How many solutions does the following system of linear equations have? y=-6x+6
y=5x+1

Answers

Answer 1

Answer: 2 this is right because 6 +1 and 6x 5x

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Two of your friends, Matt and Karen, both run to you to settle a dispute. They were working on a math problem, and got different answers. Wisely, you decide to look at their work to see if you can spot the source of confusion.Matt

6 – 4(3 – 5)2 + 30 ÷ 5
6 – 4(–2)2 + 30 ÷ 5
6 – 4(4) + 30 ÷ 5
6 – 16 + 30 ÷ 5
−10 + 30 ÷ 5
20 ÷ 5
4
Karen

6 – 4(3 – 5)2 + 30 ÷ 5
6 – 4(–2)2 + 30 ÷ 5
6 – 4(−4) + 30 ÷ 5
6 + 16 + 30 ÷ 5
6 + 16 + 6
22 + 6
28 Explain to Matt and Karen who, if either, is correct, and identify errors that you find. Provide the correct manner to fix those solutions, and identify the correct answer. Use complete sentences.

Answers

so in matt's equation, he made a mistake in the a transision from line 2 to line 3
in line 2: -4(-2)2
in line 3: -4(4)
the mistake is that -2 times 2 is not equal +4 it is equal to -4
also from lines 5 to 6 he made a mistake in order of opperations (mulit division then addition and subtract)
line 5: -10+30/5
line 6: 20/5

so he first subtracted 10 then divided, he should have divided then subtracted
so the equation should have equaled

Karen used the correct (-) times (+) property and the order of operations
so Karen is correct and Matt is wrong.

Karen is correct. (-2)2 is -4, not 4 in Matt's answer. Also, Karens, order of operations on the 4th line is correct. She does her division first, and Matt completes his subtraction first. PEMDAS, parenthesis, exponents, multiplication, division, addition, subtraction.

A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (6, 4) and (5, 2), what is the equation for a parallel street that passes through (−2, 6)?A. y = 1 half x + 5
B. y - 1 half x + 1
C. y = 2x + 10
D. y = 2x − 14

Answers

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the first street.

$(\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{2}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{6}}} \implies \cfrac{ -2 }{ -1 } \implies 2$

so we are really looking for the equation of a line whose slope is 2 and it passes through (-2 , 6)

$(\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \n\n\n \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{2}(x-\stackrel{x_1}{(-2)}) \implies y -6 = 2 ( x +2) \n\n\n y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}$

The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, what are the two numbers?

Answers

x+y= 13
2x-3y= 1
This can be found by using a system but I will try this method:
x=13-y
We replace it on the second one:
2(13-y) + y = 13
26-2y + y=13
-y= -13
y= 13

What is 31/20 in simplest form?

Answers

31/20 is already in its simplest form. The simplest form is when the two numbers no longer have a common factor

PLEASE HELP LAST TWO QUESTIONS, I USED ALL MY POINTS TO POST THIS PLEASE PLEASE PLEASE HELP VERY IMPORTANT

Answers

10.
if we were tosubsitute the points and graph the equation we would notice that theshape is the same for both: a 45 degree angle line that goes upleft andup right
the graph of y=|x| looks like a right angle corner that is facing up that is ballancing on the point (0,0)
thegraph of y=|x|-4 is the same except that the graph is shifter 4 unitsto the right ie. the point ofo the graph/rightangle is on point (4,0)

14.
slope intercept form which is y=mx+b
m=slope b=y intercept
m=4/3
y=4/3x+b
one given solution/point is (9,-1)
one solution is x=9 and y=-1 so subsitute and solve fo b
-1=4/3(9)+b
-1=36/3+b
-1=12+b
subtract 12 from both sides
-11=b
the equation si y=4/3x-11
see which one converts to the correct form
after trial and error we find that y-1=4/3(x-9) is the answer

Your parents are renting an apartment for you when you go away to college an annual contract is $502.00/month with a 2 month penalty if you break the lease the month to month contract is 615.00/month how much is the difference in payments if you stay the whole year

Answers

The difference in payments for the apartment for the whole year will be $1356.

What is an annual contract?

An annual contract is a contract where the contract is established on the basis of payment for the whole year.

What is a month to month contract?

A month to monthcontract is a contract where the contract is established on the basis of payment for every single month.

Given, the annual contract of the apartment is $502.00/month.

Therefore, for the whole year, the rent will be $502.00 × 12 = $6024.00

Again, the month to month contract is $615.00/month.

Therefore, for the whole year, the rent will be $615.00 × 12 = $7380.00

As we are calculating the rent for an year, there will not be any penalty.

Hence, the difference in payments = $(7380.00 - 6024.00) =$1356.00

Learn more about annual and month to month contract here: brainly.com/question/1393028

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Your parents are renting an apartment for you when you go away to college. An annual contract is $502.00/month with a 2-month penalty if you break the lease. The month-to-month contract is $615.00/month. How much is the difference in payments if you stay the whole year?

$1,356.00

However, lets say you leave after 6 months. How much is the difference in the amount paid between the two contracts?

$326.00

Step-by-step explanation:

I just took the test :)

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