartSMP [9]3 years ago
6 0

Answer:

A and E

Step-by-step explanation:

Given

20x² - 26x + 8 = 0 ( divide through by 2 )

10x² - 13x + 4 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 10 × 4 = 40 and sum = - 13

The factors are - 5 and - 8

Use these factors to split the x- term

10x² - 5x - 8x + 4 = 0 ( factor the first/second and third/fourth terms )

5x(2x - 1) - 4(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(5x - 4) = 0

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = \frac{1}{2} → E

5x - 4 = 0 ⇒ 5x = 4 ⇒ x = \frac{4}{5} → A

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The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the
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Answer:

The first number is 16

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Step-by-step explanation:

The information from the word problem are;

The count of the numbers in the sum = 3 numbers

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The value of the third number = 4 × The value of the first number

The value of the first number = 10 + The value of the second

Let 'x' represent the first number, let 'y' represent the second number and let 'z' represent the third number, we have;

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x = y + 10...(3)

From equation (3), we get;

x = y + 10

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Substituting the value of <em>z</em> from equation (2) and the value of <em>y</em> from equation (4) in equation (1) gives;

x + y + z = 86

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y = x - 10

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