Answer:
Step-by-step explanation:
I think you meant, "what is the value of h(10)." If that's the case, then
h(10) = 6 - 10 = -4
Answer: 5
Step-by-step explanation:
4x + 10- 25
<span><span>
It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: </span>direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)</span>
Answer:
1. B. x = 11
2. E. ![m\angle BEF=140^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20BEF%3D140%5E%7B%5Ccirc%7D)
3. D. 4.3 in
4. D. 40.8 ft
Step-by-step explanation:
1. By Angle Addition Postulate,
![m\angle KLM=m\angle KLV+m\angle VLM](https://tex.z-dn.net/?f=m%5Cangle%20KLM%3Dm%5Cangle%20KLV%2Bm%5Cangle%20VLM)
Since
![m\angle KLV=34^{\circ}\\ \\m\angle KLM=14x+19\\ \\m\angle VLM=12x+7,](https://tex.z-dn.net/?f=m%5Cangle%20KLV%3D34%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20KLM%3D14x%2B19%5C%5C%20%5C%5Cm%5Cangle%20VLM%3D12x%2B7%2C)
then
![14x+19=34+12x+7\\ \\14x-12x=34+7-19\\ \\2x=22\\ \\x=11](https://tex.z-dn.net/?f=14x%2B19%3D34%2B12x%2B7%5C%5C%20%5C%5C14x-12x%3D34%2B7-19%5C%5C%20%5C%5C2x%3D22%5C%5C%20%5C%5Cx%3D11)
2. By Angle Addition Postulate,
![m\angle FED=m\angle DEB+m\angle BEF](https://tex.z-dn.net/?f=m%5Cangle%20FED%3Dm%5Cangle%20DEB%2Bm%5Cangle%20BEF)
Since
![m\angle FED=14x+8\\ \\m\angle DEB=22^{\circ}\\ \\m\angle BEF=13x-3,](https://tex.z-dn.net/?f=m%5Cangle%20FED%3D14x%2B8%5C%5C%20%5C%5Cm%5Cangle%20DEB%3D22%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20BEF%3D13x-3%2C)
then
![14x+8=22+13x-3\\ \\14x-13x=22-3-8\\ \\x=11](https://tex.z-dn.net/?f=14x%2B8%3D22%2B13x-3%5C%5C%20%5C%5C14x-13x%3D22-3-8%5C%5C%20%5C%5Cx%3D11)
Therefore,
![m\angle BEF=(13\cdot 11-3)^{\circ}=(143-3)^{\circ}=140^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20BEF%3D%2813%5Ccdot%2011-3%29%5E%7B%5Ccirc%7D%3D%28143-3%29%5E%7B%5Ccirc%7D%3D140%5E%7B%5Ccirc%7D)
3. The area of trapezoid is
![A_{trapezoid}=\text{Midsegment}\times \text{Height}](https://tex.z-dn.net/?f=A_%7Btrapezoid%7D%3D%5Ctext%7BMidsegment%7D%5Ctimes%20%5Ctext%7BHeight%7D)
From the diagram,
![\text{Smaller base}=1.2\ in\\ \\\text{Bigger base}=4.2\ in,](https://tex.z-dn.net/?f=%5Ctext%7BSmaller%20base%7D%3D1.2%5C%20in%5C%5C%20%5C%5C%5Ctext%7BBigger%20base%7D%3D4.2%5C%20in%2C)
then
![\text{Midsegment}=\dfrac{1.2+4.2}{2}=2.7\ in](https://tex.z-dn.net/?f=%5Ctext%7BMidsegment%7D%3D%5Cdfrac%7B1.2%2B4.2%7D%7B2%7D%3D2.7%5C%20in)
Since the area of trapezoid is
then
![11.6\ in^2 =2.7\ in\times \text{Height}\\ \\\text{Height}=\dfrac{11.6\ in^2}{2.7\ in}\approx 4.3\ in](https://tex.z-dn.net/?f=11.6%5C%20in%5E2%20%3D2.7%5C%20in%5Ctimes%20%5Ctext%7BHeight%7D%5C%5C%20%5C%5C%5Ctext%7BHeight%7D%3D%5Cdfrac%7B11.6%5C%20in%5E2%7D%7B2.7%5C%20in%7D%5Capprox%204.3%5C%20in)
4. Use formula for the area of the circle to find the radius of the circle:
![A_{circle}=\pi r^2](https://tex.z-dn.net/?f=A_%7Bcircle%7D%3D%5Cpi%20r%5E2)
So,
![132.7=\pi r^2\\ \\r^2=\dfrac{132.7}{\pi}\\ \\r=\sqrt{\dfrac{132.7}{\pi}}\ ft](https://tex.z-dn.net/?f=132.7%3D%5Cpi%20r%5E2%5C%5C%20%5C%5Cr%5E2%3D%5Cdfrac%7B132.7%7D%7B%5Cpi%7D%5C%5C%20%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B132.7%7D%7B%5Cpi%7D%7D%5C%20ft)
Now, find the circumference of the circle:
![C=2\pi r\\ \\C=2\pi \cdot \sqrt{\dfrac{132.7}{\pi}}=2\sqrt{132.7\pi}\approx 40.8\ ft](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r%5C%5C%20%5C%5CC%3D2%5Cpi%20%5Ccdot%20%5Csqrt%7B%5Cdfrac%7B132.7%7D%7B%5Cpi%7D%7D%3D2%5Csqrt%7B132.7%5Cpi%7D%5Capprox%2040.8%5C%20ft)