Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
The formula for finding the length is

All we have to do is plug in the numbers.

36 + 64 = 100
Since 100 =

we have to find the square root.

The length of the slide is 10 feet.
Answer:
(d) f(x) = log₆(x)
Step-by-step explanation:
If we use y in place of f(x), we see that ...
x = 6^y
Taking logs of both sides, we get ...
log(x) = y·log(6)
y = log(x)/log(6)
y = log₆(x) . . . . . . . using the change of base formula
f(x) = log₆(x)
_____
Or you can get there more directly using the relation between logs and exponentials:

Answer:
47
Step-by-step explanation:
m∠n = m∠p = 47
Since BD is parallel to AC, the alternating angles property applies.
Alternating angles are angles that are form in a Z pattern. The angles in the little rotated "v" formed in the top and bottom of the Z are equal.
Imagine a rotated Z forms from letters C to A to D to B.
Angles p and n are alternating angles, so they have the same measure.