Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.

A limited-edition soccer ball costs $30, and the sales tax is 6%. What is the total cost?

frez [133]

Answer:

$31.80

Step-by-step explanation:

The ball will cost 100% of its price plus 6% of its price for a total of 106%.

To use percentages as a factor and multiply, they must be divide by 100, making the multiplication factor version of 106% 1.06.

Multiply the cost of the ball by your multiplication factor:

30 x 1.06 = 31.8

Money is written to two decimal places, making your answer $31.80

6 0

3 years ago

Read 2 more answers

A company produces x units of a product per month, where c(x) represents the total cost and r(x) represents the total revenue fo

Nat2105 [25]

Answer:

The total profit P(x) or the month is $P(x)=-0.5x^2+500x-350$ .

Step-by-step explanation:

A company produces x units of a product per month.

The total cost represents by the function C(x).

$C(x)=300x+250$

The total revenue represents by the function R(x).

$R(x)=-0.5x^2+800x-100$

The profit is the difference between revenue and cost.

$P(x)=R(x)-C(x)$

$P(x)=-0.5x^2+800x-100-(300x+250)$

$P(x)=-0.5x^2+800x-100-300x-250$

Combine like terms.

$P(x)=-0.5x^2+(800x-300x)+(-100-250)$

$P(x)=-0.5x^2+500x-350$

Therefore, the total profit P(x) or the month is $P(x)=-0.5x^2+500x-350$ .

5 0

3 years ago

The length of a rectangle is five more than the width. The perimeter is 130cm. What is the area?

Evgen [1.6K]

<h2>Greetings!</h2>

Answer:

≅ 586.8

Step-by-step explanation:

Take x to be the width, if the length is 5x bigger than the width, then this can be shown by 5x.

The total perimeter is:

(2 * x) + (2 * 5x) because each side has another parallel one.

This means that 2x + 10x = 130

12x = 130

Divide both sides by 12:

$\frac{12x}{12} = \frac{130}{12}$

x = $\frac{65}{6}$

So the area = length * width

x * 5x = area

Substitute the values in:

$\frac{65}{6} * (5*\frac{65}{6})$ = 586.8055... ≅ 586.8

So the approximate area is 586.8

<h2>Hope this helps!</h2>

5 0

3 years ago

The height h (in feet) of an object dropped from a ledge after x seconds can be modeled by h(x)=−16x2+36 . The object is dropped

kakasveta [241]

Check the picture below.

$\bf ~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases}$

so the object hits the ground when h(x) = 0, hmmm how long did it take to hit the ground the first time anyway?

$\bf h(x)=-16x^2+36\implies \stackrel{h(x)}{0}=-16x^2+36\implies 16x^2=36 \\\\\\ x^2=\cfrac{36}{16}\implies x^2 = \cfrac{9}{4}\implies x=\sqrt{\cfrac{9}{4}}\implies x=\cfrac{\sqrt{9}}{\sqrt{4}}\implies x = \cfrac{3}{2}~~\textit{seconds}$

now, we know the 2nd time around it hit the ground, h(x) = 0, but it took less time, it took 0.5 or 1/2 second less, well, the first time it took 3/2, if we subtract 1/2 from it, we get 3/2 - 1/2 = 2/2 = 1, so it took only 1 second this time then, meaning x = 1.

$\bf ~~~~~~\textit{initial velocity in feet} \\\\ h(x) = -16x^2+v_ox+h_o \quad \begin{cases} v_o=\textit{initial velocity}&0\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&\\ \qquad \textit{of the object}\\ h=\textit{object's height}&0\\ \qquad \textit{at "t" seconds}\\ x=\textit{seconds}&1 \end{cases} \\\\\\ 0=-16(1)^2+0x+h_o\implies 0=-16+h_o\implies 16=h_o \\\\[-0.35em] ~\dotfill\\\\ ~\hfill h(x) = -16x^2+16~\hfill$

quick info:

in case you're wondering what's that pesky -16x² doing there, is gravity's pull in ft/s².

4 0

3 years ago

What is the volume of a rectangular prism 15/4 8/3 6/5

Sonbull [250]

the volume is 69/21

Step-by-step explanation:

5 0

3 years ago