Alec earns $6 for every 3 newspapers he delivers. Is there a proportional relationship between his earnings and the number of newspapers Alec delivers? Explain.

The system of equations are solved using substitution method and there are infinite number of solutions

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

To solve the given system of equations using the substitution method, we can follow these steps:

Step 1:

Solve one of the equations for one variable in terms of the other variable.

Let's solve the first equation, y - 3x = 7, for y in terms of x:

y = 3x + 7

Step 2:

Substitute the expression for the solved variable into the other equation.

Substitute the expression for y from step 1, which is 3x + 7, into the second equation, 21 + 9x = 3y:

21 + 9x = 3(3x + 7)

Step 3:

Simplify and solve for the remaining variable.

Now we can simplify the equation and solve for x:

21 + 9x = 9x + 21

0 = 0

Hence , resulting equation is a true statement, 0 = 0, which means that the system of equations is dependent and there are an infinite number of solutions.

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The answer is B

let me show my answer

-3x+y=7;9x+21=3y

Solve -3x+y=7 for y

Add 3x to  both sides

-3x+y+3x=7+3x

y=3x+7

Substitute 3x+7 for y in 9x+21 =3y

9x+21=3y

9x+21=3(3x+7)

Simplify both sides of the equation

9x+21=9x+21

Add -9x to both sides

9x+21+-9x=9x+21+-9x

21=21

Add -21 to both sides

21+-21=21+-21

0=0

Answer : B , Infinitely many solutions

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Answer: AC = 20.5 cm   CB = 14.5 cm

Step-by-step explanation:

Since we know that segment AC is 6 cm longer than CB, we can can substitute AC as CB + 6.

CB = CB

AC = CB + 6

We know that AB is 35 cm, and AB is made up of AC and CB, so we now have the equation CB + CB + 6 = 35

Now, we solve.

CB + CB + 6 = 35

2CB = 29

CB = 29/2

CB = 14.5 cm

AC = CB + 6 = 14.5 + 6 = 20.5 cm

Answer:

AC = 20.5 cm

CB = 14.5 cm

Step-by-step explanation:

Let x be the distance from point C to point B:

Given that the distance from A to C is 6 cm longer than the distance from C to B, then:

Now, we know that segment AB is 35 cm long, and it can be expressed as the sum of AC and CB, so:

Solve for x:

So, the lengths of the two line segments are:

Answer:

650

Step-by-step explanation:

1st row has 1 ball

2nd row has 4 balls

3rd row has 9 balls

4th row has 16 balls

We can see that the number of balls is the square of the row number. There are a total of 12 rows. So, rest of the rows has:

5th row has 25 balls

6th row has 36 balls

7th row has 49 balls

8th row has 64 balls

9th row has 81 balls

10th row has 100 balls

11th row has 121 balls

12th row has 144 balls

If we add up all those, we get total number of balls

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