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Yakvenalex [24]
3 years ago
13

Find the equation of a line that is parallel to line g that contains (P, Q).

Mathematics
2 answers:
Fofino [41]3 years ago
8 0

Correct option:

\boxed{x-y=P-Q}

<h2>Explanation:</h2>

Given that the line we are looking for is parallel to g, then the slope of that line and g is the same, therefore:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ (x_{1},y_{1})=(-3,2) \\ \\ (x_{2},y_{2})=(0,5) \\ \\ \\ m=\frac{5-2}{0-(-3)}=1

So we can write the point-slope form of the equation of the line as follows:

y-y_{0}=m(x-x_{0}) \\ \\ (x_{0},y_{0})=(P,Q) \\ \\ \\ y-Q=1(x-P) \\ \\ y-Q=x-P \\ \\ \\ Arranging: \\ \\ P-Q=x-y \\ \\ \boxed{x-y=P-Q}

<h2>Learn more:</h2>

Graphying systems of linear equations: brainly.com/question/13799715

#LearnWithBrainly

Lorico [155]3 years ago
3 0

Answer:

X - Y = P - Q

Step-by-step explanation:

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7 0
3 years ago
3x−12≥15<br><br> 2x−5≤9<br><br> 5x+8≤53<br><br> 3x−5≥16
zalisa [80]

Answer:

Step-by-step explanation:

A) 3x−12≥15

3x ≥ 15 + 12

3x ≥ 27

or x≥ 9

B) 2x−5≤9

2x ≤ 9 +5

2x ≤ 14

or x ≤ 7

C) 5x+8≤53

5x ≤ 53 -8

5x ≤ 45

or x ≤ 9

D) 3x−5≥16

3x ≥ 16 + 5

3x ≥ 21

or x ≥ 7

Have a good day!

8 0
3 years ago
Identify whether the equation represents an exponential growth or exponential decay function.1. y = 1/4 (1/e)^-2x2. y = (1/e)^4x
zvonat [6]

The general formula for exponential growth and decays is:

y=y_0e^{kx}

if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.

Now we need to classify each of the functions:

1.

The function

y=\frac{1}{4}(\frac{1}{e})^{-2x}

can be wrtten as:

\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}

comparing with the general formula we notice that k=2, therefore this is an exponential growth.

2.

The function

y=(\frac{1}{e})^{4x}

can be written as:

\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}

comparing with the general formula we notice that k=-4, therefore this is an exponential decay.

3.

The function

y=2e^{-x}+1

comparing with the general formula we notice that k=-1, therefore this is an exponential decay.

5 0
1 year ago
Which of the following is a proportion? <br><br> A. 4/6 = 6/9<br><br> B. 5/6 = 10/18
worty [1.4K]
Hey there mate!

Your correct answer would be \left[\begin{array}{ccc}\boxed{\boxed{ 4/6 = 6/9}}\end{array}\right] This would be because 4/6 is almost 1 as a whole, and also, 6/9 is almost 1, as a whole, so this would totally make sense for this to be a proportional.

Hope this helps you budd!
8 0
3 years ago
Read 2 more answers
The common point between lines y = 2x + 5 and y = ½ x + 6 is (3, 1/2). true or false
mixer [17]
The common point between y = 2x + 5 and y = (1/2)x + 6 will have the same values for x and y.

Therefore, set the two y expressions equal to obtain
2x + 5 = (1/2)x + 6

Subtract (1/2)x from each side.
(3/2)x + 5 = 6

Subtract 5 from each side.
(3/2)x = 1

Multiply each side by 2/3.
x = 2/3.

From the first equation, obtain
y = 2*(2/3) + 5 = 19/3.

The common point is (2/3, 19/3). It is not equal to (3, 1/2).

Answer: False
5 0
3 years ago
Read 2 more answers
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