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Fed [463]
3 years ago
10

What is the reciprocal of 8 2/3

Mathematics
1 answer:
Paul [167]3 years ago
3 0

8 2/3 = (3 * 8 + 2)/3 = 26/3

reciprocal of 26/3 —> <u>3</u><u>/</u><u>26</u>

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Answer:

(x - 5)(x + 8)

Step-by-step explanation:

Your equation is: x² + 3x - 40

1. Factor the quadratic

(a) Find two numbers that multiply to give -40 and add to give 3.

List the positive factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

One of the numbers must be negative. Start with the numbers near the middle of the list.

By trial and error, you will find that +8 and -5 work:

-5 × 8 = -40 and -5+8 = 3

(b) Rewrite 3x as -5x + 8x

x² - 5x + 8x - 40

(c) Factor the first two and the last two terms

x(x - 5) + 8(x - 5)

(d) Separate the common factor

x² + 3x - 40  = (x - 5)(x + 8)

2. Using Desmos

You can plot the equation with Desmos.

You get a parabola with x-intercepts at x = -8 and x = 5.

These are the solutions to

x + 8 =0 and x - 5 = 0, so

x² + 3x - 40 =  (x+ 8)(x - 5)

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