Y = -7sin(x) + 2cos(x)
y = -7sin(3π/4) + 2cos(3π/4)
y = -7sin(9.42/4) + 2cos(9.42/4)
y = -7sin(2.355) + 2cos(2.355)
y = -7(0.03698381721) + 2(0.9993158646)
y = -0.2588867205 + 1.998631729
y = 1.739745009
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:
55.4176955.4176955.4176955.41769
Step-by-step explanation:
If he ate 4 of them, but it means he ate 2/5 muffins,
4 muffins = 2/5 muffins
You substitute x muffins for how much muffins she baked in all -
2/5* x muffins = 4
2/5 multiply by 2/5 to cross it out. Do the same to the other side.
x= 4 *5/2
x = 10 muffins
So there were 10 muffins in all
Answer:
distributive property
Step-by-step explanation:
(3x + 7) + (2x + 8)
each of the parenthesis has a multiplier of 1 , placed outside the parenthesis.
then multiplying the terms inside the parenthesis by 1 gives
3x + 7 + 2x + 8