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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:

Hi there,

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Read 2 more answers
An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length
shutvik [7]

Options A,B and D. The correction about the area of the triangle are

  • The apothem can be found using the Pythagorean theorem.
  • The apothem can be found using the tangent ratio.
  • The length of the apothem is approximately 2.5 cm.

<h3>How to solve for the length of the Apothem using the Pythagoras theorem</h3>

Firstly this is an equilateral triangle

3 of the sides have the length of 8.7cm

b = half of 8.7

= 4.35cm

To get A we have

a² + b² = c²

a² + 4.35² = 5²

When we solve this out we would have

a² = 25 - 18.9225

a ≈ 2.5 cm.

Hence we have proved that the first option is correct.

<u>For B,</u>

In an equilateral triangles, each of the angles = 60 degrees

60/2 = 30 is the angle that is made from the base

<h3>using tangent ratios </h3>

a / 4.35 = tan 30

then a = 4.35 tan 30

This would also give us an approximate of 2.5

For D

The calculations we have done based on the statements in A and B shows that D is correct as 2.5.

Read more on triangles here:

brainly.com/question/18404158

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