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Gnesinka [82]
10 months ago
12

Which line is parallel to the line shown below?

Mathematics
1 answer:
Travka [436]10 months ago
4 0
<h3>Answer:  Choice D</h3>

4x - 3y = 15

====================================================

Explanation:

The two points (-1,-1) and (2,3) are marked on the line

Let's find the slope of the line through those two points.

(x_1,y_1) = (-1,-1) \text{ and } (x_2,y_2)  = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - (-1)}{2 - (-1)}\\\\m = \frac{3 + 1}{2 + 1}\\\\m = \frac{4}{3}\\\\

The slope is 4/3 meaning we go up 4 and to the right 3.

-------------

Parallel lines have equal slopes, but different y intercepts. We'll need to see which of the four answer choices have a slope of 4/3.

Solve the equation in choice A for y. The goal is to get it into y = mx+b form so we can determine the slope m.

3x + 4y = -4\\\\4y = -3x-4\\\\y = -\frac{3}{4}x-\frac{4}{4}\\\\y = -\frac{3}{4}x-1

Equation A has a slope of -3/4 and not 4/3 like we want.

Therefore, this answer choice is crossed off the list.

Follow similar steps for choices B through D. I'll show the slopes of each so you can check your work.

  • slope of equation B is 3/4
  • slope of equation C is -4/3
  • slope of equation D is 4/3

We have a match with equation D. Therefore, the equation 4x-3y = 15 is parallel to the given line shown in the graph.

You can use graphing tools like Desmos or GeoGebra to confirm the answer.

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3 years ago
A41.0m guy wire is attached to the top of a 32.8 m antenna and to a point on the ground. How far is the point on the ground from
Setler79 [48]

Answer:

Step-by-step explanation:

A right angle triangle is formed.

The length of the guy wire represents the hypotenuse of the right angle triangle.

The height of the antenna represents the opposite side of the right angle triangle.

The distance, h from base of the antenna to the point on the ground to which the antenna is attached represents the adjacent side of the triangle.

To determine h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

41² = 32.8² + h²

1681 = 1075.84 + h²

h² = 1681 - 1075.84 = 605.16

h = √605.16

h = 24.6 m

To determine the angle θ that the wire makes with the ground, we would apply the the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos θ = 24.6/41 = 0.6

θ = Cos^-1(0.6)

θ = 53.1°

7 0
3 years ago
How can the decimal 0.57 be written as a fraction
Akimi4 [234]
If you want to convert 0.57 into a fraction, you can do it like this:
<span>
<span>0.57 equals to 57/100 </span></span><span>(you can't do anything else because 57 and 100 don't have common factors).

</span><span><span /><span>The result is 57/100.</span>
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3 years ago
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4 0
3 years ago
Choose any method to find the gcf of 40 16 and 24
Juli2301 [7.4K]

The GCF of 40 16 and 24 is 8

<h3>How to determine the GCF of 40 16 and 24?</h3>

The numbers are given as:

40 16 and 24

Start by listing out the factors of the numbers:

This is done as follows:

  • The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
  • The factors of 16 are: 1, 2, 4, 8, 16
  • The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Then the greatest common factor in the above list is 8.

Hence, the GCF of 40 16 and 24 is 8

Read more about GCF at:

brainly.com/question/219464

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8 0
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