Casey is 18 years old and Ralph is 3 years old.
Step-by-step explanation:
Let,
Age of Casey = x
Age of Ralph = y
According to given statement;
x = 6y Eqn 1
In two years
x+2=4(y+2)
x+2=4y+8
x = 4y+8-2
x = 4y+6 Eqn 2
Putting value of x from Eqn 1 in Eqn 2

Dividing both sides by 2

Putting y=3 in Eqn 1

Casey is 18 years old and Ralph is 3 years old.
Keywords: word problems, substitution method
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Answer:
beam, vault, uneven bars, floor
Step-by-step explanation:
<u><em>The complete question is</em></u>
A group of gymnasts were asked to name their favorite piece of equipment. 0.33 of the gymnasts chose the vault, 4/9 chose the beam, 0.08 chose the floor exercise, and 1/7 chose the uneven parallel bars. List their choices in order of preference from greatest to least.
step 1
Convert 4/9 and 1/7 to decimals in order to compare with the other values
4/9=0.44
1/7=0.14
step 2
Compare the values
0.44 > 0.33 > 0.14 > 0.08
therefore
The order of preferences from greatest to least is
beam, vault, uneven bars, floor
F - 12 = -35
f - 12 + 12 = -35 + 12
f = -23
The slope of KH is 1
The slope of GJ is -1
The product of the slopes of the diagonals is -1
Therefore, KH is perpendicular to GJ