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2 years ago

4

The sales tax in your city is 4.4\%4.4%4, point, 4, percent, and an item costs \$3$3dollar sign, 3 before tax. How much tax woul

d you pay on that item?

1 answer:

MissTica2 years ago

5 0

It is given that the cost of the item before the tax is $3

It is also given that the sales tax rate in the city is 4.4%.

Therefore, the tax on the item in your city in dollars will simply be the tax rate in decimal points (converted from percentage) multiplied to the cost of the item before tax.

This can be done as:

Tax Payable= $4.4\% {of} 3=\frac{4.4}{100}\times 3=0.132$

Thus the tax payable is 0.132 dollars or 13.2 cents.

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Find c1 and c2 such that M2+c1M+c2I2=0, where I2 is the identity 2×2 matrix and 0 is the zero matrix of appropriate dimension.

Katyanochek1 [597]

The question is missing parts. Here is the complete question.

Let M = $\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]$ . Find $c_{1}$ and $c_{2}$ such that $M^{2}+c_{1}M+c_{2}I_{2}=0$ , where $I_{2}$ is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.

Answer: $c_{1} = \frac{-16}{10}$

$c_{2}=\frac{-214}{10}$

Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:

$\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

$M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]$

$M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]$

Solving equation:

$\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]$

Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.

So, the equation is:

$\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]$

And the system of equations is:

$6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15$

There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:

$6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)$

$6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15$

$10c_{1} = -16$

$c_{1} = \frac{-16}{10}$

With $c_{1}$ , substitute in one of the equations and find $c_{2}$ :

$6c_{1}+c_{2}=-31$

$c_{2}=-31-6(\frac{-16}{10} )$

$c_{2}=-31+(\frac{96}{10} )$

$c_{2}=\frac{-310+96}{10}$

$c_{2}=\frac{-214}{10}$

<u>For the equation, </u> $c_{1} = \frac{-16}{10}$ <u> and </u> $c_{2}=\frac{-214}{10}$ <u />

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2 years ago

What is the expression in radical form? (7x^3y^2) 2/7

Gelneren [198K]

$\sqrt[7]{(7x^3y^2)^{2} } = \sqrt[7]{(49x^6y^4)}$
In a fractional exponent the denominator tells what root it is (7th root in this case) and the numerator tells what the value in the parenthesis is raised to (2nd power in this case)

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2 years ago

Read 2 more answers

Point F is on circle C. What is the length of line segment GF? 12.5 units 15.0 units 17.5 units 20.0 units

geniusboy [140]

The answer:
According to the image, <span>the length of line segment GF can be found with
</span>GF= GC +CF
CF is one the radius, so CF=7.5
to find GC, we can apply Pythagorean theorem on the right triangle GEC
it is
GC² =GE² + EC² = 10² +7.5² =156.25, and then GC= sqrt(156.25)=12.5

therefore, GF= GC +CF=12.5+7.5=20

so the answer is <span>20.0 units</span>

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2 years ago

Ben is eating some pretzels and an entire small package of mustard as a snack. Based on

olasank [31]

Please consider the attached graph.

We have been given that Ben is eating some pretzels and an entire small package of mustard as a snack. We are asked to find the equation that represents the relationship between the number of pretzels that Ben eats, x, and the total amount of sodium in his snack, y.

First of all, we will find the slope of the line using points (1,80) and (5,140).

$m=\frac{140-80}{5-1}$

$m=\frac{60}{4}$

$m=15$

Now we will use point-slope form of equation $y-y_1=m(x-x_1)$ , where m represents slope of line and point $(x_1,y_1)$ is on the line.

We will substitute $m=15$ and coordinates of point (1,80) in above equation.

$y-80=15(x-1)$

$y-80=15x-15$

$y-80+80=15x-15+80$

$y=15x+65$

Therefore, the equation $y=15x+65$ represents the relationship between the number of pretzels that Ben eats and the total amount of sodium in his snack.

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2 years ago

Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he has to go. If Ya

stich3 [128]

Answer:not A

Step-by-step explanation:

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1 year ago