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anzhelika [568]
2 years ago
6

Use a matrix to solve the system:

Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
4 0

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\

Rewrite these equations in matrix form

\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\

we can write it like this,

AX=B\\X=A^{-1}B

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]  \\

now multiply the matrix with B

X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\

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Solve for the given variable:<br> 14=63n
marin [14]

Answer:

n = 2/9

Step-by-step explanation:

switch sides: 63n=14

divide both sides by 63: 63n/63 = 14/63

simplify: n = 2 / 9

3 0
3 years ago
Saylor Henshaw earned $120 in simple interest in 9 months at an annual interest rate of 5%. How much money did he invest?
Ksju [112]
Annual interest is P*r^t, r is 0.05 here, t is 9/12=3/4=0.75
P*0.05^0.75=120
use your calculaor: P= 120÷ (0.05)^0.75=1135
so he invested about 1135 dollars
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3 0
3 years ago
For questions 1 – 6, find the area of the circle to the nearest hundredth.<br> Any help appriciated!
Ganezh [65]

Step-by-step explanation:

The area of a circle is given by :

A = πr²

r is the radius of the circle

(4) Diameter = 22 cm

Since, radius = diameter/2

r = 11 cm

Now, area of the circle,

A=\pi \times (11)^2\\\\A=380.13\ cm^2

(5) Diameter = 30 cm

Since, radius = diameter/2

r = 15 cm

Now, area of the circle,

A=\pi \times (15)^2\\\\A=706.85\ cm^2

(6) Diameter = 4cm

Since, radius = diameter/2

r = 2 cm

Now, area of the circle,

A=\pi \times (2)^2\\\\A=12.56\ cm^2

So, the area of circles 4,5 and 6 are 380.13², 706.85² and 12.56² respectively.

4 0
2 years ago
Anna enjoys dinner at a restaurant in Washington DC where the sales tax on meals is 5%. She leave a 20% tip on the price of her
Maru [420]

Answer:

52.40

Step-by-step explanation:

Discussion

Suppose the meal starts out as x.

She pays 5% of x as a sales tax

So that brings the total up to 100% + 5% = 105%

Before paying, she pays 20% on x as her tip. The tax does not touch the tip.

So that brings the total up to 100% + 5% + 20% = 125% of this is based on x, the cost of the meal.

So 125% of x = 65.50                          change the % to a fraction

125/100 * x = 65.50                             Multiply both sides by 100/125  

125/100 * 100/125x = 100/125 * 65.50

x = 100/125 * 65.50                             Multiply by 100

x = 6550 / 125                                     Divide by 125

Check

Tax = 5% * 52.40 = 5/100 * 52.40 = 2.62

Tip = 20%*52.40 = 20/100 * 52.40=10.48

Meal =                                               52.40

Total                                                  65.50  Just as it should

8 0
3 years ago
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.
hoa [83]

Answer:

The answer to your question is AC = 9.9

Step-by-step explanation:

To solve this problem use trigonometric functions. The trigonometric function that relates the hypotenuse and the adjacent side is cosine.

             cos α = \frac{adjacent side}{hypotenuse}

Solve for hypotenuse

              hypotenuse = \frac{adjacent side}{cos\alpha }

Substitution

             hypotenuse = \frac{9}{cos 24}

Simplification and result

             hypotenuse = 9.85

6 0
3 years ago
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