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4 years ago

Prove that Two lines are parallel if and only if they have the same slope

Mathematics

1 answer:

Gennadij [26K]4 years ago

8 0

Given line q and line r, with equations

y = m x + b1 y = m x + b2

such that these are different lines, with identical slopes. Prove that line q || line r.

If these lines are parallel, then they will not intersect. Assume the lines intersect. Calculate the point of intersection. Since these equations already have the same slope, we may as well subtract one equation from the other one.

This gives us the following equation:

0 = b1 - b2 b1 = b2

If b1 = b2, then line q is the same line as line r. This contradicts the given conditions.

Therefore, line q and line r cannot intersect. If line q and line r do not intersect, they must be parallel.

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How to solve math problem 1 + 3n - 8n =1

katovenus [111]

The answer is 0 bcuz it will be 5n=0

Give me a thanks if it helps!!

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3 years ago

1. Find the volume for 5 different spheres by randomly choosing different radii.

Sophie [7]

The volume of the sphere is given by :

V= $\frac{4}{3}\pi r^{3}$

And volume of cylinder is given as :

V= $\pi r^{2}h$

So, as given to select the radius randomly and the height of the cylinder will be the diameter of the sphere.

The radius are = 3, 5, 8, 10, 12

And height will be = 6, 10, 16, 20, 24

1. Volume of sphere with radius 3 = $\frac{4}{3}*3.14*3*3*3= 113.04$ units

Volume of cylinder with radius 3 and height 6 = $3.14*3*3*6=169.56$ units

2. volume of sphere with radius 5 = 523.60 units

volume of cylinder with height 10 = 785.40 units

3. volume of sphere with radius 8 = 2144.66 units

volume of cylinder with height 16 = 3216.99 units

4. volume of sphere with radius 10 = 4188.79 units

volume of cylinder with height 20 = 6283.19 units

5. volume of sphere with radius 12 = 7238.23 units

volume of cylinder with height 24 = 10857.34 units

3 0

3 years ago

Which equation can be used to find the answer? Camilla needs $65 for a pair of hiking shoes. She already has $19 saved. How much

r-ruslan [8.4K]

The answer is a. n+19=65 n=46 $46. To find out how much more she needs to save, you would add that amount with 19 to get a total of 65. So your equation would be n+19=65. Then once you have your equation, solve it. Subtract 19 from both sides to get n by itself.
n+19=65
-19 -19
n=46
So your answer for how much more she needs to save is $46.

4 0

4 years ago

Suppose a figure is located in Quadrant I. Which of the following sequences will result in an image that is located in Quadrant

vladimir2022 [97]

The answer that results in an image located in Quadrant II is C. rotate 90 degrees counterclockwise, then shift 1 unit up. This is because Quadrant II is located next (at the left) of Quadrant I. This means that a 90 degree rotation and a shift up are safe enough to estimate it to land on Quadrant II.

4 0

3 years ago

Round each number to the nearest thousand.

Gemiola [76]

472000 + 178000 = 650000


650000 is your answer


hope this helps

8 0

3 years ago