Answer:
x =(-4-√96)/10=(-2-2√ 6 )/5= -1.380
x =(-4+√96)/10=(-2+2√ 6 )/5= 0.580
Step-by-step explanation:
1) subtract the accepted value from the experimental value.
2) Take the absolute value ofvstep 1
3) Divide the answer by accepted value
4) Maltiply that answer by 100 and add the % symbol to express the answer as a percentage.
Answer:
∠ZB = 54°
Step-by-step explanation:
Given:
Pair of complementary angles
∠ZA = (2x + 10)° and m
∠ZB = (3x + 15)
Find:
Measure of ∠ZB
Computation:
complementary angles
a + b = 90°
∠ZA + ∠ZB = 90°
(2x + 10) + (3x + 15) = 90
5x + 25 = 90
x = 13
So,
∠ZB = (3x + 15)
∠ZB = 13(3) + 15
∠ZB = 54°
Answer:
b=2.5
Step-by-step explanation:
The given line has equation: ![y=b-x](https://tex.z-dn.net/?f=y%3Db-x)
The x-intercept is (b,0)
The y-intercept is (0,b)
The area of triangle QOP ![=\frac{1}{2} |OQ|*|OP|=](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%20%7COQ%7C%2A%7COP%7C%3D)
![=\frac{1}{2}b*b](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7Db%2Ab)
![=\frac{1}{2}b^2](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7Db%5E2)
The area of triangle QRS ![=\frac{1}{2} |RQ|*|RS|=](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%20%7CRQ%7C%2A%7CRS%7C%3D)
![=\frac{1}{2}(4-b)*(b-4)](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%284-b%29%2A%28b-4%29)
The area of triangle QRS and QOP are in the ratio 9:25
We must negate the area under the x-axis.
![\implies \frac{- \frac{1}{2}(4-b)(b-4)}{\frac{1}{2}b^2} =\frac{9}{25}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7B-%20%5Cfrac%7B1%7D%7B2%7D%284-b%29%28b-4%29%7D%7B%5Cfrac%7B1%7D%7B2%7Db%5E2%7D%20%3D%5Cfrac%7B9%7D%7B25%7D)
![\implies \frac{-(4-b)(b-4)}{b^2} =\frac{9}{25}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7B-%284-b%29%28b-4%29%7D%7Bb%5E2%7D%20%3D%5Cfrac%7B9%7D%7B25%7D)
![\implies {-(4-b)(b-4) =\frac{9}{25}b^2](https://tex.z-dn.net/?f=%5Cimplies%20%7B-%284-b%29%28b-4%29%20%3D%5Cfrac%7B9%7D%7B25%7Db%5E2)
![\implies b^2-8b+16=\frac{9}{25}b^2](https://tex.z-dn.net/?f=%5Cimplies%20b%5E2-8b%2B16%3D%5Cfrac%7B9%7D%7B25%7Db%5E2)
![\implies 25b^2-200b+400=9b^2](https://tex.z-dn.net/?f=%5Cimplies%2025b%5E2-200b%2B400%3D9b%5E2)
![\implies 25b^2-9b^2-200b+400=0](https://tex.z-dn.net/?f=%5Cimplies%2025b%5E2-9b%5E2-200b%2B400%3D0)
![\implies 16b^2-200b+400=0](https://tex.z-dn.net/?f=%5Cimplies%2016b%5E2-200b%2B400%3D0)
![\implies 2b^2-25b+50=0](https://tex.z-dn.net/?f=%5Cimplies%202b%5E2-25b%2B50%3D0)
![(2b-5)(b-10)=0](https://tex.z-dn.net/?f=%282b-5%29%28b-10%29%3D0)
![b=2.5\:or\:b=10](https://tex.z-dn.net/?f=b%3D2.5%5C%3Aor%5C%3Ab%3D10)
But 0<b<4
Therefore b=2.5
VERIFY
The area of triangle QOP
![=\frac{1}{2}*2.5*2.5=3.125](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%2A2.5%2A2.5%3D3.125)
The area of triangle QRS
![=|\frac{1}{2}(4-2.5)*(2.5-4)|=|-1.125|=1.125](https://tex.z-dn.net/?f=%3D%7C%5Cfrac%7B1%7D%7B2%7D%284-2.5%29%2A%282.5-4%29%7C%3D%7C-1.125%7C%3D1.125)
We must take absolute value because this area is below the x-axis.
![\frac{1.125}{3.125} =\frac{9}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B1.125%7D%7B3.125%7D%20%3D%5Cfrac%7B9%7D%7B25%7D)
Answer: 0.45 :)
Step-by-step explanation:
divide y by x