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Verdich [7]
2 years ago
8

What is an equation of the line that passes through the points (4,4) and (8.1)

Mathematics
1 answer:
andrey2020 [161]2 years ago
5 0

Answer:

  • y = - 3/4x + 7

Step-by-step explanation:

<u>Use both points and find the slope:</u>

  • m = (1 - 4) / (8 - 4) = - 3/4

<u>Find the line, using point-slope form and point (4, 4):</u>

  • y - 4 = - 3/4(x - 4)
  • y - 4 = - 3/4x + 3
  • y = - 3/4x + 7
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A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,corr
lina2011 [118]

Answer:

(a) the new angle the ladder makes with the ground is 32.7^o

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4  \,\,m

Now fro the new position of the bottom of the ladder relative to the wall:

cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

4 0
3 years ago
The diameter of a circle<br> Is 8 inches . What is the area ?
Elena L [17]

Answer:

radius=d/2 = 8/2 = 4inch.

Step-by-step explanation:

area = πr²

16π(inch)². or 352/7 (inch)².

hope this helps you.

8 0
3 years ago
Read 2 more answers
Why is it important to include the units in a rate
bija089 [108]

Answer:

Unit rates are useful because they allow you to make direct comparisons. For example, you have your choice between two bottles of ketchup.

Step-by-step explanation:

7 0
3 years ago
Please help I will mark brainliest!
Ymorist [56]

Answer:

  A

Step-by-step explanation:

You know that the negative number with the largest magnitude is farthest to the left on the number line.

  3/4 = 9/12

  2/3 = 8/12

Then 3/4 > 2/3, so ...

  -3/4 < -2/3

7 0
3 years ago
Please help with a math problem :/ Please show steps...<br><br> x^2 -13x = -36
Marianna [84]
X^2 -  13 x = -36 
add 36 to both sides

x^2 - 13x +36 = 0
figure out the factor
(x-4)(x-9) = 0
so (x-4) or (x-9) equals 0
so solution is
x-4=0 add 4 to both sides and get x = 4
x-9=0 add 9 to both sides and get x=9
x={ 4, 9}
4 0
3 years ago
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