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3 years ago

Which of the following statements are true of solving equations?

Mathematics

2 answers:

kherson [118]3 years ago

6 0

The statement A, B and C are true for solving the equations.

Further explanation:

Given:

The statements of solving equation are as follows,

A. You are using inverse operations to isolate the variable.

B. The addition property is usually used first.

C. You are making a good guess at the solution.

D. Order of operations is often done in reverse order.

E. There are usually two solutions for a linear equation.

Explanation:

By isolate the variables we can solve the linear equation.

Consider an equation as $y + 3 = 5$ .

To solve the equation isolate y.

$\begin{aligned}y&= 5 - 3\\&=2\\\end{aligned}$

Option A is true.

Now consider the two equations as $a - 3b = 4$ and $a + 3b = 8$ .

We have to add the two equations to solve the equations.

$\begin{aligned}a - 3b + a + 3b&= 4 + 8\\2a&=12\\a&=\frac{{12}}{2}\\a&= 6\\\end{aligned}$

Option B is true.

Option C is false as we cannot solve the equation by guessing the solution.

Option D is true as we can often reverse the order of the operation.

Option E is false as the linear equation can have exactly one solution or infinitely many solutions.

Hence, the statement A, B and C are true for solving the equations

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear Equation

Keywords: solving equation, inverse operation, isolate, variable, addition property, good guess, solution, order of operations, reverse order, two solution, linear equation.

katrin2010 [14]3 years ago

5 0

we will check each options

option-A:

For solving any equations , we always isolate variables on anyone side

For exp: x+7=1

so, this is TRUE

option-B:

For solving system of equations

For exp:

x-y=1

x+y=3

If we use addition , we could easily solve for x and y

so, this is TRUE

option-C:

We always solve problems using conventional method

we do not guess

so, this is FALSE

option-D:

We often reverse order of operation

For exp:

(x-2)^2-3=0

so, this is TRUE

option-E:

For linear equations , we always get one solution , infinite solutions or no solutions

so, this is FALSE

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Answer:

-a^2 + -a + 12

Step-by-step explanation:

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(3 - a) (a + 4)

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-a a + 3 a - 4 a + 12

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4 0

3 years ago

Read 2 more answers

A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.