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xz_007 [3.2K]
3 years ago
6

Solve each equation for the given variable a-2b=-10 for b

Mathematics
1 answer:
Ymorist [56]3 years ago
8 0
A-2b=-10
add 2b on both sides
a=2b-10
add 10 to both sides
a+10=2b
divide both sides by 2
a/2+10/2=a/2+5=b
b=5+a/2
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What are the features of the parabola modeled by the equation f(x) = x2 - 114x ?
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Answer:

Answers are in bold type

Step-by-step explanation:

f(x) = x^{2} -144x

The parabola opens up, so has a minimum at the vertex.

Let (h, k) be the vertex

h = -b/2a = - (-144)/2(1) = 57

k = 57^2 - 144(57) = 3249 - 6498 = -3249

Therefore, the vertex is (57, -3249)

The minimum value is -3249

The domain is the set of real numbers.  

The  range = {y | y ≥ -3249}

The function decreases when -∞ < x < 57  and increases when 57 > x > ∞

The x - intercepts:  x^{2} -144x = 0

                                x(x - 114x) = 0

                                x = 0 or x = 114

x-intercepts are (0, 0) and (0, 114)

When x = 0, then we get the y-intercept.  So, 0^2 - 114(0) = 0

y-intercept is (0, 0)

3 0
3 years ago
A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op
Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

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Volume of cone is given by

V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3

By differentiating with respect to time t, we get that

\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}

Now,  the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie \dfrac{dv}{dt}=-4\ in^3

and h = 2 inches deep.

-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0
3 years ago
Tom wants to place a photograph that is 8.5 inches wide on his science fair poster. His poster board is 21.25 inches wide. How f
SOVA2 [1]

Answer:

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Set the photo 6 3/8 inches from each edge of the poster board.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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