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line j is perpendicular to lines m and n. if the products of the slope of all three lines is -8, what is the slope of line j?

jeka94

Answer:

the slope of line j is -1/8, the slope of lines m and n are both 8.

Explanation step by step:

Suppose j is the slope of line j, m the slope of line m and n the slope of line n. Since:

1. line j is perpendicular of line m, so j*m= -1

2. J is perpendicular of line n, so j*n=-1

3. m and n and parallel so m=n

As we want to know the slope of j we clear the equations presented to us in order to find it.

(1) m* n* j = -8, since n=m we have $n^{2}$ * j = -8.

we clear j; $n^{2} * j = -8 \\ j =\frac{-8}{n^{2} }$

replacing in the equation n*j = -1 we get

n*(-8/n^2) = -1. Thus n = 8. Since j = -1/n = -1/8.

7 0

3 years ago

Tanya bought 8.05 yards of fleece fabric to make costumes for a school play. She needs 1.25 yards of fabric for each costume. Ho

juin [17]

Answer:

6

Step-by-step explanation:

8.05 divided by 1.25 is 6.44

6 0

3 years ago

8+345737377948585848484

iris [78.8K]

Answer:

3.4573738e+20

Step-by-step explanation:

6 0

3 years ago

A substance with a half life is decaying exponentially. If there are initially 12grams of the substance and after 70 minutes the

dybincka [34]

Answer:

Step-by-step explanation:

Use the half life formula

$N=N_0e^{kt}$ where N is the amount after decay, No is the initial amount, e is Euler's number, k is the decay constant, and t is the time in minutes. For us, the first equation looks like this:

$7=12e^{k(70)}$ and we will solve that for k and then use that value of k in the second equation to find time.

Begin by dividing 7 by 12 to get

$\frac{7}{12}=e^{k(70)}$ Now take the natural log of both sides since the natural log and that e are inverses. The e then disappears:

$ln(\frac{7}{12})=k(70)$

Plug the left side into your calculator and then set it equal to the right side, giving us:

$-.5389965007=70k$

Divide both sides by 70 to get the k value of

k = -.00769995

Now the second equation looks like this:

$2=12e^{(-.00769995)t$ where t is our only unknown now that we know k.

Begin by dividing both sides by 12 to get

$\frac{1}{6}=e^{-.00769995t$ and take the natural log of both sides again to eliminate the e:

$ln(\frac{1}{6})=-.00769995t$

Take care of the left side on your calculator to get

-1.791759469 = -.00769995t and divide both sides by -.00769995 to get

t = 232.697 minutes

4 0

2 years ago

Use an algebraic equation to find the measures of the two angles described below. begin by letting x represent the degree measur

Lina20 [59]

Two angles are said to be supplement when their measure add up to 180 degrees.

Assume that the angle we are looking for is a and its supplement is s (I used s instead of x).

a + s = 180
a = 180 - s ......> equation I

We know that <span>the measure of the angle is eight times greater than its supplement.
This means that:
a = 8s ......> equation II

Substitute by equation II in equation I to get s as follows:
180 - s = 8s
180 = 9s
s = 20 degrees

Substitute in equation I to get the measure of the angle as follows:
a = 180 - s = 180 - 20 = 160 degrees

Based on these calculations:
The measure of the angle is 160 degrees
The measure of its supplement is 20 degrees</span>

4 0

3 years ago