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Ugo [173]
3 years ago
14

О с. А о.

Mathematics
2 answers:
timurjin [86]3 years ago
7 0

Answer:

Step-by-step explanation:

To be parallel the slopes must be equal

4x-3y=15

3y=4x-15

y=(4x-15)/3

so m=4/3

Only line D. has a slope of 4/3

mylen [45]3 years ago
5 0

Answer:

D. <em>y</em> = (⁴/₃)<em>x</em> – 1

Step-by-step explanation:

To find the answer to this problem, we need to find the <em>slope</em> of 4<em>x</em> – 3<em>y</em> = 15 . Why? A line that is <em>parallel</em> to another line has the same slope as the other line.

The question gives the line in <em>standard form</em>, but all the options are in <em>slope-intercept form</em>. In addition, <em>standard form</em> is the only type of linear equation that does not explicitly give the slope. The slope is the change in the dependent variable, <em>y</em>, over the change in the independent variable, <em>x</em>. This means we need to solve the equation for <em>y</em> and so:

4<em>x</em> – 3<em>y</em> = 15  — original equation

4<em>x</em> – 3<em>y – </em>4<em>x</em> = 15 – 4<em>x</em>  — subtracting 4<em>x</em> on each side to isolate 3<em>y</em> and reverse the addition of 4<em>x</em>

–3<em>y</em> = 15 – 4<em>x</em>  — simplifying; the 4<em>x</em> on the left cancels out

–3<em>y</em> ÷ –3 = (15 – 4<em>x</em>) ÷ –3  — dividing both sides by –3 to isolate <em>y</em>

–3<em>y</em> ÷ –3 = (15 ÷ –3) + (–4<em>x</em> ÷ –3)  — distributing the division by –3 on the right side to make it easier to understand

<em>y</em> = (⁴/₃)<em>x</em> – 5  — simplifying; this is our expression for y, and it gives us the slope

Now, which line has a slope of ⁴/₃? That would be Option D, <em>y</em> = (⁴/₃)<em>x</em> – 1, so that's our answer.

Of course, you could have just found two points on the graph and then used <em>point-slope form</em> to solve for the slope, but that takes more time…

I hope this makes it easier to understand the concept! Have a great day!

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Step-by-step explanation:

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th
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\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}

Step-by-step explanation:

The <u>width</u> of a square is its <u>side length</u>.

The <u>width</u> of a circle is its <u>diameter</u>.

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So the ratio of the area of the circle to the original square is:

\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}

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\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)

Ratio of circle to square:

\implies \dfrac{28}{36}=\dfrac{7}{9}

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