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natulia [17]
3 years ago
10

Which value must be added to the expression x^2– 3x to make it a perfect-square trinomial?

Mathematics
1 answer:
liraira [26]3 years ago
3 0

Answer:

\frac{9}{4}

Step-by-step explanation:

Given

x² - 3x

add ( half the coefficient of the x- term)²

x² + 2(- \frac{3}{2})x + (- \frac{3}{2})²

= (x - \frac{3}{2})² + \frac{9}{4}

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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?

So

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

So

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

So

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
Write an equation for the parabolla
pentagon [3]

well, is noteworthy that an x-intercept is when y = 0 or namely is a solution or root of the quadratic, so we know then that the x-intercepts or solutions are at (-1,0) and (3,0), that simply means that

\bf (\stackrel{x}{-1},\stackrel{y}{0})\qquad (\stackrel{x}{3},\stackrel{y}{0})\qquad \begin{cases} x = -1\\ x+1=0\\ \cline{1-1} x=3\\ x-3=0 \end{cases}~\hfill \implies ~\hfill \stackrel{\textit{equation of the parabola}}{y = a(x+1)(x-3)} \\\\\\ \textit{we also know that } \begin{cases} x = 1\\ y = -8 \end{cases}\implies \underline{-8}=a(\underline{1}+1)(\underline{1}-3)

\bf -8=a(2)(-2)\implies -8=-4a\implies \cfrac{-8}{-4}=a\implies \boxed{2=a} \\\\[-0.35em] ~\dotfill\\\\ y=2(x+1)(x-3)\implies y=2(\stackrel{\mathbb{FOIL}}{x^2-2x-3})\implies y=2x^2-4x-6

4 0
3 years ago
Find the measure of < AED for m < BEC = 96
Strike441 [17]
I wish you would of put a picture but with what you gave me. if the angle is a straight line then you would just set it up like 96+x=180 bc a straight line ='s 180 and den subtract 96 from 180 which is 84 so x would = 84 if the angle is a supp. angle but til there's not a picture this might be wrong.
But i hope this helps have a nice nite!
5 0
3 years ago
Read 2 more answers
Can someone please answer the problem? Can someone also tell me what are supplementary angles?
skelet666 [1.2K]
Supplementary angles are angles that add up to 180 degrees

Answer = 180 - 142 = 38 degrees
5 0
3 years ago
Read 2 more answers
What is the area of this trapezoid? Please help me
jenyasd209 [6]

Answer:

192

Step-by-step explanation:

both triangles are 12 in and the square is 168

so 12+12+168= 192in

3 0
3 years ago
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