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kati45 [8]
3 years ago
8

Find the equation of the line that is perpendicular to the line 4x+2y=1 and passes through the point (-4,3)

Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

First find the slope of the given line:

4x +2y = 1

Subtract 4x from each side:

2y = -4x + 1

Divide both sides by 2:

y = -2x +1/2

The slope is -2.

Now use the slope to find the y-intercept. Because  the line is perpendicular, you need to use the negative inverse of the slope.

The negative inverse of -2 is 1/2

Now using the point-slope form y - y1 = m(x-x1)

Use the inverse slope for m, and the given point(-4,3) to get:

y - 3 = 1/2(x+4)

Simplify:

y - 3 = x/2 +2

Add 3 to each side:

y = x/2 + 5

Reorder the terms to get y = 1/2x +5

The answer is D.

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A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off t
nexus9112 [7]
This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon. 

Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s: 

2.6s + 7.3

Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:

1.5s + 12.4

To determine when both balloons are at the same height, we set the two equations equal to each other: 

2.6s + 7.3 = 1.5s + 12.4

Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation: 

1.1s + 7.3 = 12.4

Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation: 

1.1s = 5.1

Last, we divide both sides by 1.1. So s = 4.63. 

This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation: 

2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33

1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33

After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
6 0
3 years ago
20. what us the area of the figure:
Varvara68 [4.7K]
If the angle in B is 45º, that means the angle in A is also going to be 45º, considering it's a right triangle, so AC and BC are they have the same length.
Then using Pythagoras, you'll get that AC^{2} + BC^{2} equals AB^{2} .
Now, you know that AC=BC and that AB=24.
So you'll get 2AC^{2} =24^2 . You do the square root in both sides and you get that 2AC=24 and AC=12.

Now that you know that both AC and BC equal 12, you can find the area by just multiplying them and then diving them by 2. (The formula for the area of a triangle is half base multiplied by height, and in a right triangle, if a cathetus is the base, the other cathetus<span> will be the height)

And so the area is equal to 72.</span>
8 0
3 years ago
P(a b)=0.25 and P(b)=0.4, what is P(aub)?
irina [24]
Well Those are variables and it is using the Distributive property to solve. For example P(a+b) simplify P*a + P*b. 
5 0
3 years ago
Read 2 more answers
50 POINTS!! HELP!
Minchanka [31]

i dont have time to do all of it (sorry)

but this is how you do the point and slope questions:

use the equation: y-y1 = m(x - x1)

y1 is the y point you are given

x1 is the x point you are given

m is your slope

substitute all of those in from the question

the first one is:

y --4 = -5/6(x-8)

-- turns into a plus so the answer would be

y+4 = -5/6(x-8)

6 0
3 years ago
When 15 is subtracted from 3 times a number the result is -32. what is the number?
Vilka [71]

Answer:

15.6

Step-by-step explanation:

15+32=47

47/3=15.6

since the - is there

it will be -15.6

5 0
3 years ago
Read 2 more answers
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