Answer:
D
Step-by-step explanation:
take a calculator and try a few points.
I used x = 10.3 and x = 22.
and only D is really getting close to 0.4 and 3.5 as functional results.
Answer: (564)
Step-by-step explanation:
6 x 94
= 6(90 + 4)
= 6 x 90 + 6 x 4
= 564
9514 1404 393
Answer:
3.08 hours
Step-by-step explanation:
We assume you're interested in the time in hours.
![175\text{ mi}\times\dfrac{12\text{ s}}{1000\text{ ft}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}\times\dfrac{1\text{ h}}{3600\text{ s}}=\dfrac{175\times12\times5280}{1000\times3600}\text{ h}=\boxed{3.08\text{ h}}](https://tex.z-dn.net/?f=175%5Ctext%7B%20mi%7D%5Ctimes%5Cdfrac%7B12%5Ctext%7B%20s%7D%7D%7B1000%5Ctext%7B%20ft%7D%7D%5Ctimes%5Cdfrac%7B5280%5Ctext%7B%20ft%7D%7D%7B1%5Ctext%7B%20mi%7D%7D%5Ctimes%5Cdfrac%7B1%5Ctext%7B%20h%7D%7D%7B3600%5Ctext%7B%20s%7D%7D%3D%5Cdfrac%7B175%5Ctimes12%5Ctimes5280%7D%7B1000%5Ctimes3600%7D%5Ctext%7B%20h%7D%3D%5Cboxed%7B3.08%5Ctext%7B%20h%7D%7D)
It will take 3.08 hours to travel 175 miles at that speed.
Answer:
0.4069 ; 1.843
Step-by-step explanation:
Given:
Base of parallelogram, b = (2x - 1)
Height = (4x - 7)
Area = 1
Area of parallelogram = Base * height
Area of parallelogram = (2x - 1) * (4x - 7)
(2x - 1) * (4x - 7) = 1
8x² - 14x - 4x + 7 = 1
8x² - 18x + 7 - 1 = 0
8x² - 18x + 6 = 0
Divide through by 2
4x² - 9x + 3 = 0
Solving the quadratic equation :
Using the formula
-b ± √(b² - 4ac) / 2a
a = 4 ; b = - 9 ; c = 3
Plugging in the values :
-(-9) ± √((-9)² - 4(4)(3)) / 2(4)
9 ± √(81 - 48) / 8
9 ± √33 / 8
(9 ± 5.7445626) / 8
(9 - 5.7445626) / 8) = 0.4069
(9 + 5.7445626) / 8 = 1.843
Answer:
![21^{\circ}](https://tex.z-dn.net/?f=21%5E%7B%5Ccirc%7D)
Step-by-step explanation:
The Law of Sines is given by
and works for every triangle.
Substituting given values, we have the following equation:
![\frac{\sin 68^{\circ}}{18}=\frac{\sin C}{7}, \\\\\sin C=\frac{7\sin 68^{\circ}}{18},\\\\C=\sin^{-1}(0.36057149899),\\\\C\approx \boxed{21^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%2068%5E%7B%5Ccirc%7D%7D%7B18%7D%3D%5Cfrac%7B%5Csin%20C%7D%7B7%7D%2C%20%5C%5C%5C%5C%5Csin%20C%3D%5Cfrac%7B7%5Csin%2068%5E%7B%5Ccirc%7D%7D%7B18%7D%2C%5C%5C%5C%5CC%3D%5Csin%5E%7B-1%7D%280.36057149899%29%2C%5C%5C%5C%5CC%5Capprox%20%5Cboxed%7B21%5E%7B%5Ccirc%7D%7D)
*Note that because
, when solving for an angle with the Law of Sines, there may be two answers. However, since the problem designates angle C as an acute angle, the other angle is negligible.