Answer: Choice B
(-2, 5)
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Explanation:
The original system is
Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations
Now add straight down
The x terms add to -4x+3x = -1x = -x
The y terms add to 3y+(-3y) = 0y = 0
The terms on the right hand sides add to 23+(-21) = 2
We end up with the equation -x = 2 which solves to x = -2
Now use this to find y. You can pick any equation with x,y in it
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-4x+3y = 23
-4(-2)+3y = 23
8+3y = 23
3y = 23-8
3y = 15
y = 15/3
y = 5
Or
x-y = -7
-2-y = -7
-y = -7+2
y = -5
y = 5
Either way, we get the same y value.
So that's why the solution is (x,y) = (-2, 5)
<h3>
Answer: 3/5</h3>
Work Shown:
3 blue + 3 red = 6 pens that are either blue or red
4 black + 3 blue + 3 red = 10 pens total
6/10 = 3/5 is the probability of selecting either blue or red
3/5 = 0.60 = 60%
Answer:
90 degree rotation in the clockwise direction.
Step-by-step explanation:
Point A transforms to A'
- that is x coordinate: 2 ---> 3
and y coordinate 3 ---> -2
So the rotation is clockwise from Quadrant1 to Quadrant 4.
The slope of OA = 3/2 and the slope of OA' = -2/3.
The product of these slopes = 3/2 * -2/3 = -1 so the lines are perpendicular - that is the line has passed through an angle of 90 degrees.
A similar result occurs if we consider points B, C and D.
Answer:
52 cm
Step-by-step explanation:
Use the pythagorean theorem to solve for missing sides in a right triangle.
20²+48²= missing side
20²+48²=2704
Take the square root of 2704 to get the missing side.
