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3 years ago

When the variable is on both sides of the equation, it must be isolated on one side, and it doesn't matter which

Mathematics

1 answer:

Andreyy893 years ago

3 0

Answer:

The basic technique to isolate a variable is to “do something to both sides” of the equation, such as add, subtract, multiply, or divide both sides of the equation by the same number.

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erma4kov [3.2K]

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3 years ago

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The height of a triangle is 3cm less than twice the base. The area is 10cm2

Kamila [148]

Answer:

The base is 4cm and the height is 5cm.

Step-by-step explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

$H=2B-3$

and

$\frac{B \times H}{2}=10$

Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

$\frac{B(2B-3)}{2}=10\\\frac{2B^2-3B}{2}=10\\2B^2-3B=20\\2B^2-3B-20=0\\(2B+5)(B-4)=0\\B= - \frac{5}{2},4$

In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

$H=2(4)-3\\H=8-3\\H=5$

3 0

3 years ago

A gardener is planting two types of trees:

Scrat [10]

It will take 4 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees:

Type A is 6 feet tall and grows at a rate of 12 inches per year

Type B is 2 feet tall and grows at a rate of 24 inches per year

We need to find exactly how many years it will take for these trees to be the same height

Assume that it will take x years for these trees to be the same height

Type A:

∵ The initial height of the tree is 6 feet

∵ 1 foot = 12 inches

∴ 6 feet = 6 × 12 = 72 inches

∴ The initial height of the tree is 72 inches

∵ It grows at a rate of 12 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 72 + 12 x

Type B:

∵ The initial height of the tree is 2 feet

∴ 2 feet = 2 × 12 = 24 inches

∴ The initial height of the tree is 24 inches

∵ It grows at a rate of 24 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 24 + 24 x

Equate The heights of the two types

∴ 72 + 12 x = 24 + 24 x

- Subtract 2 from both sides

∴ 48 + 12 x = 24 x

- Subtract 12 x from both sides

∴ 48 = 12 x

- Divide both sides by 12

∴ x = 4

It will take 4 years for these trees to be the same height

Learn more:

You can learn more about the word problems in brainly.com/question/10557938

#LearnwithBrainly

3 0

3 years ago

The formula for the volume of a cylinder is v= 3.14r^2h. A cylinder has a volume of 300x feet ^3 and a radius of 5 feet

Fudgin [204]

Answer:

Height = 3.82

Step-by-step explanation:

(3.14)(5)²

(3.14)(25)

= 78.5

300 = 78.5h

300/78.5 = 78.5h/78.5

h = 3.821656051 or approximately 3.82

7 0

3 years ago

t takes Phillip 7 hours to proof a chapter of Hawkes Learning Systems' Intermediate Algebra book and it takes Kim 3 hours. How l

Leya [2.2K]

Answer:

2.1 hrs

Step-by-step explanation:

In 1 hr, Phillip would have proofed 1/7 of the chapter. In 1 hr, Kim would have proofed 1/3 of the chapter. So, together in 1 hr, they would have proofed 10/21 of the chapter. So, it would take 21/10 or 2.1 hrs to proof the whole chapter together.

5 0

3 years ago