9514 1404 393
Answer:
-101 feet
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relevant relation is ...
Tan = Opposite/Adjacent
Opposite = Adjacent × Tan
height = (0.5 × 5280 ft) × tan(47°) ≈ 2831 ft
__
The usual relation between estimates and errors is ...
error = estimate - actual
Then ...
actual = estimate - error
For the given angle and error, the actual angle is ...
actual angle = 47° -(-1°) = 48°
actual height = (2640 ft)·tan(48°) ≈ 2932 ft
Then the change in the height of the mountain due to the error is ...
2831 ft -2932 ft = -101 ft
The error of -1° in angle estimate creates an error of -101 ft in the height estimate.
Let their ages be m and t, respectively. Currently, m = 4t.
In ten years: t+10 = (1/2)(m+10).
Multiplying both sides by 2, we get 2t + 20 = m + 10. Substituting 4t for m produces
2t + 20 = 4t + 10. Then 10 = 2t, and t=5. Tamanna is currently 5 years old, and her mother is 20.
Answer:
![\huge\boxed{n=8}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bn%3D8%7D)
Step-by-step explanation:
![-\dfrac{3}{4}n=-6\qquad|\text{multiply both sides by (-4)}\\\\(-4\!\!\!\!\diagup)\left(-\dfrac{3}{4\!\!\!\!\diagup}n\right)=(-4)(-6)\\\\3n=24\qquad|\text{divide both sides by 3}\\\\\dfrac{3\!\!\!\!\diagup n}{3\!\!\!\!\diagup}=\dfrac{24\!\!\!\!\!\diagup}{3\!\!\!\!\diagup}\\\\n=8](https://tex.z-dn.net/?f=-%5Cdfrac%7B3%7D%7B4%7Dn%3D-6%5Cqquad%7C%5Ctext%7Bmultiply%20both%20sides%20by%20%28-4%29%7D%5C%5C%5C%5C%28-4%5C%21%5C%21%5C%21%5C%21%5Cdiagup%29%5Cleft%28-%5Cdfrac%7B3%7D%7B4%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7Dn%5Cright%29%3D%28-4%29%28-6%29%5C%5C%5C%5C3n%3D24%5Cqquad%7C%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cdfrac%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%20n%7D%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%3D%5Cdfrac%7B24%5C%21%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%5C%5C%5C%5Cn%3D8)
Answer:
A. -1/5
Step-by-step explanation:
-7-(-5) /5-(-5)
= -7+5 / 5+5
= -2/10
-1/5 option A
Answer:
<FGJ and <IJG
Step-by-step explanation: