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3 years ago

A boogie board that has a regular price of $6. If the sales tax on the boogie board is 7%, what is the total cost of the board?

Mathematics

1 answer:

zavuch27 [327]3 years ago

7 0

Answer:

6.42$

Step-by-step explanation:

6.00 divided by 100 equals 0.6 multiplied by 7 equals 0.42 so the sales tax is 0.42 cents and the total is 6.42$

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An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 1 unit

padilas [110]

Answer:

An electronics company can be produce 350 transistors and 340 computer chips, they can´t produce resistors.

Step-by-step explanation:

1. We will name the variables for transistors, resistors and the computer chips.

a = Transistors

b= Resistors

c = Computer chips

2. We propose three linear equations, one for the copper, one for the zinc and one for the glass.

$\left \{ {{3a+3b+2c=1730} \atop {a+2b+c=690}}\atop {2a+b+2c=1380}} \right.$

3. We write the matrix form as Ax=d

$A=\left(\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right)$

$x=\left(\begin{array}{ccc}a\\b\\c\end{array}\right)$

$A=\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)$

With this formula the solution of x is $x=\frac{d}{A}$ or $x=A^{-1}d$

4. We will find the inverse matrix $A^{-1}$ using the formula:

$A^{-1} = \frac{1}{detA} (C_{A})^{T}$

a. det A

$det A=\left[\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right] =3*(4-1)-3*(2-2)+2*(1-4)=9-0-6=3$

b. $(C_{A})^{T}$

$C_{A}=\left(\begin{array}{ccc}4-1&.(2-2)&1-4\\-(6-2)&6-4&-(3-6)\\3-4&-(3-2)&6-3\end{array}\right)$

$C_{A}=\left(\begin{array}{ccc}3&.0&-3\\-4&2&3\\-1&-1&3\end{array}\right)$

$(C_{A}) ^T=\left(\begin{array}{ccc}3&0&-3\\-4&2&3\\-1&-1&3\end{array}\right)^T$

$(C_{A}) ^T=\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)$

c. $A^{-1}$

$A^{-1}=\frac{1}{3} \left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)$

5. As $x=\frac{d}{A}$ or $x=A^{-1}d$ , the solution of x is:

$x=\frac{1}{3}\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)$

$x=\frac{1}{3}\left(\begin{array}{ccc}(3*1730)+(-4*690)+(-1*1380)\\(0*1730)+(2*690)+(-1*1380)\\(-3*1730)+(3*690)+(3*1380)\end{array}\right)$

$x=\frac{1}{3}\left(\begin{array}{ccc}1050\\0\\1020)\end{array}\right)$

$X=\left[\begin{array}{ccc}350\\0\\340\end{array}\right]$

Therefore:

a= 350 Transistors

b=0 Resistors

c=340 Computer chips

4 0

2 years ago

Y-2=-3(x-7) written in standard form

uysha [10]

Y=2-3(x-7)
You just add +2 to each side and the positive and negative cancel out and it switches it over

8 0

2 years ago

How to do 764 divided by 4

lisov135 [29]

If you are doing a very long division problem than you can do long division. If you don't know long division than you can search it up on google and you will find "Khan Academy". But if you want an answer right now.... the answer is 191.
>.< Hope this helped.

3 0

3 years ago

Read 2 more answers

Question 1

cestrela7 [59]

Answer: A subway ride for a student costs $1.25. a monthly pass costs $35.

Step-by-step explanation:

6 0

2 years ago

Michaela has 11/12 yard of orange fabric and 7/8 yard of green fabric. She uses 1/2 yard of each color for her sewing project. H

Ede4ka [16]

Answer:

19/24 yards

Step-by-step explanation:

The total Michaela started with was ...

11/12 + 7/8 = 22/24 + 21/24 = 43/24 . . . . yards

She used a total of 1 yard, so has ...

(43 -24)/24 = 19/24

yards remaining.

Michaela has 19/24 yards (or 28.5 inches) of fabric left over.

6 0

3 years ago