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3 years ago

How do you know that a =6 is a solution to a+5=11?

Mathematics

2 answers:

Mkey [24]3 years ago

8 0

We are given this equation a+5=11

here 5 is in addition on the left side

so in order to eliminate it , we perform opposite operation of addition on the right side.

opposite operation of addition is subtraction.

so subtracting 5 on the right side , we get

a=11-5

a=6

so this is how a=6 is the answer

NNADVOKAT [17]3 years ago

7 0

a + 5 = 11

You need to isolate the variable by subtracting from both sides

a + 5 - 5 = 11 - 5a = 6

The Addition/Subtraction Property of Equality states that if you add or subtract the same number to both sides of an equation the two sides still remain equal.

:))

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Show all your work to receive full credit for this problem. Solve the system of equations using the elimination method. 2a + 3b

Sindrei [870]

Given equations are;
2a + 3b = -1 ..................equation 1
3a + 5b = -2 ....................equation 2

Now multiply equation 1 with (-3)

The equation will be;

-6a -9b = 3 …………………..equation 3

Now multiply equation 2 with (2)

The equation will be;

6a + 10b = -4 ……………..equation 4

Now add equation 3 and equation 4

-6a – 9b = 3

6a + 10b = -4

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0a + b = -1

b = -1

Now put the value of b in equation 1

2a + 3(-1) = -1

2a -3 = -1

2a = -1+3

2a = 2

a=1

Thus the solution is (a,b) = (1,-1)

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2 years ago

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Stolb23 [73]

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3 years ago

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2 years ago

Read 2 more answers

larisa86 [58]

A. Every month Population will increase by a factor of 0.84%.

B. Every 3 months Population will increase by a factor of 2.5%.

C. Increase in population in every 20 months is 10% + 6.72% = 16.72%.

Step-by-step explanation:

Here, we have number of employees in a company has been growing exponentially by 10% each year. So , If we have population as x in year 2019 , an increase of 10% in population in 2020 as $x + \frac{x}{100}\times10$ which is equivalent to $\frac{11x}{10}$ .

A.

For each month: We have 12 months in a year and so, distributing 10% in 12 months would be like $\frac{10}{12} = 0.84$ . ∴ Every month Population will increase by a factor of 0.84%.

B.

In every 3 months: We have , 12 months in a year , in order to check for every 3 months $\frac{12}{3} = 4$ and Now, Population increase in every 3 months is $\frac{10}{4} = 2.5$ . ∴ Every 3 months Population will increase by a factor of 2.5%.

C.

In every 20 months: We have , 12 months in a year in which increase in population is 10% . Left number of moths for which we have to calculate factor of increase in population is 20-12 = 8. For 1 month , there is 0.84% increase in population ∴ For 8 months , 8 × 0.84 = 6.72 %.

So , increase in population in every 20 months is 10% + 6.72% = 16.72%.

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3 years ago

Alice has a total of 12 dimes and nickels. She has 2 more nickels than dimes

valkas [14]

This is a problem of system of linear equations in two variables. This concept of mathematics is very useful in real-life problems. You can solve a system by finding the solution. A solution of a system are the values of the variables that satisfies each equation in the system. So by knowing these concepts we can get a system of equation by analyzing each statement step by step, that is:

1. Alice has a total of 12 dimes and nickels.

Let the variables:

$D: Dimes \\ N:Nickles$

1st. Equation:

$D+N=12$

2. She has 2 more nickels than dimes

2nd Equation:

$N=D+2$

Therefore our system of linear equations is:

 $(1) \ D+N=12 \\ (2) \ N=D+2 \\ \\ Substituting \ (2) \ in \ (1): \\ D+(D+2)=12 \therefore 2D=10 \therefore D=5 \\ \\ Solving \ for \ N \ in \ (2): \\ N=5+2=7$

Conclusion:

Alice has 5 dimes and 7 nickels.

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3 years ago