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3 years ago

If y varies directly with x when y=8,x=20 find the value of x when y=42

Mathematics

1 answer:

Alecsey [184]3 years ago

5 0

The value of x is 105 when y=42

Step-by-step explanation:

A direct proportion means that the change in one quantity will also cause the change in other quantity

Given

y varies directly with x

x ∝ y

when the proportionality symbol is removed a proportionality constant is introduced

$x=ky\\k=\frac{x}{y}\\Putting\ y=8\ and\ x=20\\k=\frac{20}{8}\\k = \frac{5}{2}\\So,\ the\ equation\ will\ be\\x=\frac{5}{2}y\\Putting\ y=42\\x=\frac{5}{2}*42\\x=5*21\\x= 105$

The value of x is 105 when y=42

Keywords: Proportion, Direct variation

Learn more about proportion at:

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The ratio table below shows the relationship between the number of packages of gum and the total pieces of gum.

tangare [24]

The complete question is

"The ratio table below shows the relationship between the number of packages of gum and the total pieces of gum.

Gum Packages of gum Pieces of gum

How many pieces of gum are in 4 packages of gum?"

Using a proportional function, there are 60 pieces of gum in 4 packages.

<h3>What is a proportional relationship?</h3>

Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

The constant is given by:

k = 15/1

k = 30/2

k = 45/3

k = 15.

Therefore, the number of pieces of gums in x packages is given by:

y = 15x.

In 4 packages:

y = 15 x 4

y = 60 pieces of gum.

Using a proportional function, there are 60 pieces of gum in 4 packages.

More can be learned about proportional functions at brainly.com/question/10424180

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4 0

2 years ago

What is the solution of 5/2-7= 3/4x+14,

Sidana [21]

Answer:

D) x = 12

Step-by-step explanation:

Given:

$\sf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 \implies \dfrac{10}{4}x-7=\dfrac{3}{4}x+14}$

1. Multiply both sides by 4

$\sf{4\left(\dfrac{10}{4}x-7\right)=4\left(\dfrac{3}{4}x+14\right)}\\\\\implies 10x-28=3x+56$

2. Subtract 3x from both sides

$\sf{10x-3x-28=3x-3x+56}\\\\\implies 7x-28=56$

3. Add 28 to both sides

$\sf{7x-28+28=56+28}\\\\\implies 7x=84$

4. Divide both sides by 7 to isolate the variable:

$\sf{\dfrac{7x}{7}=\dfrac{84}{7}}\\\\\implies x=12$

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brainly.com/question/27844194

3 0

2 years ago

There are 10 men and 14 women in.Kthleen's math class.what is the ratio of women to the total number of students in the class?

ahrayia [7]

The ratio can be determined as,

$\begin{gathered} \text{Ratio}=\frac{14}{10+14} \\ =\frac{14}{24} \\ =\frac{7}{12} \end{gathered}$

Thus, the requried ratio is 7:12.

3 0

1 year ago

3 Ramón makes nectar for a hummingbird feeder by mixing 8 cups of water with 2 cups of sugar. Tiffany makes nectar by mixing 9 c

Butoxors [25]

Answer:

Tiffany's nectar is more sugary

Step-by-step explanation:

Given

Ramon:

$Water = 8\ cups$

$Sugar = 2\ cups$

Tiffany

$Water = 9\ cups$

$Sugar = 3\ cups$

Required

The nectar with more sugar

To do this, we simply calculate the fraction of sugar in both nectar.

This is calculated as:

$Fraction = \frac{Sugar}{Sugar + Water}$

For Ramon:

$Fraction = \frac{2}{8 + 2}$

$Fraction = \frac{2}{10} = 0.20$

For Tiffany

$Fraction = \frac{3}{3 + 9}$

$Fraction = \frac{3}{12} = 0.25$

From the calculations above:

$0.25 > 0.20$

Hence: Tiffany's nectar is more sugary

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3 years ago

Use the distributive property to simplify this expression -2x(3x + x-5)

kvasek [131]

Answer:

− 8 x ^2 + 10 x

Step-by-step explanation:

8 0

2 years ago

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