Which expression is equivalent to r^m ÷ r^n?

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for a.

boyakko [2]

9514 1404 393

Answer:

(d) A = 14.28 in², P = 14.28 in

Step-by-step explanation:

The figure is wholly contained within a 4" square, which has an area of (4 in)² = 16 in², and a perimeter of 4(4 in) = 16 in. Since the figure is smaller in area and has a shorter perimeter (the top corners are rounded, not square), both answer values must be less than 16.

The only reasonable choice is the last choice: 14.28 in², 14.28 in.

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If you want to figure this out in detail, you have the area of a rectangle that is 2 in by 4 in, and the area of a semicircle of radius 2 in. The total area is ...

A = LW +1/2πr²

A = (2 in)(4 in) + 1/2(3.14)(2 in)² = 8 in² +6.28 in²

A = 14.28 in²

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The perimeter is half that of a 4" square, plus half that of a 4" circle.

P = 1/2(4(4 in) +π(4 in)) = (2 in)(4 +π) = 2(7.14) in

P = 14.28 in

8 0

3 years ago

Find the domain of the function: <img src="https://tex.z-dn.net/?f=h%28x%29%20%3D%20%5Cfrac%7B6%7D%7Bx%5E%7B2%7D-4x%7D" id="TexF

ivolga24 [154]

Answer:All real numbers except for 0 and 4.

Step-by-step explanation:

The denominator cant be zero so we take it and equal it to zero. For the denominator to equal to zero, either x = 0 or x=4 yields 0.

8 0

4 years ago

What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

olya-2409 [2.1K]

Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.

For example:

Type of change Effect on y = f(x)

$y = f(x - c)$ horizontal shift: c units to right

So

Considering the function

$f(x) = x^2$

The graph is shown below. The first figure is representing $f(x) = x^2$ .

Now, considering the function

$\:f\left(x\right)=\left(x-6\right)^2$

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shown below in second figure. It is clear that the graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shifted 6 units to the right as compare to the function $f(x) = x^2$ .

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

5 0

3 years ago

A number is divided b 2, and then the quotient is added to 8. The result is 33. Find the number.

garri49 [273]

Answer:

x=50

Step-by-step explanation:

You must work backwards to isolate and find the answer, first making an equation and setting the unknown number as a variable, x. The answer is then the isolated value of x.

x/2+8 = 33

x/2 = 33-8

x/2 = 25

x/2(2) = 25(2)

7 0

3 years ago

What is the answer for this problem 3-3×6+2=?

liberstina [14]

Answer:

-13

Im correct!

6 0

3 years ago

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