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2 years ago

Solve using the method of elimination and determine if the system has 1 solution, no solutions, or infinite solutions

1 answer:

8 0

$\begin{array}{rrrrr} 10x&-&18y&=&2\\ -5x&+&9y&=&-1 \end{array}~\hfill \implies ~\hfill \stackrel{\textit{second equation }\times 2}{ \begin{array}{rrrrr} 10x&-&18y&=&2\\ 2(-5x&+&9y&)=&2(-1) \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{rrrrr} 10x&-&18y&=&2\\ -10x&+&18y&=&-2\\\cline{1-5} 0&+&0&=&0 \end{array}\qquad \impliedby \textit{another way of saying \underline{infinite solutions}}$

if we were to solve both equations for "y", we'd get

$10x-18y=2\implies 10x-2=18y\implies \cfrac{10x-2}{18}=y\implies \cfrac{5}{9}x-\cfrac{1}{9}=y \\\\\\ -5x+9y=-1\implies 9y=5x-1\implies y=\cfrac{5x-1}{9}\implies y = \cfrac{5}{9}x-\cfrac{1}{9}$

notice, the 1st equation is really the 2nd in disguise, since both lines are just pancaked on top of each other, every point in the lines is a solution or an intersection, and since both go to infinity, well, there you have it.

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Need help with this math question

anastassius [24]

Answer:

The vertex is: $(6, 8)$

Step-by-step explanation:

First solve the equation for the variable y

$x^2-4y-12x+68=0$

Add 4y on both sides of the equation

$4y=x^2-4y+4y-12x+68$

$4y=x^2-12x+68$

Notice that now the equation has the general form of a parabola

$ax^2 +bx +c$

In this case

$a=1\\b=-12\\c=68$

Add $(\frac{b}{2}) ^ 2$ and subtract $(\frac{b}{2}) ^ 2$ on the right side of the equation

$(\frac{b}{2}) ^ 2=(\frac{-12}{2}) ^ 2\\\\(\frac{b}{2}) ^ 2=(-6) ^ 2\\\\(\frac{b}{2}) ^ 2=36$

$4y=(x^2-12x+36)-36+68$

Factor the expression that is inside the parentheses

$4y=(x-6)^2+32$

Divide both sides of the equality between 4

$\frac{4}{4}y=\frac{1}{4}(x-6)^2+\frac{32}{4}$

$y=\frac{1}{4}(x-6)^2+8$

For an equation of the form

$y=a(x-h)^2 +k$

the vertex is: (h, k)

In this case

$h=6\\k =8$

the vertex is: $(6, 8)$

5 0

3 years ago

What is the product of x squared plus 3x minus 40

My name is Ann [436]

TWENTY ONE BA DUM DUM DUM

6 0

3 years ago

Read 2 more answers

the last sentence says "which statement best interprets the quotient" also this need to be done before 8:00 :) plzz helpp

Mandarinka [93]

Answer:

A. There are 5 1/6 Three fourths

in 4 1/8

Step-by-step explanation:

5 0

3 years ago

A $649 laptop computer cost $519.20 after a coupon is applied. What percentage off is the coupon?

Nadya [2.5K]

Answer: 20%

Step by Step Explanation: 

Start by subtracting 519.29 from 649, you would get 129.8

Then take 129.8 and divide that by 649.

You get 0.2 which equals 20%

Tip: To find the percent of a fraction you divide the numerator by the denominator. For example, if you want to find the percent on a test, and you get a 8/10 you just divide 8 by 10. Which obviously equals 80.

4 0

3 years ago

Read 2 more answers

According to the equation, which choice represents the fixed cost of

kodGreya [7K]

Answer:

A) 3500

Step-by-step explanation:

C(x) = 0.75x + 3500

C(x) = Total cost

0.75x = variable cost

3,500 = fixed cost

The fixed cost of the function = 3,500

Variable cost refers to cost of production that changes during production such as cost of raw material, wages of workers etc.

Fixed cost are cost of production that remains the same (does not change) with the production process such as building, machineries etc

Total cost is the addition of all cost of production, that is, the addition of fixed cost and variable cost

7 0

3 years ago