The solution to the system of equations is: (1, -8).
<h3>How to Find the Solution to a System of Equations?</h3>
The solution is the coordinate of the point where both lines of the equations meet.
Second equation: 3y + 30 = 6x, rewrote in slope-intercept form:
3y = 6x - 30
y = 6x/3 - 30/3
y = 2x - 10 --> eqn. 1
Find the slope (m) and y-intercept (b) of the first graphed equation:
Slope (m) = change in y/change in x = rise/run = -4/2 = -2
The line intersects the y-axis at y = -6, so, the y-intercept, b = -6.
The first equation would be: y = -2x - 6 ---> eqn. 2
Subtract eqn. 2 from eqn. 1 to eliminate x
y = 2x - 10 --> eqn. 1
y = -2x - 6 ---> eqn. 2
2y = 0 - 16
2y = -16
y = -16/2
y = -8
Substitute y = -8 into eqn. 1 to find x:
-8 = 2x - 10
-8 + 10 = 2x
2 = 2x
2/2 = x
1 = x
x = 1
The solution is therefore: (1, -8).
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Answer:
x = 59°
y = 67°
Step-by-step explanation:
x = y - 8
x + y + 54 = 180
(y - 8) + y = 180 - 54
2y - 8 = 126
2y = 134
y = 67°
x = 59°
Step-by-step explanation:
Given:
The composite figure.
To find:
The volume of the given composite figure.
Solution:
Given composite figure contains a cuboid and a pyramid.
Length, breadth and height of the cuboid are 8, 6 and 4 respectively.
Volume of a cuboid is
Length and breadth of the pyramid is same as the cuboid, i.e., 8 and 6 respectively.
Height of pyramid = 10 - 4 = 6
Volume of a pyramid is
The volume of composite figure is
It can be written as
Therefore, the correct option is A.
The correct answer to your question is k=5 .