Answer:
Step-by-step explanation:
In order to do this we need to isolate y by performing the inverse operations on the other values like so...
a) 10x + 5y = 20 ... subtract 10x on both sides
5y = 20 - 10x ... divide both sides by 5
y = 4 - 2x ... we can move the 2x to the right to make it into y = mx + b
y = -2x + 4
b) 3x - 2y = 10 + 4x ... subtract 3x on both sides
-2y = 10 + x ... divide both sides by -2
y = -5 - 0.5x ... move -0.5 to the left so it matches y = mx + b
y = -0.5x - 5
Answer:
Volume of Cone =
Thus, Volume = 16.75 cubic feet
Step-by-step explanation:
Volume of a cone is given by the formula
Where r is the radius and
h is the height
Given radius r = 2 and
height is 2 times that.
So height is 2*2 = 4
Plugging these into the formula we get:
Volume of Cone =
Thus, Volume = 16.75 cubic feet
Answer:
11/12
Step-by-step explanation:
6 7/12 - 5 2/3
=(6-5) + (7/12 - 2/3)
= 1 + 7/12 - 2*4 / 3*4
= 1 + 7/12 - 8/12
= 1 + 7-8 / 12
= 1 + -1/12
=11/12
Answer:
t = 9
Step-by-step explanation:
<em>-t = 9(t - 10)</em>
First, distribute the 9.
<em>-t = 9t - 90</em>
Next, add subtract 9t from both sides.
<em>(-t) - 9t = (9t - 90) - 9t</em>
<em>-10t = -90</em>
Divide both sides by -10. When you divide a negative by another negative, they cancel each other out.
<em>(-10t)/-10 = (-90)/(-10)</em>
<em>t = 9</em>
I'll do the first one to get you started
The equation y = x^2+16x+64 is the same as y = 1x^2+16x+64
Compare that to y = ax^2+bx+c and we see that
a = 1
b = 16
c = 64
Use the values of 'a' and b to get the value of h as shown below
h = -b/(2a)
h = -16/(2*1)
h = -8
This is the x coordinate of the vertex.
Plug this x value into the original equation to find the corresponding y value of the vertex.
y = x^2+16x+64
y = (-8)^2 + 16(-8) + 64
y = 0
Since the y coordinate of the vertex is 0, this means k = 0.
The vertex is (h,k) = (-8, 0)
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So we found that a = 1, h = -8 and k = 0
Therefore,
f(x) = a(x-h)^2 + k
f(x) = 1(x-(-8))^2 + 0
f(x) = (x+8)^2
is the vertex form
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<h3>Final answer to problem 1 is f(x) = (x+8)^2 </h3>
