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3 years ago

A line contains the points (-3, 4) and (7, -1). Calculate the equation of the line in the form y = mx + b Explain each step.

2 answers:

6 0

$\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{7-(-3)}\implies \cfrac{-5}{7+3}\implies \cfrac{-5}{10}\implies -\cfrac{1}{2}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-\cfrac{1}{2}[x-(-3)]\implies y-4=-\cfrac{1}{2}(x+3) \\\\\\ y-4=-\cfrac{1}{2}x-\cfrac{3}{2}\implies y=-\cfrac{1}{2}x-\cfrac{3}{2}+4\implies y=-\cfrac{1}{2}x+\cfrac{5}{2}$

Daniel [21]3 years ago

3 0

In order to find the equation of the line, you must first find the gradient of the line

Gradient of a line (m)= (y2-y1)/(x2-x1)
.....Now you substitute the points...
= ((-1)-4)/(7-(-3))
= (-5)/(10)
= -1/2

Therefore the gradient is negative a half (-1/2)

Now we can find the equation of the line. You can use one of the two points to find the equation of the line

Equation of a line: y-y1=m(x-x1)
... I chose to use (7,-1) as my points....
y-(-1)=-1/2(x-7)
y+1=-x/2+7/2
y=-x/2+(7/2)-1
1) y=-x/2+5/2
..... if you would like you can multiply everything by 2 to have while numbers instead of fractions ....
2) 2y=-x+5
... if you are uncomfortable of having x as negative, you can transpose it carrying both the -x and the 5 to the side of the 2y. NOTE that the sign changes and the equation will be equal to 0....
3) 2y+x-5=0

1,2 and 3 are all correct answers, just in different forms

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Benny is trying to learn how to ride a bike, but is terrified of falling. He did some research, and discovered that if he rides

Anestetic [448]

Answer:

a) 7.14% probability that Benny was learning to ride a bike using the training wheels

b) 28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.

a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that Benny was using each of these 3 methods is equal

This means that $P(B) = \frac{1}{3}$

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that $P(A|B) = 0.1$

Probability of falling:

1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

$P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667$

$P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714$

7.14% probability that Benny was learning to ride a bike using the training wheels

b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?

Similar as above, just some probabilities change.

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that he was using training wheels is 0.7

This means that $P(B) = 0.7$

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that $P(A|B) = 0.1$

Probability of falling:

0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

$P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25$

$P(B|A) = \frac{0.7*0.1}{0.25} = 0.28$

28% probability that Benny was learning to ride a bike using the training wheels

7 0

3 years ago

What is the solution of 2|2x-1|-8=18?

Maurinko [17]

Solve for $|2x-1|$ :

$2|2x-1|-8=18\implies2|2x-1|=26\implies|2x-1|=13$

Now if $2x-1\ge0$ , we have $|2x-1|=2x-1$ and

$2x-1=13\implies2x=14\implies x=7$

On the other hand, if $2x-1$ , then $|2x-1|=-(2x-1)=1-2x$ and

$1-2x=13\implies-2x=12\implies x=-6$

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3 years ago

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A cabinet door is 13 inches wide and has an area of 260 inches. Use the formula A=lw. How tall is the cabinet door?

klio [65]

Answer:

Step-by-step explanation:

260/13=20

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3 years ago

At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday

Zielflug [23.3K]

He has 87 cards then he gets 9 more which is 96, he then gives 16 away which is 80, then he is given 3 which is 83 he sells all 83 cards to the collector & the collector gives him $124.50 each card is worth $1.50

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3 years ago

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What is the value of x? <br><br> Enter your answer in the box.<br><br> X =

melamori03 [73]

Answer:

x=54

Step-by-step explanation:

2x + 2 = 3x - 52

subtract 2x from both sides, now u have:

2 = x - 52

add 52 from both sides, now u have

54 = x

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3 years ago