Answer:
a = 2, b = - 3, c = - 8
Step-by-step explanation:
Expand f(x) = a(x + b)² + c and compare coefficients of like terms, that is
a(x + b)² + c ← expand (x + b)² using FOIL
= a(x² + 2bx + b²) + c ← distribute parenthesis by a
= ax² + 2abx + ab² + c
Compare like terms with f(x) = 2x² - 12x + 10
Compare coefficients x² term
a = 2
Compare coefficients of x- term
2ab = - 12, substitute a = 2
2(2)b = - 12
4b = - 12 ( divide both sides by 4 )
b = - 3
Compare constant term
ab² + c = 10 , substitute a = 2, b = - 3
2(- 3)² + c = 10
18 + c = 10 ( subtract 18 from both sides )
c = - 8
Then a = 2, b = - 3, c = - 8
Answer:
Step-by-step explanation:
1. Lets transfer ounces ⇄ to Millimeters.
2. Lets multiply.
is: .
Hope this helps :)
Answer:
The GCF of 48 and 64 is 16
Step-by-step explanation:
To figure out GCF, you make a list of all the prime factors, pick out the numbers they have in common, and multiply them together. In this case:
48: 2 x 2 x 2 x 2 x 3
64: 2 x 2 x 2 x 2 x 2 x 2
They have four 2's in common, so you multiply 2 x 2 x 2 x 2 =16
Answer:
1.5 billion years = 3.33 meters
From the end 2.22\times 10^{-5} meters is the distance of written history.
Step-by-step explanation:
Age of earth is 4.5 billion years and we have to represent the history of earth (from birth to present ) with a 10 meter long timeline.
So on the scale every meter will represent 4.5/10 = 0.45 billion years.
∵ 0.45 billion years represent the distance = 1 meter on scale.
∴ 1 billion years will be represented by =
∴ For 1.5 billion years distance will be =
Now we have to measure the length of written history from the end of the timeline.
Since written human history extends about 10000 yrs back means distance on timeline = = from the end.
Answer:
After 15 minutes, they are moving apart at 8100 ft/sec
Step-by-step explanation:
Using the direct proportion
For the man, 4ft/sec
4ft -----1 sec
Xft ----- 60 x 15 sec
X = 3600 ft/sec
For the woman, 5ft/sec
5ft -----1 sec
Xft ----- 60 x 15 sec
X = 4500 ft/sec
After 15 minutes they are moving apart at 4500 + 3600 = 8100 ft/sec