The y value of the vertex is 121.
We can find this by first finding the x value of the vertex. The x value of the vertex in a quadratic equation will always be half way between the two zeros. We can find the zeros by setting each parenthesis equal to 0 and solving for x.
Zero #1
(x + 8) = 0 ---> subtract 8 from both sides.
x = -8
Zero #2
(x - 14) = 0 ----> add 14 to both sides.
x = 14
Since we know that the x value of the vertex must be in the middle of these two, we can take the average of them to find it.
(-8 + 14)/2 = 3
So the x value is 3. Now we can plug that into the equation for all of the x's to get the y value.
f(x) = -(x + 8)(x - 14)
f(3) = -(3 + 8)(3 - 14)
f(3) = -(11)(-11)
f(3) = 121
So the y value is 121.
Answer:
4
Step-by-step explanation:
What number should the equation x + y = 17 be multiplied by to eliminate y?
Answer:
decreasing at 390 miles per hour
Step-by-step explanation:
Airplane A's distance in miles to the airport can be written as ...
a = 30 -250t . . . . . where t is in hours
Likewise, airplane B's distance to the airport can be written as ...
b = 40 -300t
The distance (d) between the airplanes can be found using the Pythagorean theorem:
d^2 = a^2 + b^2
Differentiating with respect to time, we have ...
2d·d' = 2a·a' +2b·b'
d' = (a·a' +b·b')/d
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To find a numerical value of this, we need to find the values of its variables at t=0.
a = 30 -250·0 = 30
a' = -250
b = 40 -300·0 = 40
b' = -300
d = √(a²+b²) = √(900+1600) = 50
Then ...
d' = (30(-250) +40(-300))/50 = -19500/50 = -390
The distance between the airplanes is decreasing at 390 miles per hour.
Answer:
8h
Step-by-step explanation: Step One: Combine like terms
(both numbers have the same variable so you can combine the coefficients). Just add 1 + 7. (h is the same as 1h)
Answer:
d. 8°
Step-by-step explanation:
It appears as though you intend ∠ECF and ∠ACB to be vertical angles, hence the same measure, 47°. The angle of interest, ∠BCD, is added to that to make ∠ACD, which is 55°. The added angle must be 55° -47° = 8°.
