Answer:
x=4 x=10
Step-by-step explanation:
(x - 6) (x - 8) =8
We need to multiply out the left side
x^2 -8x -6x+48 = 8
x^2 -14x +48 = 8
Subtract 8 from each side
x^2 -14x +48-8 = 8-8
x^2 -14x+40 =0
We need to factor the left side. What two numbers multiply to give 40 and add to give -14
-4*-10 = 40
-4+-10 = -14
(x-4) (x-10) =0
Using the zero product property
x-4=0 x-10 =0
x=4 x=10
Given the figure of a regular pyramid
The base of the pyramid is a hexagon with a side length = 6
The lateral area is 6 times the area of one of the side triangles
So, the side triangle has a base = 6
The height will be:
![\begin{gathered} h^2=6^2+(\frac{\sqrt[]{3}}{2}\cdot6)^2=36+27=63 \\ h=\sqrt[]{63} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%5E2%3D6%5E2%2B%28%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%5Ccdot6%29%5E2%3D36%2B27%3D63%20%5C%5C%20h%3D%5Csqrt%5B%5D%7B63%7D%20%5Cend%7Bgathered%7D)
so, the lateral area =
![6\cdot\frac{1}{2}\cdot6\cdot\sqrt[]{63}=18\sqrt[]{63}](https://tex.z-dn.net/?f=6%5Ccdot%5Cfrac%7B1%7D%7B2%7D%5Ccdot6%5Ccdot%5Csqrt%5B%5D%7B63%7D%3D18%5Csqrt%5B%5D%7B63%7D)
Answer: 14 miles ≤ D ≤ 22 miles.
Step-by-step explanation:
The mean distance traveled per gallon, is 18 miles.
But this can fluctuate, at most, by 4 miles.
Because we have here the "at most", we know that we should use the ≤, ≥ symbols.
Then, if the mean is 18mi, the range of possible distances traveled per gallon is:
(18 miles - 4 miles) ≤ D ≤ (18 miles + 4 miles)
Where D is the distance.
14 miles ≤ D ≤ 22 miles.
So the truck can get between 14 miles and 22 miles per gallon on the highway.
It's a linear function with a slope 0.
It's a horizontal line (look at the picture).
Under ratio and proportion, there are a couple of ways you can use aside from using words to establish the relationship between 2 numbers.
One would be in a fraction form where "3 to 10" can be written as "3/10", or using a colon between the two numbers, where it would be written as "3:10". It is necessary to understand that these forms all mean the same, even if they look really different.
