Answer:
B. 
Step-by-step explanation:
The hypotenuse leg theorem (HL) requires the proof that the hypotenuse and the corresponding leg of the triangles to be equal in length. From the diagram, it can be found that 
is a common (shared) side of both triangles, so the additional fact needed is for the hypotenuses to be the same length.
∴ is the additional fact needed to prove 
Hope this helps :)
Answer:
109.5; B
Step-by-step explanation:
From your identity,
CosA = adjacent/ hypothenus
A represent an arbitrary angle between the sides in question.
In the question above, A=64
Hypothenus is the longest side and adjacent is the side just below the angle .
In the above case,
Hypothenus= X
adjacent =48
This means;
Cos64 = 48 /X
X = 48 / cos64; [ from cross multiplication and diving through by cos64]
X = 48 /0.4383 [ cos64 in radian = 0.4383]
= 109.51
= 109.5 to the nearest tenth.
Note( do your calculation of angle in radian or else, you won't get the answer)
Answer:
24 quarters and 49 nickels
Step-by-step explanation:
This situation has two unknowns - the total number of nickels and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.
- n+q=73 is an equation representing the total number of coins
- 0.05n+0.25q=8.45 is an equation representing the total value in money based on the number of coin. 0.05 and 0.25 come from the value of a nickel and quarter individually.
We write the first equation in terms of q by subtracting it across the equal sign to get n=73-q. We now substitute this for n in the second equation.
0.05(73-q)+0.25q=8.45
3.65-0.05q+0.25q=8.45
3.65+0.20q=8.45
After simplifying, we subtract 3.65 across and divide by the coefficient of q.
0.20q=4.8
q=24
We now know of the 73 coins that 24 are quarters. To find the number of nickels, we subtract 24 from 73 and get 49 nickels.
Answer:
Step-by-step explanation:
Using the parallelogram theorem
3x-8 = 10x+13
-7x = 21
x = -3
Substitute
3(-3) - 8
-17
10(-3) + 13
-17
Answer:
P(x) = -5(x² - 12)² + 405
Step-by-step explanation:
P(x) = -5x² + 120x - 315
Factor out -5 from the first two terms
P(x) = -5(x² - 24x) - 315
Complete the square
P(x) = -5(x - 12)² - (-5(-12)²) -315
P(x) = -5(x - 12)² + 720 - 315
P(x) = -5(x - 12)² + 405
