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STALIN [3.7K]
3 years ago
15

1. Use the distributive property to write 13y-(5x-3y)+x (can u also answer) 2. The state sales tax rate is 4.75% harold would li

ke to buy a shirt with sales price of $20.If harold buys the shirt how much would he pay for sales tax?
Mathematics
1 answer:
slava [35]3 years ago
4 0

Answer:

Step-by-step explanation:

1) The given expression is

13y-(5x-3y)+x

Applying the distributive property, we would multiply each term inside the bracket by the - 1 which is outside the bracket first. it becomes

13y - 5x + 3y + x

- 5x + x + 13y + 3y

- 4x + 16y

2) The state sales tax rate is 4.75%. If Harold buys a shirt whose sales price is $20, the amount that he would pay for sales tax is

4.75/100 × 20 = 0.0475 × 20 = $0.95

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Express the system as AX = B; then solve using matrix inverses
Wittaler [7]

Answer with explanation:

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A=\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right] ,\\\\ X=\left[\begin{array}{c}x&y\end{array}\right],\\\\B=\left[\begin{array}{c}2&0\end{array}\right]

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Adj.A=\left[\begin{array}{cc}2&1\\5&3\end{array}\right] ,\\\\ |A|=6-5\\\\|A|=1\\\\\left[\begin{array}{c}x&y\end{array}\right]=\left[\begin{array}{cc}2&5\\1&3\end{array}\right] \times \left[\begin{array}{c}2&0\end{array}\right]\\\\x=4, y=2

2.

The given equations are

x+y-z=2

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⇒The matrix in the form of , AX=B, is

   A=\left[\begin{array}{ccc}1&1&-1\\1&0&1\\2&1&1\end{array}\right]\\\\ X=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\\\\B= \left[\begin{array}{ccc}2\\7\\13\end{array}\right]\\\\\rightarrow X=A^{-1}B\\\\\rightarrow X=\frac{Adj.A}{|A|}\times B\\\\a_{11}=-1,a_{12}=1,a_{13}=1,a_{21}=-2,a_{22}=3,a_{23}=1,a_{31}=1,a_{32}=-2,a_{33}=-1\\\\|A|=1\times(0-1)-1\times(1-2)-1\times(1-0)\\\\=-1+1-1\\\\|A|=-1\\\\Adj.A=\left[\begin{array}{ccc}-1&-2&1\\1&3&-2\\1&1&-1\end{array}\right]

\frac{Adj.A}{|A|}=\left[\begin{array}{ccc}1&2&-1\\-1&-3&2\\-1&-1&1\end{array}\right]\\\\X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}1&2&-1\\-1&-3&2\\-1&-1&1\end{array}\right]\times\left[\begin{array}{ccc}2\\7\\13\end{array}\right]\\\\x=3,y=3,z=4

7 0
3 years ago
the doctor recommended that Matt increase the number of calories you consume from 2000 to 2800 by what percent did the number of
nikdorinn [45]

Answer:

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Old Value ( Calories consume before)  = 2000

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To find percent increase, the formula used is:

Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100%

Putting values in formula and finding percent increase

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So, 40% number of calories have increased

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