The perimeter of a rectangle is 36 inches. If the width of the rectangle is 6 inches, what is the length?A.30 inches
B.24 inches
C.18 inches
D.12 inches

Answers

Answer 1

Answer: $P=2(w+l)$
P - perimeter
w - width
l - length

$P=36 \ in \nw=6 \ in \n \n36=2(6+l) \n36=12+2l \n36-12=2l \n24=2l \nl=(24)/(2) \n l=12$

The answer is D. 12 inches.

Answer 2

Answer:

P=36in, W=6in.

The width of the rectangle is 6 for one side and 12 total for both. So 36-12 is 24. That means the length total has to be 24 and that would be 12.

So the answer is D.12 inches.

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Matthew scored a total of 168 points in basketball this season. He scored 147 of those in the regular season, and and the rest were scored in his only playoff game. What percent of his total points did he score in the playoff game?

Answers

Answer:

Matthew scored 12.5% of his points in the playoff game.

Step-by-step explanation:

1. First write the total points that Matthew scored in basketball this season:

Total points = Points in regular season + Points in only playoff game (Eq.1)

Total points = 168

2. Then find the points he scorred in his only playoff game.

As he scored 147 points in the regular season, the points scored in his only playoff game will be found using the Eq. 1:

Points in regular season = 147

Total points = Points in regular season + Points in only playoff game (Eq.1)

168 = 147 + Points in only playoff game

Solving for Points in only playoff game:

Points in only playoff game = 168 - 147

Points in only playoff game = 21

Therefore Matthew scored 21 points in the playoff game.

3. Find the percent of the total points Matthew scored in the playoff game:

$Percent=(Pointsintheplayoffgame)/(Totalpoints)$

$(21)/(168)*100=12.5%$

To find the percent we do:
168-147=21 points scored in the playoff
21/168=0.125
0.125*100=12.5%
The percentage is 12.5%.

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

Answers

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.

A recipe calls for 3 cups of sugar and 9 cups of water. How many cups of water should be used with 2 cups of sugar?

Answers

First you do 9/3
9 divided by 3 is 3
This means there is 3 cups of water for every cup of sugar
Then do 2 times 3
You would need 6 cups of water to go with 2 cups of sugar

since 3cups = 9cups ... and they are asking how much water would go in 2cups of sugar .. then the answer would be ..
6cups of water

because you cross multiply.

Inside a rectangle ABCD with AB = 10 cm and BC = 5cm constructed a square and a triangle ABMN ECB rectangle with equal sides. Find the perimeter of the new figures