Answer:
Given: A triangle ABC and a line DE parallel to BC.
To prove: A line parallel to one side of a triangle divides the other two sides proportionally.
Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have
∠A=∠A (Common)
∠ADE=∠ABC (Corresponding angles)
Thus, by AA similarity, ΔABC is similar to ΔADE, therefore
AB/AD= AC/AE
⇒AD+DB/AD = AE+EC/AE
⇒1+DB/AD = 1+ EC/AE
⇒DB/AD = EC/AE
Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.
⇒Therefore Proved
Hope this helps!!!
Answer:
L(w) = 8 mm + (2 mm/wk)(wk)
Step-by-step explanation:
L(w) = length of beard as a function of time in weeks
L(w) = 8 mm + (2 mm/wk)(wk)
Answer:
Step-by-step explanation:
"f (x) = StartRoot 4 x + 9 EndRoot + 2" should be written as
Note that √(4x + 9) is a variation of the basic function y = √x, whose domain is [0, ∞ ).
The domain of f(x) = √(4x + 9) + 2 is found by taking the "argument" 4x + 9 of √(4x + 9) and setting it equal to zero:
4x + 9 ≥ 0, or
4x ≥ -9, or
x ≥ -9/4
This is the domain of the given function f(x) = √(4x + 9) + 2. So long as x is ≥ -9/4, the function f(x) will be defined.
Answer:
box 1: monomial
box 2: binomial
Step-by-step explanation:
reasoning: Box 1’s volume is modeled by a monomial times a monomial, so it will be a monomial.
Box 2’s volume is modeled by a monomial times a binomial, so it will be a binomial.
Answer:
The possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares by purchasing land.
Step-by-step explanation:
Let the variable <em>X</em> represent the amount of land used for planting trees and <em>Y</em> represent the amount of land purchased.
The goal of the environmental initiative is to save at least 25 million hectares of rain forest.
That is:
<em>X</em> + <em>Y</em> = 25....(i)
Now it is provided that:
- The cost of planting trees is $ 400 per hectare.
- The cost of purchasing land is $ 260 per hectare.
- The initiative has a budget of $8,250 million.
Using the above data it can be said that:
400<em>X</em> + 260<em>Y</em> = 8250....(ii)
Solve equations (i) and (ii) simultaneously.
![\ \ \ \ x+y=25]\times 260\\400x+260y=8250\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\\Rightarrow\\\\260x+260y=6500\\400x+260y=8250\\(-)\_\_\_\_\_\ (-)\_\_\_\_(-)\_\_\_\\\\\Rightarrow\\\\-140x=-1750\\\\x=\frac{1750}{140}\\\\x=12.5](https://tex.z-dn.net/?f=%5C%20%5C%20%5C%20%5C%20x%2By%3D25%5D%5Ctimes%20260%5C%5C400x%2B260y%3D8250%5C%5C%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C%5C%5C%5C%5CRightarrow%5C%5C%5C%5C260x%2B260y%3D6500%5C%5C400x%2B260y%3D8250%5C%5C%28-%29%5C_%5C_%5C_%5C_%5C_%5C%20%28-%29%5C_%5C_%5C_%5C_%28-%29%5C_%5C_%5C_%5C%5C%5C%5C%5CRightarrow%5C%5C%5C%5C-140x%3D-1750%5C%5C%5C%5Cx%3D%5Cfrac%7B1750%7D%7B140%7D%5C%5C%5C%5Cx%3D12.5)
Then the value of <em>y</em> is:
Thus, the possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares for purchasing land.
