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son4ous [18]
3 years ago
7

What is the justification for the step taken from line 2 to line 3?

Mathematics
2 answers:
stiv31 [10]3 years ago
3 0

Step-by-step explanation:

3x+9-7x=x+10+x\\-4x+9=2x+10\\-6x+9=10\\

  • In the line 2, only variables were operated with a reduction of similar terms in each side of the equation, giving as result -4x at one side, and 2x at the other side.
  • In the line 3, terms with variables were joined together in one side of the equation, and then, they were operate it, given as result -6X.
brilliants [131]3 years ago
3 0

Answer:

the subtraction property of equality

Step-by-step explanation:

up up up uppity

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Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. Th
zvonat [6]

The labor fee is $13.55 and each quart of oil is $2.25

Step-by-step explanation:

Let,

x be the amount of each quart of oil

y be the amount of labor fee

According to given statement;

5x+y=24.80        Eqn 1

7x+y=29.30        Eqn 2

Subtracting Eqn 1 from Eqn 2

(7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50

Dividing both sides by 2

\frac{2x}{2}=\frac{4.50}{2}\\x=2.25

Putting x=2.25 in Eqn 1

5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55

The labor fee is $13.55 and each quart of oil is $2.25

Keywords: linear equation, subtraction

Learn more about subtraction at:

  • brainly.com/question/116715
  • brainly.com/question/11680012

#LearnwithBrainly

6 0
3 years ago
Solve the following equation by completing the square. 3x^2-3x-5=13
mr Goodwill [35]

we'll start off by grouping some

\bf 3x^2-3x-5=13\implies (3x^2-3x)-5=13\implies 3(x^2-x)-5=13 \\\\\\ 3(x^2-x)=18\implies (x^2-x)=\cfrac{18}{3}\implies (x^2-x)=6\implies (x^2-x+~?^2)=6

so we have a missing guy at the end in order to get the a perfect square trinomial from that group, hmmm, what is it anyway?

well, let's recall that a perfect square trinomial is

\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

so we know that the middle term in the trinomial, is really 2 times the other two without the exponent, well, in our case, the middle term is just "x", well is really -x, but we'll add the minus later, we only use the positive coefficient and variable, so we'll use "x" to find the last term.

\bf \stackrel{\textit{middle term}}{2(x)(?)}=\stackrel{\textit{middle term}}{x}\implies ?=\cfrac{x}{2x}\implies ?=\cfrac{1}{2}

so, there's our fellow, however, let's recall that all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add (1/2)², we also have to subtract (1/2)²

\bf \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2-\left[ \cfrac{1}{2} \right]^2 \right)=6\implies \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2 \right)-\left[ \cfrac{1}{2} \right]^2=6 \\\\\\ \left(x-\cfrac{1}{2} \right)^2=6+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{25}{4}\implies x-\cfrac{1}{2}=\sqrt{\cfrac{25}{4}} \\\\\\ x-\cfrac{1}{2}=\cfrac{\sqrt{25}}{\sqrt{4}}\implies x-\cfrac{1}{2}=\cfrac{5}{2}\implies x=\cfrac{5}{2}+\cfrac{1}{2}\implies x=\cfrac{6}{2}\implies \boxed{x=3}

6 0
3 years ago
Name the parallel segment
ratelena [41]
MN would be the answer to your question because they are parallel
4 0
3 years ago
13.20/5ft=x dollars/1 inch
matrenka [14]

Answer:

2.64

Step-by-step explanation:

  1. 13.20 × 1 = 13.20
  2. 13.20 ÷ 5 = 2.64
4 0
3 years ago
Raleigh went to a gaming arcade for his birthday. His parents gave him $55 to spend. He purchased $14.25 in
amid [387]

Answer:

23 games

Step-by-step explanation:

40.75 divide by 1.25 comes out 23.28

8 0
3 years ago
Read 2 more answers
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