Step-by-step explanation:
this problem seeks to test our knowledge on word problems and algebra
<u>Solution</u>
let the base be x, and
the height h = 2x+4
We know that area of a triangle is given as
![A= \frac{1}{2} b*h](https://tex.z-dn.net/?f=A%3D%20%5Cfrac%7B1%7D%7B2%7D%20b%2Ah)
substituting our given values we have
![168= \frac{1}{2} x*(2x+4)\\\\168= \frac{2x^2+4x}{2} \\\\168= x^2+2x\\\\](https://tex.z-dn.net/?f=168%3D%20%5Cfrac%7B1%7D%7B2%7D%20x%2A%282x%2B4%29%5C%5C%5C%5C168%3D%20%5Cfrac%7B2x%5E2%2B4x%7D%7B2%7D%20%5C%5C%5C%5C168%3D%20x%5E2%2B2x%5C%5C%5C%5C)
re-arranging we have
![x^2+2x-168=0\\\\](https://tex.z-dn.net/?f=x%5E2%2B2x-168%3D0%5C%5C%5C%5C)
we can now find two factors that will add up to give 2 and multiply to give -168
they are 14 and -12
The possible base of the triangle is 14 in
and the height is
![h= 2x+4\\\\h=2(14)+4\\\\h= 28+4\\\\\h= 32 in](https://tex.z-dn.net/?f=h%3D%202x%2B4%5C%5C%5C%5Ch%3D2%2814%29%2B4%5C%5C%5C%5Ch%3D%2028%2B4%5C%5C%5C%5C%5Ch%3D%2032%20in)
Answer:
Explanation:
The time to cross the finish line may be found using the speed vs. time equation:
From which you can solve for time:
Using the last equation, you can find the difference in the times for Malcolm and Joshua, but, since the speed must be expressed in miles per minutes, and the given data are minutes per mile, first you must convert the data.
Miles per minute is the inverse of minutes per mile, so the corresponding speeds are:
- Malcolm's speed: 1 / (6 min/mile) = (1/6) miles/min
- Joshua's speed: 1 / (8 min/mile) = (1/8) miles/min
- Time for Malcom: 10 miles / [ 1/ (6 miles/min) ] = 10/(1/6) min = 60 min
- Time for Joshua: 10 miles / [ 1/ ( 8 miles/min) ] = 10/(1/8) min = 80 min
- Difference in times: 80 min - 60 min = 20 min
Hence, Joshua will cross the finish line 20 minutes after Malcolm crosses the finish line.
You can not solve this because the values are different... If the values were both Px and Px or Qx and Qx you will be able to solve the problem but you can not according to the fact that they aren't the same letters. So therefore, this equation has no solution.
Hope this helped!!!
Answer:
X=22° ; Exterior Angle = 125°
Step-by-step explanation:
The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
(2x) + (103 - x) = (6x - 7)
103 + 7 = 6x - 2x + x
110 = 5x -->(Divided by 5)--> x=22°
6(22) - 7 = 125°
9514 1404 393
Answer:
$6.80/fortnight
Step-by-step explanation:
You need to know there are 13 weeks in a quarter, and 2 weeks in a fortnight. The conversion is straightforward.
![\dfrac{\$44.20}{\text{quarter}}\times\dfrac{1\text{ quarter}}{13\text{ weeks}}\times\dfrac{2\text{ weeks}}{1\text{ fortnight}}=\dfrac{\$44.20\times2}{13\text{ fortnight}}\\\\=\boxed{\$6.80\text{/fortnight}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5C%2444.20%7D%7B%5Ctext%7Bquarter%7D%7D%5Ctimes%5Cdfrac%7B1%5Ctext%7B%20quarter%7D%7D%7B13%5Ctext%7B%20weeks%7D%7D%5Ctimes%5Cdfrac%7B2%5Ctext%7B%20weeks%7D%7D%7B1%5Ctext%7B%20fortnight%7D%7D%3D%5Cdfrac%7B%5C%2444.20%5Ctimes2%7D%7B13%5Ctext%7B%20fortnight%7D%7D%5C%5C%5C%5C%3D%5Cboxed%7B%5C%246.80%5Ctext%7B%2Ffortnight%7D%7D)