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2 years ago

Given the points below, are the two lines parallel, perpendicular, or neither.

Mathematics

1 answer:

Nookie1986 [14]2 years ago

6 0

Answer:

perpendicular

Step-by-step explanation:

First we need to dtemine the slopes of the line

For line 1

L1: (-4, 6) (-3,-1)

m1 = y2-y1/x2-x1

m1= -1-6/-3+4

m1 = -7/1

m1 = -7

For line 2:

L2: (8,9) (15, 10)

m2 = 10-9/15-8

m2 = 1/8

Take their product

m1 * m2 = -7 * 1/7

m1m2 = -1

Since the product of their slopes is -1, hence they are perpendicular

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Which values of k are solutions to the inequality StartAbsoluteValue negative k minus 2 EndAbsoluteValue less-than 18? Check all

Stella [2.4K]

Answer:

You could just replace all the given possible values of k in the inequality and see which ones are solutions, but let's solve this in a more interesting way:

First, remember how the absolute value works:

IxI = x if x ≥ 0

IxI = -x if x ≤ 0

Then if we have something like:

IxI < B

We can rewrite this as

-B < x < B

Now let's answer the question, here we have the inequality:

I-k -2I < 18

Then we can rewrite this as:

-18 < (-k - 2) < 18

Now let's isolate k:

first, we can add 2 in the 3 parts of the inequality:

-18 + 2 < -k - 2 + 2 < 18 + 2

-16 < -k < 20

Now we can multiply all sides by -1, remember that this also changes the direction of the signs, then:

-1*-16 > -1*-k > -1*20

16 > k > -20

Then k can be any value between these two limits.

So the correct options (from the given ones) are:

k = -16

k = -8

k = 0

6 0

2 years ago

Read 2 more answers

Find the lateral area of the prism. 4cm 3cm 6cm 5cm Lateral Area = [?]cm2

kolbaska11 [484]

Answer:

The lateral surface area of a prism is the sum of the surface areas of the sides of the prism.

Since the bases of the prism are triangles, there are three sides. The area of each lateral is the product of a side of the triangle times the height of the prism.

We can express this as Lateral Surface Area LSA = (s1xh) + (s2xh) + (s3+h), where "s1, s2, s3" are the lengths of the sides of the triangle and "h" is the height of the prism.

We can factor out "h" to get LSA = hx(s1+s2+s3) where the factor "s1+s2+s3" is the perimeter of the triangle.

Solving for "h", we get h = LSA / (s1+s2+s3)

For your specific problem, h = 300 / (4 + 5 + 6) = 300 / 15 = 20

4 0

2 years ago

Nelson purchased a 3 pound bunch

sveticcg [70]

Step-by-step explanation:

you would do 3 ÷ .99 and then when you get the answer from that you would multiply it by 5.

8 0

2 years ago

Read 2 more answers

Determine the equation of the line that is parallel to the given line, through the given point

bixtya [17]

The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

= -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

3 = 10 + c

c = 3 - 10

= -7

Hence, equation of line is y = -5x - 7.

To learn more about equation of the line here:

brainly.com/question/21511618

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8 0

6 months ago

two high school students are hired to rake leaves. They will work a couple hours each afternoon until the job is completed. They

Schach [20]

Answer:

x = 14 days

Step-by-step explanation:

To answer the question, find a function that represents the payment mode of plan A and an equation that represents the mode of payment of plan B.

For Plan B the payment is constant every afternoon, $ 11.5 (or 1150 cents) so the equation to represent this form of payment is as follows:

A = 1150x (with units in cents)

This equation represents the line of a line of slope 1150, which passes through point (0,0). Where x is the number of days {1, 2, 3 ....}

In form of payment B, the amount of payment is doubled each day. And the first payment is 2 cents. Therefore this model is represented by an exponential base 2 equation of the form:

$B = (2) ^ x$

Where x represents the number of days, which is always greater than 0 {1, 2, 3, 4 ...}

To know in which day the salary will be approximately the same we equate both equations and we clear x.

A = B

$1150x = (2) ^ x\\1150x- (2) ^ x = 0$

It is a somewhat difficult equation to solve, so I recommend iterating to get a value where the function approaches 0 (when this difference is zero it means that the A and B salaries are the same).

Suppose

x = 13 days

$1150(13) - (2) ^ {13} = 6758$ cents

It is not equal to 0.

Let's try with x = 15

$1150(15) - (2) ^ {15} = -15518$ cents

Then the value that makes the function zero is between x = 13 and x = 15

Let's try with x = 14

$1150(14) - (2) ^ {14} = -284$ cents = 2.84 $ difference. X = 14 is the whole number where functions A and B are closer together (the salary is approximately the same). Therefore the answer is

x = 14 days

4 0

3 years ago