Answer:
2a^4+5a^3-6a^2+19a-20
Step-by-step explanation:
(a^2+3a-4)(2a^2-a+5)
2a^4-a^3+5a^2+6a^3-3a^2+15a-8a^2+4a-20
2a^4-a^3+6a^3+5a^2-3a^2-8a^2+15a+4a-20
2a^4+5a^3+2a^2-8a^2+19a-20
2a^4+5a^3-6a^2+19a-20
Answer as a fraction: 17/6
Answer in decimal form: 2.8333 (approximate)
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Work Shown:
Let's use the two black points to determine the equation of the red f(x) line.
Use the slope formula to get...
m = slope
m = (y2-y1)/(x2-x1)
m = (4-0.5)/(2-(-1))
m = (4-0.5)/(2+1)
m = 3.5/3
m = 35/30
m = (5*7)/(5*6)
m = 7/6
Now use the point slope form
y - y1 = m(x - x1)
y - 0.5 = (7/6)(x - (-1))
y - 0.5 = (7/6)(x + 1)
y - 0.5 = (7/6)x + 7/6
y = (7/6)x + 7/6 + 0.5
y = (7/6)x + 7/6 + 1/2
y = (7/6)x + 7/6 + 3/6
y = (7/6)x + 10/6
y = (7/6)x + 5/3
So,
f(x) = (7/6)x + 5/3
We'll use this later.
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We ultimately want to compute f(g(0))
Let's find g(0) first.
g(0) = 1 since the point (0,1) is on the g(x) graph
We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.
We now use the f(x) function we computed earlier
f(x) = (7/6)x + 5/3
f(1) = (7/6)(1) + 5/3
f(1) = 7/6 + 5/3
f(1) = 7/6 + 10/6
f(1) = 17/6
f(1) = 2.8333 (approximate)
This ultimately means,
f(g(0)) = 17/6 as a fraction
f(g(0)) = 2.8333 as a decimal approximation
Answer:
It's a rotation clockwise of 90 degrees about the origin.
Step-by-step explanation:
The given point moves from y = 5 to x = 5 so it has passed through 90 degrees about the origin.
It's a rotation clockwise of 90 degrees about the origin.
Answer:
Step-by-step explanation:
The answer is 20.
5*10-5*6=50-30=20
