Answers:
So the solution is (x,y) = (4, -1)
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Work Shown:
6x + 7y = 17
6x + 7( y ) = 17
6x + 7( -3x+11 ) = 17 ... replace every copy of y with -3x+11
6x - 21x + 77 = 17
-15x = 17-77
-15x = -60
x = -60/(-15)
x = 4
We'll use this x value to find y
y = -3x+11
y = -3(4)+11 ... replace x with 4
y = -12+11
y = -1
We have x = 4 and y = -1 pair up together to give us the solution (x,y) = (4, -1)
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To check the solution, we plug x = 4 and y = -1 into each equation
Plugging the values into the first equation leads to...
y = -3x+11
-1 = -3(4)+11
-1 = -1
This is effectively already done in the last part of the previous section. But it doesn't hurt to verify like this regardless.
We'll need to verify the second equation as well.
6x + 7y = 17
6(4) + 7(-1) = 17
24 - 7 = 17
17 = 17
We get a true equation, so the solution is confirmed with both equations. Overall, the solution to the system of equations is confirmed. This system is independent and consistent.
Answer:
The measurement of EF is 1.98 units
Step-by-step explanation:
In Δ DEF
∵ m∠E = 90°
∴ FD is the hypotenuse of the triangle
∵ m∠D = 26°
∵ EF is opposite to angle D
- We can use the sine ratio to find it
∵ sin D = 
⇒ (opposite side / hypotenuse)
∵ FD = 4.5 units
∴ sin(26) = 
- Multiply both sides by 4.5
∴ 4.5 sin(26) = EF
∵ sin 26° ≈ 0.44
∴ 4.5(0.44) = EF
∴ 1.98 = EF
The measurement of EF is 1.98 units
Volume=length times width times height
this should be easy
a.
the volume of a box is 2.5 times 1 times 1 or 2.5 cubic meters
b.
number of boxes times volume per box=volume of container
number of boxes=volumecontainer/volumebox
find volumecontianer
volumecontainer=5 times 2 times 3=30 cubic meters
number of boxes=30/2.5
number of boxes=12
12 boxes needed to fill container
c.
box
1m=100cm
1m by 1m by 2.5m convert so (times everybody by 100)
100cm by 100cm by 250cm
multiply
2,500,000 cubic centimeters
Step-by-step explanation:
for some reason the equation at the top says 7(x+2) but both of the equations at the bottom say 7(x-2)... I'm just going to do 7(x-2)
Emmanuels Work:
7(x-2)=91
distribute the 7 by multiplying both x and -2 by it
7x-14=91
add 14 to both sides
7x=105
divide both sides by 7
x=15
Mauricio's Work:
7(x-2)=91
to get rid of the 7 multiplication, divide both sides by 7
x-2=13
add 2 to both sides
x=15
Okay so what we know is that there are 6 sides.
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3separate groups have the same measurements. So really 3 groups of 2 that have the same measurements.
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2 sides are 3*2 —————>an area of 6
2 sides are 3*2—————>an area of 6
2 sides are 2*2—————>an area of 4
—————————————————————so, we add those #s up and get 6+6+4 which equals 16 as your answer.
