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2 years ago

Consider the line y=4x-4.

Mathematics

1 answer:

erica [24]2 years ago

4 0

9514 1404 393

Answer:

parallel: y = 4x -6
perpendicular: y = -1/4x +27/4

Step-by-step explanation:

If we want the new line to be written in slope-intercept form, we need to find the new value of the y-intercept. The equation of the line is ...

y = mx +b . . . . . . . for slope m and y-intercept b

Solving for b gives ...

b = y -mx . . . . . . . subtract mx from both sides.

The values of x and y come from the point we want the line to pass through. The value of m will be the same for the parallel line as for the given line: 4. For the perpendicular line, it will be the opposite reciprocal of this: -1/4.

<u>Parallel line</u>

b = 6 -4(3) = 6 -12 = -6

y = 4x -6

Perpendicular line

b = 6 -(-1/4)(3) = 6 +3/4 = 27/4

y = -1/4x +27/4

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There were 512 cups of water in a cooler before a soccer game. After the soccer game there were 384 cups of water in the cooler.

shusha [124]

Answer:

Step-by-step explanation:

you need to find how many cups of water were used in the game:

512-384=128

and then you can begin to calculate the number after that:

128/16=8(gallons)

hope it'll help! have a good day!

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2 years ago

What’s the 4 terms of the sequence defined by the rule f(n)=n+10

wariber [46]

Answer:

Step-by-step explanation:

f(n) = n + 10

f(4) = 4 + 10 = 14

6 0

2 years ago

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is c

vlabodo [156]

Let

x--------> the length side of the original square paper

we know that

<u>the area of the original square paper is equal to</u>

$A1=x*x=x^{2} \ units^{2}$

<u>the area of the remaining piece of paper is equal to</u>

$A2=x^{2} -2x\\ A2=120\ units^{2} \\ so\\ x^{2} -2x=120\\ x^{2} -2x-120=0$

therefore

<u>the answer is the option </u>

x2 − 2x − 120 = 0

6 0

2 years ago

Read 2 more answers

What is the LCM of x^2+4x, x^2

nordsb [41]

$x^2+4x=x\cdot (x+4)\\
x^2= x\cdot x\\\\
\text{lcm}(x^2+4x,x^2)=x^2\cdot(x+4)=x^3+4x^2$

5 0

3 years ago

The perimeter of a basketball court is 278ft. The length is 41ft longer than the width. Find the dimensions of the court.

inysia [295]

Since Perimeter is Length+ Width, and there are "two lengths" and "two widths", the formula needed here is p=2l+2w. We have the P, so using that, along with knowing that l is 41ft longer than w;
p = 278 , l = w+41
278 = 2l + 2w

278 = 2(w+41) + 2w

We'll use the DISTRIBUTIVE PROPERTY first: 278 = 2w + 82 + 2w

Then we'll COMBINE LIKE TERMS: 278 = 4w + 82

Next we'll subtract 82 from both sides: 196 = 4w

And finally divide both sides by 4:
49 = w

Since the length is w+41 and we now know the width, we can see what the length is: l = w+41 , l = 49 + 41 , l = 90.

Now that we know the length, we can see what the dimensions of the court are:
Perimeter is 278ft
Width is 49ft
And the Length is 90ft.

7 0

3 years ago