Answer:
a) x = 12 y = 9
b) x = -2 y = -4
c) x = 6 y = -2
Step-by-step explanation:
a)
Equation 1: 6x - 7y = 9
Equation 2: 3x + 2y = 54
Multiply Equation 2 by 2:
⇒ 6x + 4y = 108
Subtract equations:
6x + 4y = 108
<u>- 6x - 7y = 9 </u>
11y = 99
Divide both sides by 11:
⇒ y = 9
Substitute found value of y into Equation 1 and solve for x:
⇒ 6x - 7(9) = 9
⇒ 6x - 63 = 9
⇒ 6x = 72
⇒ x = 12
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b)
Equation 1: 4x - 5y = 12
Equation 2: 2x - 3y = 8
Multiply Equation 2 by 2:
⇒ 4x - 6y = 16
Subtract equations:
4x - 6y = 16
<u>- 4x - 5y = 12 </u>
-y = 4
Divide both sides by -1:
⇒ y = -4
Substitute found value of y into Equation 1 and solve for x:
⇒ 4x - 5(-4) = 12
⇒ 4x + 20 = 12
⇒ 4x = -8
⇒ x = -2
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c)
Equation 1: 4x - 2y = 28
Equation 2: 3x + 3y = 12
Multiply Equation 1 by 3:
⇒ 12x - 6y = 84
Multiply Equation 2 by 4:
⇒ 12x + 12y = 48
Subtract equations:
12x - 6y = 84
<u>- 12x + 12y = 48 </u>
-18y = 36
Divide both sides by -18:
⇒ y = -2
Substitute found value of y into Equation 1 and solve for x:
⇒ 4x - 2(-2) = 28
⇒ 4x + 4 = 28
⇒ 4x = 24
⇒ x = 6
Hello!
A triangle is 180 degrees, and you are given one of the angles, which is ∠P = 26 degrees.
Angle Q is a right angle, and this triangle is therefore a right triangle, so one angle has to be 90 degrees, and the other two angles are acute.
So we can create a simple equation:
m∠P + m∠Q + m∠x = 180 degrees
26 + 90 + m∠x = 180
116 + m∠x = 180
-116 - 116
m∠x = 64 degrees.
The measure of angle x is equal to 64 degrees, which is the fourth choice.
Answer: Choice A. 
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Explanation:
Every point in the shaded region has an x coordinate that is equal to -7 or smaller.
Example points include
The y coordinate does not matter. All that matters is the x coordinate. The boundary line is the equation x = -7, representing all points that have x coordinate of -7. The solid boundary line says to the reader "any point on this boundary line is part of the shaded region solution set". This inclusion is due to the "or equal to" of the inequality sign.
To find the volume of a triangular pyramid, the formula is:
So we start by finding the area of the base, which is in the shape of a right triangle in this case.
The area of a right triangle is equal to 1/2 x base x height.
We use this area to find the volume.
The volume of the triangular pyramid is 30 cubic feet.
