Answer:
The score in third quiz must be lie between 84 to 99 inclusive.
Step-by-step explanation:
Y = T+3 (i)
T = H+2 (ii)
Y = 2*H (iiii)
T = H+2 therefore H = T-2
Substitute H=T-2 into (iii)
Y=2*H
Y=2*(T-2)
Y=2T-4
Now substitute that Y into (i)
(i) says Y = T+3
2T-4=T+3
2T-T-4=3
T-4=3
T=3+4
T=7
Then from (i) Y=T+3 = 7+3 =10
Y=10
And from (iii) Y=2*H
If Y = 10, then H = 5
Answer:
a. a = 1, b = -5, c = -14
b. a = 1, b = -6, c = 9
c. a = -1, b = -1, c = -3
d. a = 1, b = 0, c = -1
e. a = 1, b = 0, c = -3
Step-by-step explanation:
a. x-ints at 7 and -2
this means that our quadratic equation must factor to:

FOIL:

Simplify:

a = 1, b = -5, c = -14
b. one x-int at 3
this means that the equation will factor to:

FOIL:

Simplify:

a = 1, b = -6, c = 9
c. no x-int and negative y must be less than 0
This means that our vertex must be below the x-axis and our parabola must point down
There are many equations for this, but one could be:

a = -1, b = -1, c = -3
d. one positive x-int, one negative x-int
We can use any x-intercepts, so let's just use -1 and 1
The equation will factor to:

This is a perfect square
FOIL:

a = 1, b = 0, c = -1
e. x-int at 
our equation will factor to:

This is also a perfect square
FOIL and you will get:

a = 1, b = 0, c = -3
Answer:
d = 4
Step-by-step explanation:
The n th term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁ = - 2 and a₈ = 26 , then
- 2 + 7d = 26 ( add 2 to both sides (
7d = 28 ( divide both sides by 7 )
d = 4
Cos theta = 75/115
theta = cos^-1 (75/115)
theta = 49.2 degrees