<h3>
Answer: 0.5</h3>
This is equivalent to the fraction 1/2
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Explanation:
The distance from A to B is 3 units. We can count out the spaces, or subtract the x coordinates of the two points and apply absolute value.
|A-B| = |-5-(-8)| = |-5+8| = |3| = 3
or
|B-A| = |-8-(-5)| = |-8+5| = |-3| = 3
We can say that segment AB is 3 units long.
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The distance from A' to B' is 1.5 units because...
|A'-B'| = |-2.5-(-4)| = |-2.5+4| = |1.5| = 1.5
or
|B'-A'| = |-4-(-2.5)| = |-4+2.5| = |-1.5| = 1.5
The absolute values ensure the distance is never negative.
We can say A'B' = 1.5
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Now divide the lengths of A'B' over AB to get the scale factor k
k = (A'B')/(AB)
k = (1.5)/(3)
k = 0.5
0.5 converts to the fraction 1/2.
The smaller rectangle A'B'C'D' has side lengths that are exactly 1/2 as long compared to the side lengths of ABCD.
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116
Answer:
y=2x+5
Step-by-step explanation:
Let's solve for y.
−2x+y=5
Step 1: Add 2x to both sides.
−2x+y+2x=5+2x
y=2x+5
The first thing we must do for this case is to look for the area of each rectangle.
We have then:
A1 = (40) * (x)
A2 = (1.25 * 40) * (y)
Then, we have the following relationship between areas:
"the area of Q is 10% less than the area of p"
A2 = 0.9 * A1
Substituting values we have:
(1.25 * 40) * (y) = 0.9 * ((40) * (x))
We rewrite:
50y = 36x
The relationship x: y is:
x / y = (50) / (36)
Simplifying:
x / y = (25) / (18)
Answer:
the ratio of x:y is:
25:18
