Find the sum. Enter your answer in simplest terms, using the slash (/) as the fraction bar.

Mathematics

1 answer:

disa [49]3 years ago

4 0

Step-by-step explanation:

the answer is in the picture

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Suppose that y varies directly with x and y=10 when x=20. What is y when x=15

Likurg_2 [28]

Answer:

y=kx

subst y=10 and x=20 into the above

10=k20

k=10/20

k=1/2

therefore relationship: y=1/2x

subst x=15 into the relationship

y=1/2(15)

y=7,5

Step by step explanation:

Step 1: when they say y varies directly with x they mean y is proportional to x
step 2: so y=kx where k is the constant
step 3: is to substitute y=10 and x=20 into the above equation y=kx
step 4: you will end up with 10=k20 then divide both sides by 20 so that k becomes the subject of the formula 
step 5: your answer from the above will be k=10/20 so the relationship is y is directly proportional to 1/2 x what you did here is that you substituted k for 1/2 in the equation in step 3
step 6: is to finally substitute x=15 into the equation y=1/2x to finally get your answer y=7,5.

4 0

3 years ago

the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions

KIM [24]

Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft