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Verdich [7]
3 years ago
15

Four students are trying to find the rule that translates point N(–2, –4) to N prime (2, 4). Each student’s reasoning is shown b

elow.
Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4.
Casey: The rule is (x + 2, y + 4) because the image is (2, 4).
Andrew: The rule is (x + 4, y + 0) because the coordinates are opposites.
Lo: The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4.

Which student is correct?
Raheem
Casey
Andrew
Lo
Mathematics
2 answers:
liraira [26]3 years ago
6 0

Answer:

Lo's answer is correct and it is a translation because applying the rule (x+4, y+8) on the coordinates N(-2, -4) will gives us N'(2,4).

Step-by-step explanation:

i) though Raheem is mathematically correct the question asks for a translation which means that we can only use addition and/or subtraction and not multiplication. So Raheem's answer is therefore incorrect.

ii) Casey's answer is incorrect as applying the rule (x+2, y+4) on the coordinates N(-2, -4) will gives us (0,0) and not N'(2,4)

iii) Andrew's answer is also incorrect as applying the rule (x+4, y+0) on the coordinates N(-2, -4) will gives us (2,-4) and not N'(2,4).

iv) Lo's answer is correct and it is a translation because applying the rule (x+4, y+8) on the coordinates N(-2, -4) will gives us N'(2,4).

slega [8]3 years ago
6 0

Answer:

Lo is correct

Step-by-step explanation:

I just got it correct in e d g e n u i t y

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Answer:

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Step-by-step explanation:

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4 0
2 years ago
Find the solution of this system of equations -x-4y=-37 -2x-5y=-53
zzz [600]

Answer:

The solution in point form is (9,7) and the equation would be x+9, y=7

Step-by-step explanation:

By using moving the -4y to the right side and by flipping the signs you can turn the equation -x-4y=-37 into x=37-4y.

With this new equation you can use the substitution method and replace the x in -2x-5y=-53 with 37-4y, making it look like this: -2(37-4y)-5y=-53.

Then you solve for y getting y=7.

With the value of y, you can plug that into the equation x=37-4y so it will look like x=37-4(7)

Then you solve for x getting x=9

And with that you get the point (9,7)

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3 years ago
10 2/3 + 2h < 4 1/3.
Snezhnost [94]
Well i got -19/6 but if you simplify it it would be -3.16667
5 0
4 years ago
Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the qua
goblinko [34]
<h2>Hello!</h2>

The answer is:  There is a total of 5.797 gallons pumped during the given period.

<h2>Why?</h2>

To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)

The given function is:

D(t)=\frac{5t}{1+3t}

So, the integral will be:

\int\limits^4_0 {\frac{5t}{1+3t}} \ dx

So, integrating we have:

\int\limits^4_0 {\frac{5t}{1+3t}} \ dt=5\int\limits^4_0 {\frac{t}{1+3t}} \ dx

Performing a change of variable, we have:

1+t=u\\du=1+3t=3dt\\x=\frac{u-1}{3}

Then, substituting, we have:

\frac{5}{3}*\frac{1}{3}\int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du\\\\\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u}{u} -\frac{1}{u } \ du

\frac{5}{9} \int\limits^4_0 {(\frac{u}{u} -\frac{1}{u } )\ du=\frac{5}{9} \int\limits^4_0 {(1 -\frac{1}{u } )

\frac{5}{9} \int\limits^4_0 {(1 -\frac{1}{u })\ du=\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du

\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du=\frac{5}{9} (u-lnu)/[0,4]

Reverting the change of variable, we have:

\frac{5}{9} (u-lnu)/[0,4]=\frac{5}{9}((1+3t)-ln(1+3t))/[0,4]

Then, evaluating we have:

\frac{5}{9}((1+3t)-ln(1+3t))[0,4]=(\frac{5}{9}((1+3(4)-ln(1+3(4)))-(\frac{5}{9}((1+3(0)-ln(1+3(0)))=\frac{5}{9}(10.435)-\frac{5}{9}(1)=5.797

So, there is a total of 5.797 gallons pumped during the given period.

Have a nice day!

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