Answer:
1. LI=18
2. x=10
3. Yes (Y)
4. Yes (Y)
5. x=15
6. x=18
7. x=8
8. x=6
y=6.5
Step-by-step explanation:
1. LI/JL=KH/JK
Replacing the given values:
LI/6=21/7
Dividing on the right side of the equation:
LI/6=3
Solving for LI: Multiplying both sides of the equation by 6:
6(LI/6)=6(3)
LI=18
2.TV/VS=RU/US
Replacing the given values:
x/17.5=8/14
Simplifying the fraction on the right side of the equation: Dividing numerator and denominator by 2:
x/17.5=(8/2) / (14/2)
x/17.5=4/7
Solving for x: Multiplying both sides of the equation by 17.5:
17.5(x/17.5)=17.5(4/7)=(17.5/1)(4/7)
Multiplying:
x=(17.5 x 4) / (1 x 7)
x=70/7
Dividing:
x=10
3. BC is parallel to DE if AD/DB is equal to AE/EC:
AD/DB=15/12=(15/3) / (12/3)→AD/DB=5/4
AE/EC=10/8=(10/2) / (8/2)→AE/EC=5/4
Like AD/DB=5/4=AE/EC → BC is parallel to DE
4. BC is parallel to DE if AD/DB is equal to AE/EC:
AD/DB= 2DB / DB→AD/DB=2
AE/EC=30 / (AC-AE)=30 / (45-30)=30/15→AE/EC=2
Like AD/DB=2=AE/EC → BC is parallel to DE
5. If JH is a midsegment of triangle KLM:
x=(1/2)(30)
x=15
6. If JH is a midsegment of triangle KLM:
x=2(9)
x=18
7. If JH is a midsegment of triangle KLM: x=8
8. 2x+1=x+7
Solving for x. Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
2x+1-x=x+7-x
Subtracting:
x+1=7
Subtracting 1 both sides of the equation:
x+1-1=7-1
Subtracting:
x=6
2x+1=2(6)+1=12+1→2x+1=13
x+7=6+7→x+7=13
(3y-8)/(y+5)=(2x+1)/(x+7)
(3y-8)/(y+5)=13/13
(3y-8)/(y+5)=1
3y-8=y+5
Solving for y. Grouping the y's on the left side of the equation: Subtracting y both sides of the equation:
3y-8-y=y+5-y
Subtracting:
2y-8=5
Adding 8 both sides of the equation:
2y-8+8=5+8
Subtracting:
2y=13
Dividing both sides of the equation by 2:
2y/2=13/2
Dividing:
y=6.5
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