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.
Related Questions
8^ 1/3 what is it simplified
Answers
Step-by-step explanation:
Simplifying mixed numbers
Following are the steps to simplify mixed fractions: Find the highest common factor (HCF) of numerator and denominator of the fraction part. Divide both the numerator and the denominator by HCF. The whole number part will remain the same.
Answer:
8^1/3= 2
:-))))
Which is an irrational number?
Answers
Answer:
[tex]\sqrt{\frac{5}{3} }[/tex]
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal. [tex]\sqrt{\frac{5}{3} }[/tex] is irrational.
Hope this helps! o(〃＾▽＾〃)o
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
+8x +8x
27 = 14x + 8
-8 -8
19 = 14x
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]
-2(39% + **)+(855 + 2K)
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Step-by-step explanation:
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answer in picture
Step-by-step explanation:
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Answer:
b
Step-by-step explanation:
used a calucator
Need help asap
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Answers
Answer:
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Step-by-step explanation:
2xy+15x
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2(-4)(-9) + 15(-4)
Multiply
72 -60
Subtract
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Answer:
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Step-by-step explanation:
2(4)(-9)+15(4) is what it should look like.
What is the displacement of the red ball between 0 s and 24 s
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Please help fast
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Answers
Answer:
The resulting line will be the same for all three because the verbal statement, the equation, and the table all represent the same situation. They just do it in different ways.
Answer:
The resulting line will be the same for all three because the verbal statement, the equation, and the table all represent the same situation. They just do it in different ways.
Step-by-step explanation:
Lana uses factoring by grouping to factor the polynomial 8x2y−10xy2+12x−15y. Her work follows, but the last two lines of work are missing.
Which answers correctly fill in the blanks?
Select two answers: one for blank 1 and one for blank 2.
Answers
Answer:
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Blank 2: (2xy+3)(4x-5)
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The only correct answer are:
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Blank 2: (2xy+3)(4x-5)
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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 !
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Answer:
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12 in
x =
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Answers
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Step-by-step explanation: Hopefully this helped a lot ;D
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Answers
Answer:
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Step-by-step explanation:
It says Jenny ran 5 more miles than last week so you find the number from last week then add 5. X is the miles she ran this week
Answer:
t + 5
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In this problem, you have to recognize what the information is telling you in terms of the vocabulary used. For example, the first sentence tells us that she ran 5 more miles than last week. This is key because it lets us know that our expression will have an addition sign.
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Answers
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Answers
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Step-by-step explanation:
Find the GCF of the terms of the polynomial.
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Answers
Answer:
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WILL GIVE BRAINLIEST
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angle measurements of 30°, 409, and 50°
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
Answers
Answer:
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
Step-by-step explanation:
At the gym, Garson always completes 3 pull-ups for every 8 sit-ups he does. Last night, Garson completed 24 sit-ups. Which ratio represents the relationship between the number of pull-ups and the number of sit-ups Garson completed last night?
Answers
Answer:
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Step-by-step explanation:
3:8
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Answers
Answer:
Pretty sure its 525.74
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Answers
Answer:
$1.92 a gallon!!
Step-by-step explanation:
Answer:
You will pay $1.92 per gallon.
Step-by-step explanation:
Divide 25.00 by 13 to by how much money per gallon:
[tex]25.00/13=1.923[/tex]
You cannot round up.
You will pay $1.92 per gallon.
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You deposited a check for $1,200 into your checking account that had a balance of $625 and it "bounced". You had written checks for $450, $225, $215, and $187. Your bank will pay the largest check that you wrote first. Your account is overdrawn, and the remaining checks written to pay monthly bills did not clear. Your bank charged you a $35 overdraft fee and each of the remaining creditors receiving bounced checks charged you a $25 late payment fee. What did the $1,200 check that "bounced" on you cost you?
Answers
Answer:
total cost = $110
Step-by-step explanation:
Your bank will charge you $35 as overdraft fee.
The bank will only pay one check for $450, so that means that 3 more checks will remained unpaid. Since your creditors charge you $25 per bounced check, then they will charge you 3 x $25 = $75.
Total costs = $35 + $75 = $110
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
PLEASE HELP AND SHOW WORK PLS
Answers
(x=5x) (x+3)
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2x
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x^2+8x+c
Answers
Answer:
16
Step-by-step explanation:
(x + 4)(x + 4)
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x² + 8x + 16
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2) Slope = -1/3, y-intercept = 1
Answers
Answer:
1.) y= 6x+5
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Step-by-step explanation:
Slope Intercept Form is y=mx+b,
where slope is m
the y-intercept is b
So I just plugged in the slope and y-int to get the equation
please help me with this!!!!!
Answers
All you have to do is add up all of the numbers and then yo uwill have your answer