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3 years ago

If F(x) = 2 - xand w(x) = x - 2, what is the range of (w•p(x)?

Mathematics

1 answer:

hoa [83]3 years ago

4 0

Answer:

Th Range is [0, -∞)

Step-by-step explanation:

f(x) = 2 - x

w(x) = x - 2

We want to find the range of (f * w)(x).

First, we need to find (f * w)(x), which is the multiplication of the function f(x) and the function w(x). Lets use algebra to find (f * w)(x):

$(f*w)(x)=(2-x)(x-2)\\=2x-4-x^2+2x\\=-x^2+4x-4$

This is a quadratic function (U shaped), or a parabola. The graph is attached.

The range is the set of y-values for which the function is defined.

We see from the graph that the parabola is upside down and the highest value is y = 0 and lowest goes towards negative infinity. So the range is from 0 to negative infinity. Or,

0 < y < ∞

In interval notation, that would be:

[0, -∞)

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You have decided to start saving for college and open up a 529 account. You invest $5,000 into the account at a 2% interest rate

raketka [301]

You will have $5,525.39 after 5 years.

Because the interest is compounded monthly, you need to convert the interest rate and the term of investment to a monthly basis.

Monthly interest = 2% / 12 = 2/12%

Term of investment = 5 x 12 = 60 months

To find the amount you will have in 5 years, use the formula:

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= 5,000 x ( 1 + 2/12%)⁶⁰

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In conclusion, your investment will have compounded to $5,525.39 in 5 years.

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6 0

3 years ago

How are 2-D and 3-D objects related to each other in real world

stich3 [128]

Answer:

You can see 2-D flat shapes on the faces of 3-D objects.

For example: You go to the store and you see a box,

the box has 6 faces. The bottom of the box is one of It's faces which is 2-D.

Step-by-step explanation:

8 0

2 years ago

How do you solve -2/3(12c-9)+14c

Oliga [24]

You can't solve it, but you can simplify it
-2/3 * (12c - 9) + 14c = -2/3*12c - (-2/3)*9 + 14c = -8c + 6 + 14 c = 6c + 6

6 0

3 years ago

A rectangular prism has a height of 12 cm and a square base with sides measuring 5 cm. A pyramid with the same base and the heig

Ksju [112]

The answer is 200 cm³

The volume of the rectangular prism (V1) is:
V1 = l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
Thus: V1 = 12 · 5 · 5 = 300 cm³

The volume of pyramid (V2) is:
V2 = 1/3 · l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³

The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):
V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³

3 0

2 years ago

Plot on graph.

amid [387]

Answer:

Axis of symmetry: x=-2

Maximum point: (-2,8)

Step-by-step explanation:

The given function is $h(x)=-\frac{1}{2}x^2-2x+6$ .