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Pie
3 years ago
9

As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor shou

ld she multiply both sides of the other equation so that she can add the equations and eliminate a variable? What one-variable equation is she left with after adding?
5x + 6y = 18
2x – 3y = 12

Factor:________
Equation:________x=_________
Mathematics
1 answer:
GenaCL600 [577]3 years ago
7 0

Answer:

Yumiko should multiply the other equation by 3.

If she adds the two equations she would be left with the variable 'x'.

Step-by-step explanation:

Given the two equations are as follows:

$ 2x - 3y = 12 \hspace{5mm} \hdots (1) $

$ 5x + 6y = 18 \hspace{5mm} \hdots (2) $

It is given that she multiplies the first equation by 6. Therefore, (1) becomes

$ 12x - 18y = 72 \hspace{15mm} \hdots (a) $

Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.

The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.

Therefore, Equation (2) becomes:

$ 15x + 18y = 54 \hspace{5mm} \hdots (b) $

Now, we add Equation (a) and Equation (b).

$ \implies 12x - 18y + 15x + 18y = 72 + 54 $

$ \implies 27x = 126 $

Factor: 3

Equation: 27x = 126

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B

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x=3

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3 years ago
Alejandro wants to adopt a puppy from an animal shelter. At the​ shelter, he finds eight puppies that he​ likes: a male and fema
alexgriva [62]

Answer:

Hence the required probability is, 3/4

Step-by-step explanation:  

At the shelter, he likes :  

a male coolie, a female coolie, a male boxer, a female boxer, a male beagle, a female beagle, a male Labrador, and a female Labrador.  

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Here the probability of selecting a puppy except A & B is,  

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7 0
3 years ago
A rectangle is plotted on the coordinate grid. It has vertices at (-3, 5), (4, 5), (4, -1), and (-3, -1). Which choices below ar
zhannawk [14.2K]

A rectangle is plotted on the coordinate grid. It has vertices at (-3, 5), (4, 5), (4, -1), and (-3, -1). Which choices below are the dimensions of the rectangle?

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3 0
2 years ago
18. You are standing beside the Colorado River, 400 feet
Veseljchak [2.6K]
<h3>Answer: B. 781.6 feet approximately</h3>

=======================================================

Work Shown:

The horizontal portion is 400+166 = 566 feet. Label this as 'a', so a = 566. The vertical side is unknown, so b = x. The hypotenuse is c = 965

Use the pythagorean theorem

a^2+b^2 = c^2

566^2+x^2 = 965^2

x^2 = 965^2 - 566^2

x = sqrt( 965^2 - 566^2 )

x = 781.58108984289 which is approximate

x = 781.6 feet when rounding to one decimal place

6 0
3 years ago
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