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KATRIN_1 [288]
2 years ago
11

Luis wants to buy a skateboard that usually sells for $79.74. All merchandise is discounted by 12%. What is the total cost of th

e skateboard if Luis has to pay a state sales tax of 7.25%. Round your intermediate calculations and answer to the nearest cent.
Mathematics
1 answer:
eduard2 years ago
7 0

Answer:

75.26

Step-by-step explanation:

Most sales taxes work by not being calculated until cash in some form changes hands. So you take the discount first and then you add the sales tax on the new amount.

Take the discount first

Original cost = 79.74

Discount amount = 79.74 * 12% = 79.74 * 12/100 = 9.57

New price = 79.74 - 9.57 = 70.17

Now you are ready to add on the sales tax

70.17 * 7.25/100 = 5.09

The total is 70.17 + 5.09 = 75.26

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the center of a circle is on the line y=2x and the line x=1 is tangent to the circle at (1,6).find the center and the radius
Julli [10]

The radius and the center of the circle are 4 units and (1,2), respectively

<h3>How to determine the center and the radius?</h3>

The center of the circle is on

y = 2x and x = 1

Substitute x = 1 in y = 2x

y = 2 * 1

Evaluate

y = 2

This means that the center is

Center = (1, 2)

Also, we have the point of tangency to be:

(x, y) = (1, 6)

This point and the center have the same x-coordinate.

So, the distance between this point and the center is

d = 6 - 2

d = 4

This represents the radius

Hence, the radius and the center of the circle are 4 units and (1,2), respectively

Read more about circle equation at:

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6 0
2 years ago
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lana66690 [7]

Answer:

Step-by-step explanation:

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4 0
3 years ago
2x^2+3x-2, a=0 How do I find the derivative?
Ghella [55]

You can use the definition:

\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h

Then if

f(x) = 2x^2+3x-2

we have

f(x+h) = 2(x+h)^2+3(x+h) - 2 = 2x^2 + 4xh+2h^2+3x+3h-2

Then the derivative is

\displaystyle f'(x) = \lim_{h\to0}\frac{(2x^2+4xh+2h^2+3x+3h-2)-(2x^2+3x-2)}h \\\\ f'(x) = \lim_{h\to0}\frac{4xh+2h^2+3h}h \\\\ f'(x) = \lim_{h\to0}(4x+2h+3) = \boxed{4x+3}

I'm guessing the second part of the question asks you to find the tangent line to <em>f(x)</em> at the point <em>a</em> = 0. The slope of the tangent line to this point is

f'(0) = 4(0) + 3 = 3

and when <em>a</em> = 0, we have <em>f(a)</em> = <em>f</em> (0) = -2, so the graph of <em>f(x)</em> passes through the point (0, -2).

Use the point-slope formula to get the equation of the tangent line:

<em>y</em> - (-2) = 3 (<em>x</em> - 0)

<em>y</em> + 2 = 3<em>x</em>

<em>y</em> = 3<em>x</em> - 2

5 0
3 years ago
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Alexxandr [17]
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7 0
3 years ago
Read 2 more answers
Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, –5).
posledela
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\bf \textit{middle point of 2 points }\\ \quad \\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%  (a,b)&#10;&({{ 7}}\quad ,&{{ 3}})\quad &#10;%  (c,d)&#10;&({{ 7}}\quad ,&{{ -5}})&#10;\end{array}\qquad &#10;\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)&#10;\\\\\\&#10;\left(\cfrac{{{ 7+7}}}{2}\quad ,\quad \cfrac{{{ -5}} + {{ 3}}}{2} \right)\implies \left( \cfrac{14}{2}\ ,\ \cfrac{-2}{2} \right)\implies \boxed{(7,-1)}

now.. that we know what the center is, and what the radius is, well

\bf \textit{equation of a circle}\\\\ &#10;(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2&#10;\qquad &#10;\begin{array}{lllll}&#10;center\ (&{{ h}},&{{ k\quad }})\qquad &#10;radius=&{{ r}}\\&#10;&7&-1&4&#10;\end{array}

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3 years ago
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