Answer:
C. 20 feet
Step-by-step explanation:
The question has given you tan∅ = 20/50. You know that tan is opposite over adjacent. So if the opposite end is 20, that means the tree is 20 feet tall and the girl is <em>50 feet away</em>.
Answer:
10 five-point questions and 40 two-point questions
Step-by-step explanation:
Let x represent the total number of five-point questions and y represent the total number of two-point questions.
Equation 1: 5x+2y=130
Equation 2: x+y=50
Multiplying Equation 2 by 2: 2x+2y=100 (Equation 3)
(Equation 1) - (Equation 3): 3x=30
x=10
Substituting x=10 into x+y=50: 10+y=50
y=40
Therefore, there are 10 five-point questions and 40 two-point questions.
<h2><u>Check</u></h2>
Substituting x=10 and y=40 into Equation 1:
LHS=5x+2y=5(10)+2(40)=50+80=130
RHS=130
LHS=RHS
Substituting x=10 and y=40 into Equation 2:
LHS=x+y=10+40=50
RHS=50
LHS=RHS
Since in both cases the left-hand side is equal to the right-hand side, the answer is correct.
(LHS: left-hand side, RHS: right-hand side)
Answer:
47
Step-by-step explanation:
the lines are parrele which explains
why its 47
Answer:
The net perfect number would be 28
Step-by-step explanation:
When you add up all the factors of 28 (other than 28) you get 28.
1 + 2 + 4 + 7 + 14 = 28
You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.