Answer:
Step-by-step explanation:
Let x represent the speed of the slower plane. The faster plane's speed is then x+40. The sum of speeds is ...
x + (x+40) = 1180
2x = 1140 . . . . subtract 40
x = 570 . . . . . .divide by 2
x+40 = 610 . . . . the speed of the faster plane
The two speeds are 570 mph and 610 mph.
Answer:
q = -8, k = 2.
r = -6.
Step-by-step explanation:
f(x) = (x - p)^2 + q
This is the vertex form of a quadratic where the vertex is at the point (p, q).
Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.
The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.
So we have:
f(x) = 1/2(x - -2)^2 + q
f(x) = 1/2(x + 2)^2 + q
Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:
0 = 1/2(2 + 2)^2 + q
0 = 1/2*16 + q
0 = 8 + q
q = -8.
Now convert this to standard form to find k:
f(x) = 1/2(x + 2)^2 - 8
f(x) = 1/2(x^2 + 4x + 4) - 8
f(x) = 1/2x^2 + 2x + 2 - 8
f(x) = 1/2x^2 + 2x - 6
So k = 2.
The r is the y coordinate when x = 0.
so r = 1/2(0+2)^2 - 8
= -6.
Answer:
the first one is -4 2. is -2 3. is -70, 4. 20 5. 6 6. -45 7. 35 8. -20
Step-by-step explanation:
Answer:
Rate of Change = -77.9 feet/year
My interpretation: "Is Bad."
Step-by-step explanation:
The rate of change is the number of feet that Lake Powell dropped, divided by the number of years the drop took place. We want a value with a unit of feet/year.
<u>Year</u> <u>Feet</u>
1999 3893
2005 3425.6
<u>Change</u>
Year = (2005 - 1999) or 6 years
Feet = (3425.6 - 3893) or -467.4 feet
Rate of Change = (-467.4 feet)/(6 years)
Rate of Change = -77.9 feet/year
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FYI: Lake Powell is 22.39 feet lower today (June 23, 2022) than it was 1 year ago.
