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Pie
3 years ago
13

Priya has five pencils each X inches in length when she lines of pencils and and they measure 34.5 in. Select all the equations

that represent this situation.
Mathematics
1 answer:
Sphinxa [80]3 years ago
3 0

Answer:

You would have to divid 34.5 and 5 to be able to find out what each pencil measurement the answer is 6.9.

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2x + 4y = 15<br> 6x +12y = 45<br><br> What would the solution to the system of equations be?
Dimas [21]

Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

<u>where:</u>

  • m is the slope
  • b is the y-intercept (when x = 0)

Rewrite <em>both</em> equations into slope-intercept form:

<em>a) 2x + 4y = 15 </em>

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75

<em>b) 6x + 12y = 45</em>

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75

New equations:

\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

<u><em>No Solution:</em></u> the same slope (both lines will be parallel)

<u><em>One Solution:</em></u> different slopes and different y-intercepts

<u><em>Infinitely Many Solutions:</em></u> the same slope and y-intercept

Learn more about system of equations here:

brainly.com/question/19575460

brainly.com/question/12198631

7 0
2 years ago
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