Answer:
x = -19 or x = -1
Step-by-step explanation:
We need the quadratic equation in the form
,
so we add 8 to both sides.
Now we have an equation of the form x^2 + ax + b = 0.
We need to factor the quadratic equation. To factor it, we need two numbers, p and q, whose product is b and whose sum is a. Then the factoring is (x + p)(x + q).
In our case, b = 19 and a = 20. We need two numbers that multiply to 19 and add to 20. The numbers are 19 and 1. Our p and q are 19 and 1.
(x + 19)(x + 1) = 0
Since a product of two factors equals zero, either one factor equals zero, or the other factor equals zero. We set each factor equal to zero and solve both equations for x.
x + 19 = 0 or x + 1 = 0
x = -19 or x = -1
<span>During the indicated time block of 6 PM-4 AM, the movies should go as follows:
Since the G rating movies needs to be shown during the first time block, it would be first at 6 pm until around 8 pm. The NC-17 movie would also need to be LAST and from 2 am to 4 am. That leaves 3 movies left to be shown from around 8 pm to 2 Am, which could be shown in 6 different ways. If we assigned EACH movie a title of A, B or C, you get these different showing possibilities- ABC, ACB, BAC, BCA, CAB, and CBA. Since the first and last movies never change, they would default to the first and last positions while the rest is filled in.</span>
The answer is y=3x.
y=21, x=7
y=mx (m is the variable for slope)
21=m(7)
m=21/7
m=3
Answer:
m∠QPR = 35° m∠QPM =40° m∠PRS = 30°
Step-by-step explanation:
ΔPRQ is a right triangle with right angle at R. So m∠QPR = 90 - 55 = 35
ΔQPM is a right triangle with right angle at M. So m∠QPM = 90 - 40 = 40
Arc RQ = 2(35) = 70 and arc SR = 2(25) = 50.
So arc PS = 180 - (arc RQ + arc SR) = 180 - (70 + 50) = 180 - 120 = 60
Now arc PS is the intercepted arc for ∠PRS.
Therefore, m∠PRS = 60/2 = 30
I used the fact that an inscribed angle has a measure 1/2 the measure of the intercepted arc several times. Also, I used the fact that the acute angles of a right triangle are complementary. And, finally I used the fact that an inscribed angle in a semicircle is a right angle.
I hope this helped.
