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anygoal [31]
3 years ago
11

Triangle abc is such that ab=4 and ac=8 if m is the midpoint of bc and am=3, what is the length of bc?

Mathematics
1 answer:
zavuch27 [327]3 years ago
4 0
This is an interesting question. I chose to tackle it using the Law of Cosines.
  AC² = AB² + BC² - 2·AB·BC·cos(B)
  AM² = AB² + MB² - 2·AB·MB·cos(B)
Subtracting twice the second equation from the first, we have
  AC² - 2·AM² = -AB² + BC² - 2·MB²

We know that MB = BC/2. When we substitute the given information, we have
  8² - 2·3² = -4² + BC² - BC²/2
  124 = BC² . . . . . . . . . . . . . . . . . . add 16, multiply by 2
  2√31 = BC ≈ 11.1355

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Complete the following statements using m(x) = x² and n(x) = x – 3.
larisa [96]

Answer: x-3, 3, is not equal to

Step-by-step explanation:

7 0
2 years ago
What values of a and b would make the equation shown have infinitely many solutions? 3x=ax+b
Wittaler [7]
Infinitely many solutions means that you have the same thing on both sides of the equation no matter what value of x you plug in, right?

We just need both sides to be 3x then, correct?

If a were equal to 3 and b were equal to 0, we'd have

3x = (3)x + 0

Which is essentially 3x = 3x

So that means a = 3 and b = 0 must work!
Let's say x = 5

3(5) = 3(5) + 0

15 = 15 + 0

15 = 15

That means that a = 3 and b = 0 is your final answer :)
7 0
3 years ago
A gymnasium can hold no more than 650 people.A permanent bleacher in the gymnasium holds 136 people. The event organizers are se
ValentinkaMS [17]

Answer:

  20 chairs

Step-by-step explanation:

After 136 people are seated in the bleacher, there can be 514 people seated in chairs. We know that 514 = 25×20 +14, so there can be 20 rows of 25 chairs. We require an equal number of chairs in each row, so there cannot be some rows with 21 chairs, nor can there be a 26th row with 14 chairs.

There can be 20 chairs in each row.

3 0
2 years ago
Read 2 more answers
Please help me I can’t fail it
Hoochie [10]

Answer:

Step-by-step explanation:

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8 0
2 years ago
An amusement park would like to determine if they want to add in a new roller coaster. In order to decide whether or not they sh
Rzqust [24]

Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

In this problem, we have a 90% confidence level, hence\alpha = 0.9, z is the value of Z that has a p-value of \frac{1+0.9}{2} = 0.95, so the critical value is z = 1.645.

The sample size and the estimate are given by:

n = 600, \pi = \frac{400}{600} = 0.6667

Hence, the bounds of the interval are given by:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6667 - 1.645\sqrt{\frac{0.6667(0.3333)}{600}} = 0.6350

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6667 + 1.645\sqrt{\frac{0.6667(0.3333)}{600}} = 0.6984

The 90% confidence interval is given by: (0.6350, 0.6984).

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

5 0
2 years ago
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