All categories

3 years ago

describe how do you know if two lines are parallel if all you knew were the equations of the two lines

Mathematics

2 answers:

Marrrta [24]3 years ago

7 0

Two lines are parallel if they intersect.

Andreyy893 years ago

5 0

Answer:

Step-by-step explanation:

Put what you are given in the form of

y = mx + b

If both equations have the same m, the lines are parallel. For example

y = 4x + 10

y = 4x + 20

These two lines are parallel.

However

y = 8x + 40

y = 4x + 10 are not parallel even though it looks like m could be made the same by taking out 4 in each. Check them out on the graph below.

You might be interested in

<img src="https://tex.z-dn.net/?f=%3Cbr%3E%0Ay%3D%20x%5E%7B2%7D%20-9" id="TexFormula1" title="&#10;y= x^{2} -9" alt="&#1

svp [43]

Simple...

y= $x^{2} -9$

$y= x^{2} -9$

It's quite easy to see $x^{2} = x^{2}$

Thus, any value of x makes the equation true.

Thus, your answer.

7 0

3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

Micheal has been awarded a pay rise of 4%.His salary is £ 24 492 <br> What was his apart before?

Nesterboy [21]

Because there was a pay rise, we can write the equation as x+0.04x = 24.492 and solve for x.

x+0.04x = 24.492
1.04x = 24.492
x=23.55

His original pay was £23.55

6 0

3 years ago

The Big Falcon Rocket (BFR or Starship) from Space X can carry approximately 220,000 pounds. If they only carried $100 bills, ho

kifflom [539]

Answer:

$9,979,032,100 or $9.979 billion

Step-by-step explanation:

The approximate weight of a $100 bill is 1 gram.

All of the calculations bellow assume that the volume of the bills would not be an issue and only concerns weight.

1 pound is equivalent to approximately 453.59237 grams.

The weight in grams that the Big Falcon Rocket can carry is:

$W= 220,000*453.59237=99,790,321.4\ g$

Since each bill weighs 1 gram, the number of bills it could carry, rounded to nearest whole bill is 99,790,321. The total amount it could carry is:

$A=99,790,321*\$100=\$9,979,032,100$

4 0

4 years ago

Ivan makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.

Vlada [557]

Answer: p=8h

Hope this helped

Step-by-step explanation:

5 0

3 years ago