Answer:
40
- 147x - 216
Step-by-step explanation:
(5x - 24) (8x + 9)
First start with multiplying 5x to 8x and 9
40
+45x
then multiply -24 by 8x and 9
-192 x -216
40
+45x
-192 x -216
+
________________
40
- 147x - 216
It's D, $49.00/wk for x weeks is 49x, plus $18.00 bonus is 49x+18, add the fact that Mini worked for y weeks, 49y.
Read it slowly and out loud till you get it.
The word POWER has 5 different letters ( n = 5 ):
P ( n ) = n !
P ( 5 ) = 5 ! = 5 * 4 * 3 * 2 * 1 = 120
Answer:
A ) 120
![\lim_{x \to \pi /4} \frac{tan x - 1}{x- \pi /4} = \frac{0}{0}](https://tex.z-dn.net/?f=%20%5Clim_%7Bx%20%5Cto%20%20%5Cpi%20%2F4%7D%20%20%5Cfrac%7Btan%20x%20-%201%7D%7Bx-%20%5Cpi%20%2F4%7D%20%20%3D%20%20%5Cfrac%7B0%7D%7B0%7D%20)
With L` Hospital`s Rule ( ( tan x ) ` = 1/ cos^2 x ) :
![\lim_{x \to \pi /4} \frac{1}{cos ^{2} x} = \\ = \frac{1}{cos ^{2} ( \pi /4)} = \\ \frac{1}{1/2}](https://tex.z-dn.net/?f=%20%5Clim_%7Bx%20%5Cto%20%20%5Cpi%20%2F4%7D%20%20%5Cfrac%7B1%7D%7Bcos%20%5E%7B2%7D%20x%7D%20%3D%20%20%5C%5C%20%3D%20%5Cfrac%7B1%7D%7Bcos%20%5E%7B2%7D%20%28%20%5Cpi%20%2F4%29%7D%20%20%3D%20%5C%5C%20%20%5Cfrac%7B1%7D%7B1%2F2%7D%20%20)
=
2
Answer: The answer is 381.85 feet.
Step-by-step explanation: Given that a window is 20 feet above the ground. From there, the angle of elevation to the top of a building across the street is 78°, and the angle of depression to the base of the same building is 15°. We are to calculate the height of the building across the street.
This situation is framed very nicely in the attached figure, where
BG = 20 feet, ∠AWB = 78°, ∠WAB = WBG = 15° and AH = height of the bulding across the street = ?
From the right-angled triangle WGB, we have
![\dfrac{WG}{WB}=\tan 15^\circ\\\\\\\Rightarrow \dfrac{20}{b}=\tan 15^\circ\\\\\\\Rightarrow b=\dfrac{20}{\tan 15^\circ},](https://tex.z-dn.net/?f=%5Cdfrac%7BWG%7D%7BWB%7D%3D%5Ctan%2015%5E%5Ccirc%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B20%7D%7Bb%7D%3D%5Ctan%2015%5E%5Ccirc%5C%5C%5C%5C%5C%5C%5CRightarrow%20b%3D%5Cdfrac%7B20%7D%7B%5Ctan%2015%5E%5Ccirc%7D%2C)
and from the right-angled triangle WAB, we have'
![\dfrac{AB}{WB}=\tan 78^\circ\\\\\\\Rightarrow \dfrac{h}{b}=\tan 15^\circ\\\\\\\Rightarrow h=\tan 78^\circ\times\dfrac{20}{\tan 15^\circ}\\\\\\\Rightarrow h=361.85.](https://tex.z-dn.net/?f=%5Cdfrac%7BAB%7D%7BWB%7D%3D%5Ctan%2078%5E%5Ccirc%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7Bh%7D%7Bb%7D%3D%5Ctan%2015%5E%5Ccirc%5C%5C%5C%5C%5C%5C%5CRightarrow%20h%3D%5Ctan%2078%5E%5Ccirc%5Ctimes%5Cdfrac%7B20%7D%7B%5Ctan%2015%5E%5Ccirc%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20h%3D361.85.)
Therefore, AH = AB + BH = h + GB = 361.85+20 = 381.85 feet.
Thus, the height of the building across the street is 381.85 feet.