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dimulka [17.4K]

2 years ago

14

Write an algebraic equation based on the description. Two angles form a linear pair. The measure of one angle is 24° more than t

he measure of the other angle.

1 answer:

IgorC [24]2 years ago

4 0

<h2><u>Answer:-</u></h2>

Given:

Two angles form a linear pair.

It means sum of their measures = 180°.

And,

Measure of one angle is 24° greater than the other.

Let the other angle be x.

→ First angle = (x + 24)

According to the question,

<h3>→ x + x + 24 = 180</h3>

→ 2x = 180 - 24

→ 2x = 156

→ x = 156/2

<h3>→ X = 78°</h3>

<u>There</u><u>fore</u><u>,</u>

1st angle = 78°
2nd angle = 78° + 24° = 102°

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Question:

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Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read.

Answer:

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Step-by-step explanation:

For Jesse:

$Rate = 30\ pages/day$

This implies that Jesse will cover 30y in y days

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$Rate = 35\ pages/day$

This implies that Amir will cover 35x in x days

Because Amir starts a day later,

$y = x + 1$

So, we have the following equations:

$Jesse = 30y$

$Amir= 35x$

$y = x + 1$

To get the number of days when they read the same number of pages, we have:

$Jesse = Amir$

Substitute values for Jesse and Amir

$30y = 35x$

Substitute x + 1 for y

$30(x+1) = 35x$

Open bracket

$30x+30 = 35x$

Collect Like Terms

$30 = 35x-30x$

$30 = 5x$

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$\frac{30}{5} = x$

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Answer:

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Step by Step:

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$y-k = a(x-h)^2$

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Substitute the value of $h, k, x, y$ in equation $(i)$ and find the value of $a.$

$21=a(8-0)^2+35$

$\Rightarrow 21=a\times 8^2+35$

$\Rightarrow 21=64a+35$

$\Rightarrow 64a=21-35$

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$\Rightarrow a=\frac{-14}{65}$

$\Rightarrow a=-0.215$

Hence, the equation of the parabola is:

$y=-0.215x^2+35$

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