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3 years ago

What is the value of the x variable in the solution to the following system of equations?

Mathematics

1 answer:

defon3 years ago

7 0

ANSWER

The correct answer is C $x=3$ .

<u>EXPLANATION</u>

We have

$4x+2y=12---(1)$

and

$x-y=3---(2)$ .

We solve the two equation simultaneously by elimination method. We need to be smart and eliminate y, since we are looking for $x$ .

We first multiply equation (2) by 2

$2x-2y=6---(3)$ .

We add equation (3) and (1).

$\Rightarrow 6x=18$ .

Dividing through by 6 gives

$x=3$ .

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Answer:

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3 years ago

A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What

vladimir2022 [97]

Answer:

The perimeter of the triangle is $12\ units$

Step-by-step explanation:

Let

$A(-3,1),B(1,1),C(1,-2)$

we know that

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$P=AB+BC+AC$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

$A(-3,1),B(1,1)$

substitute in the formula

$AB=\sqrt{(1-1)^{2}+(1+3)^{2}}$

$AB=\sqrt{(0)^{2}+(4)^{2}}$

$AB=4\ units$

step 2

Find the distance BC

$B(1,1),C(1,-2)$

substitute in the formula

$BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}$

$BC=\sqrt{(-3)^{2}+(0)^{2}}$

$BC=3\ units$

step 3

Find the distance AC

$A(-3,1),C(1,-2)$

substitute in the formula

$AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}$

$AC=\sqrt{(-3)^{2}+(4)^{2}}$

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step 4

Find the perimeter

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substitute the values

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3 years ago

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Shtirlitz [24]

1. Given a group of n people. There are C(n, r) ways of forming groups of r out of n.

2. Where C(n, r)= $\frac{n!}{r!(n-r)!}$

3. For example, given {Andy, John, Julia}. We want to pick 2 people to give a gift: we can pick {(Andy, John), (Andy, Julia), (John, Julia)}, so there are 3 ways. So we can list and count.

4. Or we could do this with the formula C(3, 2)= $\frac{3!}{2!(1)!}= \frac{3*2*1}{2*1}=3$

5. C(8, 6)= $\frac{8!}{2!6!}= \frac{8*7*6!}{2*6!}= \frac{8*7}{2}= 4*7=28$

So there are C(8,6)=28 ways of chosing 6 out of 8 people to form the subcommittees. <span />

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3 years ago

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Ierofanga [76]

Answer:

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3 years ago