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Ede4ka [16]
3 years ago
12

what is the equation of the line that is parallel to the line y= 3x-4 and passes through the point (4, -2)

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
5 0

Answer:

y = 3x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 is in this form with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (4, - 2) into the partial equation

- 2 = 12 + c ⇒ c = - 2 - 12 = - 14

y = 3x - 14 ← equation of parallel line

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3 years ago
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At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women,
Lisa [10]

Answer:

I believe the answer is c.) x=4

Step-by-step explanation:

I saw this on a webpage:

The moment we see “x,” we can consider picking numbers. The key here is contemplating how complicated the number should be. Swim with the current – let the question tell you. A quick look at the answer choices reveals that x could be something simple. Ultimately, we’re just dividing this value by 2, 3, 4, 5, or 6.

Keeping this in mind, let’s think about the first line of the question. If there are 3 times as many adults as children, and we’re keeping things simple, we can say that there are 3 adults and 1 child, for a total of 4 people. So, x = 4.

Now, we know that among our 3 adults, there are twice as many women as men. So let’s say there are 2 women and 1 man. Easy enough. In sum, we have 2 women, 1 man, and 1 child at this picnic, and a total of 4 people. The question is how many men are there? There’s just 1! So now we plug x = 4 into the answers and keep going until we find x = 1. Clearly x/4 will work, so C is our answer. The key was to let the question dictate our approach rather than trying to impose an approach on the question.

7 0
3 years ago
Read 2 more answers
A school wishes to enclose its rectangular playground using 480 meters of fencing.
Harlamova29_29 [7]

Answer:

Part a) A(x)=(-x^2+240x)\ m^2

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

P=2(L+W)

we have

P=480\ m\\L=x\ m

substitute

480=2(x+W)

solve for W

240=x+W\\W=(240-x)\ m

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

A=LW

we have

L=x\ m\\W=(240-x)\ m

substitute

A=x(240-x)\\A=-x^2+240x

Convert to function notation

A(x)=(-x^2+240x)\ m^2

Part b) What side length x gives the maximum area that the playground can have?

we have

A(x)=-x^2+240x

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

A(x)=-x^2+240x

Factor -1

A(x)=-(x^2-240x)

Complete the square

A(x)=-(x^2-240x+120^2)+120^2

A(x)=-(x^2-240x+14,400)+14,400

A(x)=-(x-120)^2+14,400

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

x=120\ m

W=(240-120)=120\ m

The playground is a square

A=120^2=14,400\ m^2

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Answer:

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Step-by-step explanation:

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check the picture below.

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2 years ago
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