Consider the system below. 4x-2y=-12 3x-y=-3 Solve the system by using a matrix equation. Show your work.

Answers

Answer 1

Answer: The matrix equation AX=B, where A and B are numerical matrices and X is unknown matrix has a solution $X= A^(-1) B$ , where $A^(-1)$ is inverse matrix of X.
1. We rewrite given system as matrix equation $\left[\begin{array}{cc}4&-2\n3&-1\end{array}\right] X=\left[\begin{array}{c}- 12\n- 3\end{array}\right]$ ;
2. Find $A^(-1) = \left[\begin{array}{cc}4&-2\n3&-1\end{array}\right] ^(-1)$ by the rule $A^(-1)= (1)/(det \ A) [ A_(ij) ] ^(T)$ . So, $det\ A=4$ × $(-1)-3$ × $(-2)=-4+6=2$ and algebraic supplements are
$A_(11) =-1 \n A_(12) =-3 \n A_(21)=2 \n A_(22) =4$ . Then $A^(-1) = (1)/(2) \left[\begin{array}{cc}-1&-3\n2&4\end{array}\right] ^(T)= \left[\begin{array}{cc}- (1)/(2) &1\n- (3)/(2) &2\end{array}\right]$ ;
3. Calculate $X= \left[\begin{array}{cc}- (1)/(2) &1\n- (3)/(2) &2\end{array}\right] \left[\begin{array}{c} -12\n-3\end{array}\right]=$ $\left[\begin{array}{c}3\n12\end{array}\right]$ ;

4. We obtain $X= \left[\begin{array}{c}3\n12\end{array}\right]$ , from where x=3 and y=12.

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A store sells a gallon of milk for $3.A baker buys 30 gallons of milk for his bakery.How much will he have to pay?

Answers

$3 x 30 gallons of milk = $90

90 because 30 x 3 = 90

Mr. Walker was hiking across Massachusetts. He has three days to cover 70 miles. On the first day, he walked 6 hours at a speed of 4 mph. On the second day he walked the same number of hours, but his speed was only 3 mph. On the third day, he walked 8 hours to cover the remaining distance. What was his speed on the third day?

Answers

so 6 hours at 4 miles per hour
4 miles per hour means 4 mieles in one hour
6 hours
distance=time times (distance pers unit of time)
distance=6 times 4=24

second day
same number of hours=6
speed=3

distance=time times (distance per units of time)
distance=6 times 3=18

so we add 1 and 2 days together
24+18=42
so he has covered 42 mles
he eed to cover 70
70=42+rest
subtract 42
28=rest

so he traveled 28 miles on third day
in 8 hours
sppeed=distance divided by time
time=8
distance=28
28/8=14/4=7/2=3 and 1/2 miles per hour=3.5 miles per hour

answer is 3.5 miles per hour

If 5 friends want to share 1.25 of a pizza evenly, how mauch pizza would each person get?

Answers

Answer:

Each person will get .25 of a pizza

Step-by-step explanation:

Take the amount of pizza and divide by the number of people who want to share

1.25/5

.25

Each person will get .25 of a pizza

Answer:

.25 or 1/4

Step-by-step explanation:

You divide 1.25 and 5

Is 0.6 greater or less than 0.60

Answers

it is same because if u see there is 0 behind 0.6 but u can't see it so it is equal

It is the same. Even though you put a 0 in the end can't change the number

ITS A MULTI CHOSE QUESTION!! And help as fast as you can! Thank you

Answers

Answer:

Step-by-step explanation:

What is 3x - 20 + 40

Answers

3x-20=-40
3x=-40+20
3x=-20
X=-20/3

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