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2 years ago

6

Cody's new car cost $15,200. With a sales tax of 7%, determine the total price of the car.

2 answers:

kogti [31]2 years ago

8 0

Answer: 16264

Step-by-step explanation: 15,200 times 1.07 (1.07 is the sales tax plus the original amount which is expressed as 1%)

Paul [167]2 years ago

4 0

Answer:

$16,264

Step-by-step explanation:

.07(15200)=1064

1064+15200(original price)=16264

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bearhunter [10]

I = prt

p = 7430
r = 5%....turn to decimal = 0.05
t = 3

I = (7430)(0.05)(3)
I = 1114.50 <===

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2 years ago

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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1 year ago

Given your sister's incomplete text,

egoroff_w [7]

Explanation:

Quadrants 2 and 3 houses points that have negative x-values, while as Quadrants 1 and 4 houses points that have positive x-values.

If 'your sister' completes the text with negative y-value, the point would be in Q3.

If 'your sister' completes the text with positive y-value, the point would be in Q2.

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2 years ago

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Which is the simplified form of x Superscript negative 12?

chubhunter [2.5K]

Answer:

C. $\frac{1}{x^{12}}$

Step-by-step explanation:

We are given that an expression

$(x)^{-12}$

We have to find the simplified form of given expression.

We know that

$a^{-b}=\frac{1}{a^b}$

Using the property then we get

$x^{-12}=\frac{1}{x^{12}}$

Hence, the simplified form of $x^{-12}$ is given by

$\frac{1}{x^{12}}$

Option C is true.

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2 years ago

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Geometry: Line QS bisects angle PQR. Solve for x and find the measure of angle PQR.

Kazeer [188]

It is given in the question that,

Line QS bisects angle PQR. Solve for x and find the measure of angle PQR.

And

$m \angle PQS = 2x+1
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Since QS bisects angle PQR, therefore

$m \angle PQS = m \angle RQS$

Substituting the values, we will get

$2x+1=4x-15
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1 year ago

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