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zmey [24]
2 years ago
10

Proportional relationships, please help!

Mathematics
1 answer:
Vaselesa [24]2 years ago
7 0

Answer:

y = 5/2 x

Step-by-step explanation:

y varies directly with x meaning this equation : y=kx

you plug in the information given

10 = k(4) and then solve ... k = 10/4 which simplifies to 5/2

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What is the simplified form of the expression k^3(K^7/5)^-5
Vladimir79 [104]
\bf k^3\left( \cfrac{k^7}{5} \right)^{-5}\implies k^3\left( \cfrac{5}{k^7} \right)^5\implies k^3\left( \cfrac{5^5}{k^{7\cdot 5}} \right)\implies k^3\cdot \cfrac{5^5}{k^{35}}
\\\\\\
k^3\cdot 5^5\cdot k^{-35}\implies 5^5\cdot k^{3-35}\implies 5^5k^{-32}\implies \cfrac{5^5}{k^{32}}\implies \cfrac{3125}{k^{32}}
3 0
3 years ago
A party planner is making gift bags for an event. He has 96 pencils,
Yuliya22 [10]

Considering the greatest common divisor, you obtain:

  • the greatest number of gift bags that the party planner can make is 12.
  • the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

<h3>Greatest common divisor </h3>

The greatest common divisor is the largest number that exactly divides two or more numbers at the same time. That is, it is the largest number by which two or more numbers can be divided, resulting in a whole number.

A method to calculate the greatest common factor must follow the following steps:

  • Decompose or separate each number into prime factors.
  • Common factors are noted.
  • In each of the commons, the factor with the smallest exponent is chosen.
  • Multiply the chosen factors.

<h3>This case</h3>

To find the greatest number of gift bags the party planner can make, you find the greatest common divisor.

To do this, decompose the numbers 96, 36 and 24:

  • 96= 2⁵×3
  • 36= 2²×3²
  • 24= 2³×3

The common factors with the smallest exponent are: 2² and 3

So, the greatest common divisor between 96, 26 and 24 is calculated as: 2²×3= 4×3= 12

This means that the greatest number of gift bags that the party planner can make is 12.

To calculate the number of each item present in each bag, you divide the quantity of each item by the quantity of gift bags:

  • 96 pencils÷ 12= 8 pencils
  • 36 erasers÷ 12= 3 erasers
  • 24 pencil toppers÷ 12= 2 pencil toppers

Finally, the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

Learn more about greatest common divisor:

brainly.com/question/11993520

brainly.com/question/18635265

brainly.com/question/6032811

#SPJ1

5 0
1 year ago
A rectangular rug has an area of 84 square feet. If its length is 2 feet more than twice its​ width, find the dimensions of the
weeeeeb [17]

L=2W+2

W=(L-2)/2

A=LW, using W from above makes this

A=L(L-2)/2

2A=L^2-2L

L^2-2L-2A=0, given A=84

L^2-2L-168=0

(L-14)(L+12)=0, since L>0

L=14

The length of the rug is 14 ft

(W=(L-2)/2=6 ft)

3 0
2 years ago
oscar bought some markers notebooks and packs of sticky notes for his office he bought the same number of markers as notebooks h
s2008m [1.1K]

The number of each kind of office supply oscar bought is = markers= (43.2 - 4.2y)/3 notebooks = (43.2-3x)/4.2, sticky notes = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3.

<h3>Calculation of total office supply</h3>

The number of markers he bought = X

The number of notebooks he bought= y

The number of sticky notes he bought= z= 3 + X+y

The amount he paid for markers = $1.05*X

The amount he paid for notebooks = $2.25*y

The amount he paid for sticky notes= $1.95 (3 + X+y)

The total amount he paid is = $49.05

That is;

$49.05 = $1.05x + $2.25y + $1.95 (3 + X+y)

$49.05 = $1.05x + $2.25y + $5.85 + $1.95x + $1.95y

$49.05 - $5.85 = 3x + 4.2y

$43.2 = 3x + 4.2y

Make X the subject of formula,

3x = 43.2 - 4.2y

X = (43.2 - 4.2y)/3

y= (43.2-3x)/4.2

z = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3

Learn more about addition here:

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4 0
1 year ago
!!!URGENT!!!<br> WILL GIVE YOU BRAINLIEST!!!<br> 10 POINTS!!!<br> Solve 4x+9=4x+13
pickupchik [31]

Answer:

No solution

Step-by-step explanation:

4x+9=4x+13

9 ≠ 13

No solution

7 0
3 years ago
Read 2 more answers
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