Answer:
15 feet
Step-by-step explanation:
525 = ½(30+40)h
525 = 35h
h = 525/35
h = 15 feet
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
3/4 times 7/6 in simplest form = 0.875
I believe the answer is 2
Answer:
Step-by-step explanation:
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<u>Distance formula</u>
Let P(x, y) = any point on the locus
Let A = (0, 2)
Let B = (-2, 3)
If a point moves such that its distance from (0, 2) is one third distance from (-2, 3):
Therefore, using the distance formula:
Square both sides:
![\implies x^2+(y-2)^2=\dfrac{1}{9}[(x+2)^2+(y-3)^2]](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2%2B%28y-2%29%5E2%3D%5Cdfrac%7B1%7D%7B9%7D%5B%28x%2B2%29%5E2%2B%28y-3%29%5E2%5D)
Multiply both sides by 9:
