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1 answer:
Answer:
36°
Step-by-step explanation:
Given,
Measurement of <3 = 2x+8
Measurement of <4 = 6x+12
Since both are supplementary,
Therefore,
<3 + <4. = 180° [linear pair]
=> 2x + 8 + 6x + 12 = 180
=> 2x + 6x + 8 + 12 = 180
=> 8x + 20 = 180
=> 8x = 180 - 20 = 160
=> x = 20
Now as we have got the value of x,
According to the question measurement of <4 is,
<4 = 6×4 + 12 = 24 + 12 = <u>36</u><u>°</u><u> (Ans)</u>
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Answer:
Step-by-step explanation:
<u>Step 1:</u>
<em>Equation should be:</em>
<u>Step 2:</u>
<em>Equation should be:</em>
<u>Step 3:</u>
- Factoring
- The first term is
. It's coefficient is 3.
- The middle term is +18x, it's coefficient is 18.
- The last term, "the constant", is -13.
<em>Step 1</em>:
- Multiply the coefficient of the first term by the constant 3 * -13 = -39
<em>Step 2:</em>
- Find two factors of -39 whose sum equals the coefficient of the middle term, which is 18 .
- -39 + 1 = -38
- -13 + 3 = -10
- -3 + 13 = 10
- -1 + 39 = 38
- Observation : No two such factors can be found !!
- Conclusion : Trinomial can not be factored
<u>Solution:</u>
- <u />
.
Answer:
x intercept is (45/2,0)
y intercept is (0,-36)
Step-by-step explanation:
Slope intercept form of equation of line is
y=mx+b where m is the slope and b is the y intercept
use any two points to find the slope
(10,20) (15,12)
m = -8/5
now we find out b using (10,20)
20 = -16 + b
add 16 on both sides , so b = 36
b is the y intercept , so y intercept is (0,-36)
Now we find x intercept
equation of line is y=mx+b that is
To find x intercept plug in 0 for y
subtract 36 on both sides
Multiply by -5/8 on both sides
x intercept is (45/2,0)
Law of Sines can help with this problem. Law of Sines can help find a missing angle or side if given two sides with respective opposite angles or two angles with respective sides. The formula for Law of Sines is sin(A)/a = sin(B)/b. A and B are the angles and a and b are the sides opposite the angles. Hopefully, the picture above helps you visualize everything.
Anyways, we know two sides and one angle, so Law of Sines is possible to use. The side opposite the right angle is 11. So, we have sin(90)/11. The other angle, we're looking for but we do know the side. The side opposite of angle M is 5. So, we have sin(M)/5. The Law of Sines formula tells us that Sin(A)/a = Sin(B)/b = Sin(C)/c but we don't need all the angles but just angle M. So we're going to just use Sin(A)/a = Sin(B)/b. We have already set up the equations so plug them in.
Sin(90)/11 = Sin(M)/5. Cross multiplication will get 5 × Sin(90) = Sin(M) × 11.
Sin(90) = 1. So, we get 1 × 5 and get after simplifying, 5 = Sin(M) × 11. We divide both sides by 11 to get Sin(M) by itself.
5/11 = Sin(M). Now we run into a problem. How do we get the angle M? We do the inverse sin or sin^-1 key if you're using a calculator. So, (5/11)sin^-1 = M. Our final answer is angle M = 27.03569... Hope this helped!
Side Notes: Make sure if you're using a calculator that you're in degrees and NOT radians unless the question calls for radians. Also, if you wanted to find all the angles of the triangle then once you find M, you could add that to the 90 degree angle and then subtract that from 180. You will find the other angle since you know two of them and there are only three of them that have to add to 180 degrees. I just like triangles, ;-) Good luck!
Anyways, we know two sides and one angle, so Law of Sines is possible to use. The side opposite the right angle is 11. So, we have sin(90)/11. The other angle, we're looking for but we do know the side. The side opposite of angle M is 5. So, we have sin(M)/5. The Law of Sines formula tells us that Sin(A)/a = Sin(B)/b = Sin(C)/c but we don't need all the angles but just angle M. So we're going to just use Sin(A)/a = Sin(B)/b. We have already set up the equations so plug them in.
Sin(90)/11 = Sin(M)/5. Cross multiplication will get 5 × Sin(90) = Sin(M) × 11.
Sin(90) = 1. So, we get 1 × 5 and get after simplifying, 5 = Sin(M) × 11. We divide both sides by 11 to get Sin(M) by itself.
5/11 = Sin(M). Now we run into a problem. How do we get the angle M? We do the inverse sin or sin^-1 key if you're using a calculator. So, (5/11)sin^-1 = M. Our final answer is angle M = 27.03569... Hope this helped!
Side Notes: Make sure if you're using a calculator that you're in degrees and NOT radians unless the question calls for radians. Also, if you wanted to find all the angles of the triangle then once you find M, you could add that to the 90 degree angle and then subtract that from 180. You will find the other angle since you know two of them and there are only three of them that have to add to 180 degrees. I just like triangles, ;-) Good luck!