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Ne4ueva [31]
3 years ago
14

​If \left| OA\right| =5∣OA∣=5 and \left| OA'\right| =7.5∣OA ′ ∣=7.5, what is the scale factor, rr, of this dilation?

Mathematics
1 answer:
Igoryamba3 years ago
6 0

Answer:

The scale factor is 1.5

Step-by-step explanation:

Given

\left| OA\right| =5

\left| OA'\right| =7.5

Required

Determine the scale factor

The scale factor (k) is calculated using:

k = \frac{\left| OA'\right|}{\left| OA\right|}

Substitute values for OA and OA'

k = \frac{7.5}{5}

k = 1.5

<em>The scale factor is 1.5</em>

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Answer:

4.375 miles

Step-by-step explanation:

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Long Division: (3x^4-8x^3-x^2+9x+5) / (x-2) pleaseee answer this
Drupady [299]

3<em>x</em>⁴ = 3<em>x</em>³ • <em>x</em>, and

3<em>x</em>³ (<em>x</em> - 2) = 3<em>x</em>⁴ - 6<em>x</em>³

Subtract this from the numerator to get a remainder of

(3<em>x</em>⁴ - 8<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) - (3<em>x</em>⁴ - 6<em>x</em>³) = -2<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5

-2<em>x</em>³ = -2<em>x</em>² • <em>x</em>, and

-2<em>x</em>² (<em>x</em> - 2) = -2<em>x</em>³ + 4<em>x</em>²

Subtract this from the previous remainder to get a new remainder of

(-2<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) - (-2<em>x</em>³ + 4<em>x</em>²) = -5<em>x</em>² + 9<em>x</em> + 5

-5<em>x</em>² = -5<em>x</em> • <em>x</em>, and

-5<em>x</em> (<em>x</em> - 2) = -5<em>x</em>² + 10<em>x</em>

Subtract this from the last remainder to get a new one of

(-5<em>x</em>² + 9<em>x</em> + 5) - (-5<em>x</em>² + 10<em>x</em>) = -<em>x</em> + 5

-<em>x</em> = -1 • <em>x</em>, and

-1 (<em>x</em> - 2) = -<em>x</em> + 2

This gives a new remainder of

(-<em>x</em> + 5) - (-<em>x</em> + 2) = 3

3 does not divide <em>x</em>, so we're done.

So, we have

(3<em>x</em>⁴ - 8<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) / (<em>x</em> - 2) = 3<em>x</em>³ - 2<em>x</em>² - 5<em>x</em> - 1 + 3/(<em>x</em> - 2)

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3 years ago
Wahab wants to donate at least $6000 in books and pairs of shoes. Let B represent the number of books and S represent the number
malfutka [58]

Wahab has to donate at least 50 books to reach his goal

<h3><u>Solution:</u></h3>

Given that, Wahab wants to donate at least $6000 in books and pairs of shoes.  

Let "B' represent the number of books

Let "S" represent the number of pairs of shoes that Wahab must donate to achieve his goal.  

20B+50S ≥ 6000 ⇒ this is the inequality for total donation.  

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Now, as he donated 100 pairs of shoes, S = 100, so substitute this in inequality.

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