Answer:
(-1, -1) Let me know if the explanation didn't make sense.
Step-by-step explanation:
If we graph the three points we can see what looks like a quadrilateral's upper right portion, so we need a point in the lower left. This means M is only connected to N here and P is only connected to N. So we want to find the slope of these two lines.
MN is easy since their y values are the same, the slope is 0.
NP we just use the slope formula so (y2-y1)/(x2-x1) = (-1-3)/(5-4) = -4.
So now we want a line from point M with a slope of -4 to intersect with a line from point P with a slope of 0. To find these lines weuse point slope form for those two points. The formula for point slope form is y - y1 = m(x-x1)
y-3 = -4(x+2) -> y = -4x-5
y+1 = 0(x-5) -> y = -1
So now we want these two to intersect. We just set them equal to each other.
-1 = -4x -5 -> -1 = x
So this gives us our x value. Now we can plug that into either function to find the y value. This is super easy of we use y = -1 because all y values in this are -1, so the point Q is (-1, -1)
Answer:
x = 65, y = 63
Step-by-step explanation:
∠ EGA = ∠ HBG = 52° ( corresponding angles )
ED is a straight angle, thus
52 + y + 65 = 180, that is
y + 117 = 180 ( subtract 117 from both sides )
y = 63
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∠ HGB = y = 63° ( vertical angles )
The sum of the 3 angles in a triangle = 180°, thus
x + 63 + 52 = 180
x + 115 = 180 ( subtract 115 from both sides )
x = 65
If all were dimes, the value would be $3.30. Brendan has $2.85 more than that. Each quarter that replaces a dime increases the value by $0.15, so Brendan must have $2.85/$0.15 = 19 quarters.
Brendan has 14 dimes and 19 quarters.
The angles of a triangle always add up to 180°.
By simply adding the angles and checking the total, you can tell if they make a triangle or not.
Using this property, 5 won't make a triangle, 6 will.
Hope this helps! :D
