19) In the xy-plane, what is the y-intercept of the graph of the equation y=3(x-1)(x+2)?

Mathematics

1 answer:

Dahasolnce [82]4 years ago

3 0

Answer:

- 6

Step-by-step explanation:

Given

y = 3(x - 1)(x + 2) ← expand factors using FOIL

= 3(x² + x - 2) ← distribute by 3

= 3x² + 3x - 6

To find the y- intercept let x = 0, thus

y = 3(0)² + 3(0) - 6 = 0 + 0 - 6 = - 6

Thus y- intercept = - 6 ⇒ (0, - 6 )

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So,

Let x represent Joe's weight and y represent Jeff's weight.

"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20

"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
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We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250

Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250

We will use Elimination by Substitution.
2y - 20 + y + 10 = 250

Collect Like Terms.
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Add 10 to both sides.
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Divide both sides by 3.
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Substitute again.
$x = 2(86 \frac{2}{3} )-20$

Multiply.
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Subtract.
$Joe's\ weight = 153 \frac{1}{3}\ lbs.$

Check.

"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.

"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.

$Joe's\ weight\ is\ 153 \frac{1}{3} \ lbs.$
$Jeff's\ weight\ is\ 86 \frac{2}{3} \ lbs.$

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