Point A is the midpoint of side XZ and point B is the midpoint of side YZ. Triangle X Y Z is cut by line segment A B. Point A is
the midpoint of side X Z and point B is the midpoint of side Y Z. The length of X Y is 5 x minus 7, the length of A B is x + 1, and the lengths of X A and Z A are 2 x minus 2. The lengths of Y B and B Z are congruent. What is AX? 2 units 4 units 6 units 8 units
1 answer:
Answer:
<h3>B. 4units</h3>Step-by-step explanation:
Find the diagram attached. The diagram is a similar triangle.
From the diagram, XZ/XY = CA/AB
Given XZ = 2x-2+2x-2 = 4x-4
XY =5x-7
CA = 2x-2
AB= x+1
On substituting this parameters into the formula to get x first
4x-4/5x-7 = 2x-2/x+1
cross multiply
(4x-4)(x+1) = 5x-7(2x-2)
open the parenthesis
4x²+4x-4x-4 = 10x²-10x-14x+14
4x²-4 = 10x²-24x+14
10x²-4x²-24x+14+4 = 0
6x²-24x+18 = 0
x²-4x+3 = 0
x²-3x-x+3 = 0
x(x-3)-1(x-3) =0
(x-3)(x-1) = 0
x = 3 and 1
Next is to get length AX.
Given AX = 2x-2
Substitute x = 3 into the expression
AX = 2(3)-2
AX = 6-2
AX = 4 units
Hence the measure of length AX is 4 units
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Answer:
You would expect 75 cartons with at least 1 broken egg.
There are likely to be 222 DVD players that are defective.
Step-by-step explanation:
Both examples given in this question represent a ratio of broken or defective to a sample number of cartons or DVD players. In order to find how many would be broken or defective overall, you can set up equivalent ratios, or proportions.
Egg Cartons:
'x' represents the number of cartons out of 500 that would be expected to have at least 1 broken egg. To solve for 'x' you can cross-multiply and divide, or you can find what factor you would multiply the denominator by to get 500 and then multiply the same factor by the numerator to find 'x'. In this case 500/20 = 25, so the factor is 25. 3 x 25 = 75, so you have 75 expected cartons with a broken egg.
DVD Players:
'x' represents the number of DVD players out of 3700 that would be expected to be defective. To solve for 'x' you can cross-multiply and divide, or you can find what factor you would multiply the denominator by to get 3700 and then multiply the same factor by the numerator to find 'x'. In this case 3700/50 = 74, so the factor is 74. 3 x 74 = 222, so you have 22 likely defective DVD players.