Answer:
Step-by-step explanation:
height of pyramid = √(10²-(5/2)²) = √93.75
volume of pyramid = ⅓b²h = ⅓·5²√93.75 ≅ 80.69 in³
lateral area = 2×5×10 = 100 in²
base area = 5² = 25 in²
surface area = 100+25 = 125 in²
Step-by-step explanation:
<h2>
Sum of two complementary angle is 90°</h2><h2 /><h2>
so. </h2><h2>
<R+<S =90°</h2><h2>
12x-3+7x-2=90°</h2><h2>
19x-5=90°</h2><h2>
19x=95°</h2><h2>
X= 5</h2>
<h2>
<R= 60-3=57°</h2>
Answer:
The transformed points of the triangle ABC are
,
, ![C'(x,y) = \left(\frac{1}{2}, \frac{9}{2}\right)](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B9%7D%7B2%7D%5Cright%29)
Step-by-step explanation:
The new points after applying the scale factor are, respectively:
![A' (x,y) = \frac{1}{2}\cdot (1,1)](https://tex.z-dn.net/?f=A%27%20%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%281%2C1%29)
![A' (x,y) = \left( \frac{1}{2}, \frac{1}{2}\right)](https://tex.z-dn.net/?f=A%27%20%28x%2Cy%29%20%3D%20%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B1%7D%7B2%7D%5Cright%29)
![B' (x,y) = \frac{1}{2}\cdot (9,1)](https://tex.z-dn.net/?f=B%27%20%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%289%2C1%29)
![B'(x,y) = \left(\frac{9}{2}, \frac{1}{2} \right)](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%5Cleft%28%5Cfrac%7B9%7D%7B2%7D%2C%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29)
![C'(x,y) = \frac{1}{2}\cdot (1,9)](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%281%2C9%29)
![C'(x,y) = \left(\frac{1}{2}, \frac{9}{2}\right)](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B9%7D%7B2%7D%5Cright%29)
![\dfrac{b^{-1}}{ca^{-1}-ac^{-1}}=\dfrac{\frac1b}{\frac ca-\frac ac}](https://tex.z-dn.net/?f=%5Cdfrac%7Bb%5E%7B-1%7D%7D%7Bca%5E%7B-1%7D-ac%5E%7B-1%7D%7D%3D%5Cdfrac%7B%5Cfrac1b%7D%7B%5Cfrac%20ca-%5Cfrac%20ac%7D)
Multiply the numerator and denominator by
:
![\dfrac{\frac1b}{\frac ca-\frac ac}\cdot\dfrac{ac}{ac}=\dfrac{\frac{ac}b}{c-a}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac1b%7D%7B%5Cfrac%20ca-%5Cfrac%20ac%7D%5Ccdot%5Cdfrac%7Bac%7D%7Bac%7D%3D%5Cdfrac%7B%5Cfrac%7Bac%7Db%7D%7Bc-a%7D)
Since
, we have
. So substituting the values of <em>a</em>, <em>b</em>, and <em>c</em> gives us
![\dfrac{\frac{ac}b}{c-a}=\dfrac{3\cdot5\cdot4}{5-3}=\dfrac{60}2=\boxed{30}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7Bac%7Db%7D%7Bc-a%7D%3D%5Cdfrac%7B3%5Ccdot5%5Ccdot4%7D%7B5-3%7D%3D%5Cdfrac%7B60%7D2%3D%5Cboxed%7B30%7D)