Answer:
Step-by-step explanation:
We need to factor out numerator and denominator in order to simplify the rational expression by cancelling common factors.
Numerator : x^3 - 4 x = x (x^2 - 4) = x (x - 2) (x + 2)
Denominator (factoring by grouping):
x^2 - 5 x + 6 = x^2 - 3 x - 2 x + 6 = x (x - 3) - 2 (x - 3) = (x - 3) (x - 2)
Then we can cancel out the common factor (x - 2) in both numerator and denominator, leading to:
x (x + 2) / (x - 3) = (x^2 + 2)/ (x-3)
Answer:
2/6 = 48/144
7/8 = 168/192
Step-by-step explanation:
Use the least common denominator to write an equivalent fraction for each fraction. 2/6 , 7/8 The least common denominator is 24 .
2/6 can be rewritten as __
We Multiply both numerator and Denominator by 24
48/144
7/8 can be rewritten as __
We Multiply both numerator and Denominator by 24
168/192
Answer:
The proof is given below.
Step-by-step explanation:
Given the two triangles which are similar we have to prove that the ratio of their angle bisectors and the side or we can say that the ratio of their altitude are proportional.
In ΔABP and ΔDEQ
∠1=∠2 (Given)
∠3=∠4 (each 90°)
By AA similarity rule ΔABP≅ΔDEQ
As if the two triangles are similar then their corresponding sides are proportional
⇒ 
Hence, Corresponding angle bisectors of similar triangles are proportional and their ratio is equal to the ratio of altitude.
To solve this we need to figure out what 7.5% of 15,500 is. (It’s 1162.5). Now we know that after one year it is a total of 16,662.5. We then figure out what 7.5% of 16,662.5 is, which is 1,249.6875. You then add that to 16,662.5 which comes out to 17,912.1875. We then figure out 7.5% of that is 1,343.4140625. We then add that to the last total which is 19,255.6015625 and we simplify that to 19,256 and we find out that the final total is $19,256. But it wants how much have we earned which means we need to subtract the original from the new, which is 3756 and we add a unit.
Meaning the final answer is $3,756.
Answer:
b) 1 / 4
c) -3
Step-by-step explanation:
b) line passing through points (0,-1) (4,0)
slope = (y2 - y1) / (x2 - x1)
= (0 - (-1) ) / (4 - 0)
= 1 / 4
c) line passing through points (-1,2) (0, -1)
slope = (y2 - y1) / (x2 - x1)
= (-1 - 2) / (0 - (-1) )
= -3 / 1
= -3
