Which multiplication problem is modeled on the number line? 2(– 4) 4(2) 2(4) 4(– 2)
2 answers:
4(-2) is modeled on the number line.
Step-by-step explanation:
Step 1:
The multiplication problem's answer is -8, so first, we need to determine which options actually equal the answer.
We individually determine how much each of the options equal.
Step 2:
, option 1 equals -8, so it could be the answer.
option 2 does not equal -8, so it cannot be the answer.
option 3 also does not equal -8, so it cannot be the answer.
option 4 does, so it could be the answer.
Step 3:
In the number line, 4 arrows are equalling -2 every time. So the answer is option 4. .
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Answer:
(A) see below
(B) the right angle is at vertex B(-4,11)
(1) 3x -4y = -46
(E) the midpoint is (-4, 8.5)
Step-by-step explanation:
(A) The slope of line AB is Δy/Δx = (11-7)/(-4-(-6)) = 4/2 = 2. The slope of line BC is (10-11)/(-2-(-4)) = -1/2. The slopes of AB and BC have a product of 2(-1/2) = -1, so are the slopes of perpendicular lines. The points are distinct, and lines joining two pairs of them are at right angles, so the points form a right triangle.
(B) Point B(-4,11) is the point of intersection of perpendicular segments AB and BC, so is the location of the right angle.
(1) The slope of the hypotenuse AC is ...
Δy/Δx = (10-7)/(-2-(-6)) = 3/4
In point-slope form, the equation for the line through point A with this slope is ...
y -7 = 3/4(x +6) . . . . point-slope form of the equation of the hypotenuse
4y -28 = 3x +18 . . . . multiply by 4
-46 = 3x -4y . . . . . . subtract 18+4y
3x -4y = -46 . . . . . . . standard form equation of the hypotenuse
(E) The midpoint of the hypotenuse is the average of the endpoint coordinates:
M = (A + C)/2 = (-6-2, 7+10)/2 = (-4, 8.5)
The midpoint of the hypotenuse is M(-4, 8.5).
