Answer:
y = x + 53
Step-by-step explanation:
Let x be the number of flowers Jamal planted and y the number of flowers Heidi planted.
Jamal planted 53 fewer flowers than Heidi:
x = y - 53
Isolate the y.
x + 53 = y (Change the - sign to + sign when switching from different sides of an equation)
y = x + 53
Answer:
k=24
Step-by-step explanation:
The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.
f=-x^2+8x+20
Differentiating both sides:
f'=(-x^2+8x+20)'
By sum rule:
f'=(-x^2)'+(8x)'+(20)'
By constant multiple rule:
f'=-(x^2)'+8(x)'+(20)'
By constant rule:
f'=-(x^2)+8(x)'+0
By power rule:
f'=-2x+8
f' at x=a is -2a+8
This is the slope of any tangent line to the curve f.
The slope of g is 4 if you compare it to slope intercept form y=mx+b.
So we gave -2a+8=4.
Subtracr 8 on both sides: -2a=-4
Divide both sides by -2: a=2
The tangent line to the curve at x=2 is y=4x+k.
To tind y we must first know the y-coordinate of the point of tangency.
If x=2, then
f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32
So the point is (2,32).
g(x)=4x+k and we know g(2)=32.
This gives us:
32=4(2)+k
32=8+k
k=32-8
k=24
You would move the decimal point two times to the left for the decimal. 0.076
For the fraction, we would make it 76/1000 because the 6 converted in the decimal is in the thousandth place. We can simplify it and get 19/250.
Answer:
Step-by-step explanation:
2x² - 8x - 24 = 0
2x² - 12x + 4x - 4*6 = 0
2x(x-6) + 4(x - 6) = 0
(x - 6)(2x + 4) = 0
Answer:
-4.9
Step-by-step explanation:
