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2 years ago

Solve the system of equations: x – 4y = –8 and –3x + 12y = 24.

Mathematics

2 answers:

NISA [10]2 years ago

8 0

Answer:

<h2>C. There are an infinite number of solutions.</h2>

Step-by-step explanation:

$\left\{\begin{array}{ccc}x-4y=-8\\-3x+12y=24&\text{divide both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x-4y=-8\\-x+4y=8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=0\qquad\bold{TRUE}$

ale4655 [162]2 years ago

4 0

It should be C
Because when u multiply ( -3)*(x-4y= -8)

It’ll equal to -3x+12y=24 which is the same equation to the other one.
When the equations r the same, it means everything on the line is the solution for this system of equation.

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On Naomi's cell phone plan, the amount she pays each month for international text messages is proportional to the number of inte

Lostsunrise [7]

A) The constant of proportionality in this proportional relationship is $k = \frac{y}{x}$

B) The equation to represent this proportional relationship is y = 0.2x

<h3><u>Solution:</u></h3>

Given that,

The amount Naomi pays each month for international text messages is proportional to the number of international texts she sends that month

Therefore,

This is a direct variation proportion

$\text{ amount Naomi pays each month } \propto \text{ number of international texts she sends that month}$

Let "y" be the amount that Naomi pays each month

Let "x" be the number of international texts she sends that month

Therefore,

$y \propto x$

y = kx -------- eqn 1

Where, "k" is the constant of proportionality

Thus the constant of proportionality in this proportional relationship is:

$k = \frac{y}{x}$

<em><u>Last month, she paid $3.20 for 16 international texts</u></em>

Therefore,

y = 3.20

x = 16

Thus from eqn 1,

$3.20 = k \times 16\\\\k = \frac{3.20}{16}\\\\k = 0.2$

Substitute k = 0.2 in eqn 1

y = 0.2x

The equation would then be y = 0.2x

8 0

2 years ago

What is bigger 3/14 or 1/6?

Ksju [112]

3/14 is 0.214 and 1/6 is 0.16

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3 years ago

Helpp me with this please!

Dmitry [639]

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Use a graphing calculator to find the value of the correlation coefficient r and determine if there is a strong correlation amon

Natali [406]

The value of the correlation is -0.0721 and it is a weak negative correlation

<h3>How to determine the correlation coefficient?</h3>

The points are given as:

(12, 28), (15, 50), (18, 14), (21, 28), (24, 36)

Enter the above points in a graphing calculator.

From the graphing calculator, we have the following summary:

<u>X Values</u>

Sum X = 90
Mean = 18
∑(X - Mx)^2 = SSx = 90

<u>Y Values</u>

Sum Y = 156
Mean = 31.2
∑(Y - My)^2 = SSy = 692.8

<u>X and Y Combined</u>

N = 5
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<u>R Calculation</u>

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

r = -18 / √((90)(692.8)) = -0.0721

So, the correlation coefficient is -0.0721

The above is a negative correlation because it is less than 0 and it is a weak correlation because it is closer to 0 than -1

Hence, the correlation is a weak negative correlation

Read more about correlation coefficient at:

brainly.com/question/27226153

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