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3 years ago

A line is perpendicular to y = 3x - 8

Mathematics

1 answer:

sleet_krkn [62]3 years ago

7 0

Since the line is perpendicular, we know that the slope is reciprocal and negative to the other one.

So,

y = -4x + b

We want to find the y-intersect (b) so substitute the intersected points and solve for it.

2 = -4(2) + b

2 = -8 + b

2 + 8 = b

10 = b

So the complete equation would be:

y = -4x + 10

You might be interested in

There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once.

pychu [463]

Answer:

When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen. Here the card is chosen with replacement. This implies probability for choosing a prime number remains the same as the previously drawn card is replaced.

The sample space= {1,2,3,4,5,6,7,8,9,10}

Prime numbers = {2,3,5,7}

Prob for drawing prime number = 4/10 = 0.4

is the same when replacement is done.

Also there are two outcomes either prime or non prime. Hence in this case, X the no of times a prime number is chosen, is binomial with p =0.4 and q = 0.6 and n=5

When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.

Prob for an even number = 0.5

But after one card drawn say odd number next card has prob for even number as 5/9 hence each draw is not independent of the other. Hence not binomial.

When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.

Here since every time replacement is done, probability of drawing a 3 remains constant = 1/10 = 0.3

i.e. each draw is independent of the other and there are only two outcomes , 3 or non 3. Hence here X is binomial.

When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen

Here X is the number of times a card is chosen with replacement till 5 is chosen. This is not binomial. Here probability for drawing nth time correct 5 is P(non 5 in the first n-1 draws)*P(5 in nth draw) = 0.1^(n-1) (0.9)

Because nCr is not appearing i.e. 5 cannot appear in any order but only in the last draw, this is not binomial.

Step-by-step explanation:

6 0

3 years ago

Find the range for the measurement of the third side of a triangle, x, given the measures of the two sides: 6 ft and 13 ft.

Rudik [331]

|13-6| < x < |13+6|

So the range will be:

7 < x < 19

8 0

3 years ago

State whether each pair of terms are like terms. (so yes or no)

Rom4ik [11]

Answer: 4xy and 3xy are, 2s and 5s are, but -10 and -10b aren't.

Step-by-step explanation: 4xy and 2xy have the same terms. 2s and 5s have the same terms but -10a and -10b have different variables.

7 0

3 years ago

Please help with imaginary numbers worksheet!

mihalych1998 [28]

Problem 5

<h3>Answer: 6i</h3>

------------------

Explanation:

We have these four identities

i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i

Notice how computing i^4 leads us back to 1. So i^4 = i^0. The pattern repeats every 4 terms. So we divide the exponent by 4 and look at the remainder. We ignore the quotient entirely. We can see that 28/4 = 7 remainder 0. Meaning that i^28 = i^0 = 1.

We can think of it like this if you wanted

i^28 = (i^4)^7 = 1^7 = 1

Then the sqrt(-36) becomes 6i

So overall, we end up with the final answer of 6i

=============================================

Problem 6

<h3>Answer: -3i</h3>

------------------

Explanation:

We'll use the ideas mentioned in problem 5

46/4 = 11 remainder 2

i^46 = i^2 = -1

sqrt(-9) = 3i

The two outside negative signs cancel out, but there's still a negative from -1 we found earlier. So we end up with -3i

In other words, here is one way you could write out the steps

$-i^{46}*-\sqrt{-9}\\\\-i^{2}*-3i\\\\i^{2}*3i\\\\-1*3i\\\\-3i\\\\$

=============================================

Problem 7

<h3>Answer: -1</h3>

------------------

Work Shown:

i^10 = i^2 because 10/4 = 2 remainder 2

i^19 = i^3 because 19/4 = 4 remainder 3

i^7 = i^3 because 7/4 = 1 remainder 3

Again, all we care about are the remainders.

$i^{10}+i^{19} - i^{7}\\\\i^{2}+i^{3} - i^{3}\\\\i^{2}\\\\-1$

=============================================

Problem 8

<h3>Answer: -1 + i</h3>

------------------

Work Shown:

i^22*i^6 = i^(22+6) = i^28

Earlier in problem 5, we found that i^28 = i^0 = 1

So,

$i^1 - \left(i^{22}*i^{6}\right)\\\\i^1 - i^{28}\\\\i^1 - i^{0}\\\\i - 1\\\\-1+i$

8 0

3 years ago

Read 2 more answers

Help please this is so hard I don't understand it

Zina [86]

Answer:

<ABC = 15

< BAC = 150

Step-by-step explanation:

<C = <B since this is an isosceles triangle. We know this because AC = AB

<C = 15 so <ABC = 15

The sum of the angles of a triangle is 180

A + B+ C = 180

A + 15+15 = 180

A +30 =180

A = 180-30

A = 150

< BAC = 150

5 0

3 years ago