The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 8 cases and its height are shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 13 cases.
Answers
Answer:
a. The equation is y = 19 x
b. The height of 13 DVD cases is 247 mm
Step-by-step explanation:
- A proportional relationship is about two quantities vary directly with
each other
- Ex: If y proportion to x, then y is varies directly with x
That means y ∝ x ⇒ y = k x, where k is the constant of variation
- The height of a stack of DVD case is proportional to the number of
case in the stack
- That means the height of DVD cases varies with the number of cases
- The height of 6 DVD case is 114 mm
a.
∵ The number of cases = x
∵ The height of the cases = y
∴ y ∝ x
∴ y = k x
- To find k lets use the first information above
∵ y = 114 mm when x = 6
- Substitute these values in the equation above to find k
∵ 114 = 6 k
- Divide both sides by 6
∴ k = 19
- Substitute the value of k in the equation above
∴ y = 19 x
* The equation is y = 19 x
b.
- We need to find the height of 13 DVD cases
∵ y = 19 x
∵ x = 13
- Substitute the value of x in the equation
∴ y = 19 × 13
∴ y = 247 mm
* The height of 13 DVD cases is 247 mm
The height will be 143 mm for a stack of 13 DVD cases.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
The overall height of the 8 cases stacked on top of each other is 88 mm.
Because you need to know the height of each individual DVD case, divide the height (88 mm) by the number of DVD cases (8):
⇒ 88/ 8 = 13
⇒ 88 ÷ 8 = 13
Then it asks for the height of a stack of 13 cases, so multiply the 11 (the height of each DVD case) by 13:
11 × 13= 143
Therefore, 13 DVD cases stacked on top of each other have a height of 143 mm.
To learn more about the constant of proportionality here:
https://brainly.com/question/17302514
#SPJ2
The question seems to be incomplete the correct question would be:
The height of a stack of DVD cases is in proportional relationship to the number of cases in the stack. A stack of 8 cases and its height is shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 13 cases.
The height of the 8 cases stacked on top of each other is 88 mm.
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Step-by-step explanation:
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Answer:
[tex]\sqrt{\frac{5}{3} }[/tex]
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Solve for AB. Round your answer to the nearest tenth if necessary.
Answers
Answer:
See Below
Step-by-step explanation:
You want to find AB.
They give the equation for AB, BC, and AC
AC - BC = AB
substitute the equations
(30) - (8x + 3) = 6x + 8
30 - 8x - 3 = 6x + 8
27 - 8x = 6x + 8
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27 = 14x + 8
-8 -8
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19/14 = 14x/14
1.3571428 = x
0.1 = tenth
1.4 = x
Substitute x into the equation for AB
6(1.4) + 8
16.4
[tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]
______________________________
[tex]\bold{Solution~Steps:}[/tex]
[tex]1.)~First~you~need~to~make~an~equation:[/tex]
[tex]\bold{30-8x+3=6x+8}[/tex][tex]\bold{You~do~this~by~using~all~the~information~available~and~set~it~up~to~solve~for~AB.}[/tex][tex]2.)~Add~30~and~3~to~get~33:[/tex]
[tex]\bold{33-8x=6x+8}[/tex][tex]3.)~Subtract~6x~from~both~sides:[/tex]
[tex]\bold{33x-8x-6x=8}[/tex][tex]\bold{Causes~signs~to~change~and~the~equation~gets~rearranged.}[/tex][tex]4.)~Combine -8x~and~-6x:[/tex]
[tex]\bold{-8x-(-6x)=-14x}[/tex][tex]\bold{33-14x=8}[/tex][tex]5.)~Subtract~33~from~both~sides:[/tex]
[tex]\bold{33-33=Cancels~out}[/tex][tex]\bold{8-33=-25}[/tex][tex]5.)~Divide~both~sides~by~-14:[/tex]
[tex]\bold{-14x}[/tex] ÷ [tex]\bold{-14=x}[/tex][tex]\bold{-25}[/tex] ÷ [tex]\bold{-14=-1.78571429}[/tex][tex]6.)~Simplify:[/tex]
[tex]\bold{1.78571429}~(Take~Away~the~Negative!)[/tex][tex]\bold{1.8}~(Round~to~the~Nearest~Tenth!)[/tex][tex](To~Round~look~at~that~number~in~the~tenth~place:~7,\\~now~look~to~the~number~to~the~right:~8.~\\\\So~if~that~number~is~greater~than~or~equal~to~5,~then~you~round~up.\\If~that~number~is~less~than~or~equal~to~5,~then~you~round~down.)[/tex]
______________________________
[tex]\bold{Answer:}[/tex]
[tex]\bold{AB=1.8}[/tex]______________________________
[tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~-TotallyNotTrillex}[/tex]
joe needs to transfer 28 quarts of oil into containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error
Answers
This question is incomplete
Complete Question
Joe needs to transfer 28 quarts of oil into gallons containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error
Joe's error:
28 quarts × 4 quarts/ 1 gallon
= 28 quarts/1 × 4 quarts/ 1 gallon
= (28 × 4)/ ( 1 × 1) = 112 gallons
Answer:
7 gallons is the correct answer
Joe needs to transfer 28 quarts of oil into 7 gallons
Step-by-step explanation:
Joe's error:
28 quarts × 4 quarts/ 1 gallon
= 28 quarts/1 × 4 quarts/ 1 gallon
= (28 × 4)/ ( 1 × 1) = 112 gallons
Correcting Joe's error, we have:
4 quarts = 1 gallon
28 quarts = x
Cross Multiply
4 quarts × x = 28 quarts × 1 gallon
x = 28 quarts × 1 gallon/ 4 quarts
x = 7 gallons
= 28 quarts/x gallons × 1 gallon/4 quarts
= (28 × x)/ ( 1 /4) = 7 gallons
Therefore, Joe needs to transfer 28 quarts of oil into 7 gallons
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
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Answers
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Step-by-step explanation:
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Answers
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Answers
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Answer:
Step-by-step explanation:
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Answers
Answer:
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Blank 2: (2xy+3)(4x-5)
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Answers
Answer:
total cost = $110
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Answers
7.2
Step-by-step explanation:Hi there !
10.7 + (-3.5) =
= 10.7 - 3.5
= 7.2
Good luck !