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schepotkina [342]
3 years ago
11

Julia has 2 identical rooms in her house. If each room measures 8 feet on one side and 12 feet on another, what is the total are

a of the rooms?
Mathematics
1 answer:
levacccp [35]3 years ago
6 0
L = 12 ft
W = 8 ft
One room has area:
A1 = L · W = 12 · 8 = 96 ft²
The total area of rooms:
A = 2 · 96 = 192 ft² 
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Solve the system of equations: <br> X+y+z=5<br> -3x-4y+4z=15<br> 2x-y-4z=-8
atroni [7]

Answer:

  (x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

  z = 5 -(3 +(-2)) = 4

The solution is (x, y, z) = (3, -2, 4).

__

Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

  \left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]

__

If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

  -3x -4y +4(5 -x -y) = 15   ⇒   -7x -8y = -5

  (-3x -4y +4z) +(2x -y -4z) = (15) +(-8)   ⇒   -x -5y = 7

This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...

  -7(-5y -7) -8y = -5   ⇒   27y = -54   ⇒   y = -2

  x = -5(-2) -7 = 3

  z = 5 -(3) -(-2) = 4

_____

<em>Additional comment</em>

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.

6 0
2 years ago
If DM = 35, what is the value of r?
Gennadij [26K]

Answer:

r = 11

Step-by-step explanation:

Given

DM = 35

DG = r + 5

GM = 3r - 14

Required

Find r

From the question, we understand that G is a point between D and M:

This implies that:

DM = DG + GM

Substitute values for DM, DG and GM

35 = r + 5 + 3r - 14

Collect Like Terms

r + 3r = 35 - 5 + 14

4r = 44

Solve for r

r = 44/4

r = 11

3 0
3 years ago
I need help the question is on the picture
Genrish500 [490]

Answer:

Blank 1: 12.5 mph

Blank 2: .36 hours

Step-by-step explanation:

1. 3.75/.3 = 12.5

2. 4.5/12.5 = .36

7 0
2 years ago
A limousine company charges a flat fee of $35 plus $2 per mile to ride a limousine. Write an equation in slope intercept-form wh
Anna35 [415]

Answer:

y=2x+35

Step-by-step explanation:

so y is what it's equal too so you put y=

then since its $2 every mile you put them next to eachother like

2x so y=2x

then there is just a plain fee of $35 so you add that to the equation which is what makes it look like

y=2x+35

Hope this helps!! :D

5 0
3 years ago
Use the distributive property to remove the parentheses. -6(2v - 4w-6)​
lilavasa [31]
Just multiple. -12v+24w+35
7 0
3 years ago
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