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2 years ago

Triangle ABC has vertices of A(–6, 7), B(4, –1), and C(–2, –9). Find the length of the median from angle B in triangle ABC

Mathematics

1 answer:

julsineya [31]2 years ago

7 0

Answer:

Step-by-step explanation:

The median is the segment from vertex B to the midpoint of AC. That midpoint (D) is ...

D = (A + C)/2 = ((-6, 7) +(-2, -9))/2 = (-8, -2)/2

D = (-4, -1)

The length of the midpoint is the length of the segment DB between (-4, -1) and (4, -1). These points both have the same y-coordinate, so the length is the difference of x-coordinates: 4 -(-4) = 8.

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Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was

SSSSS [86.1K]

<h2>Answer:</h2>

First of all let's write the slope-intercept form of the equation of a line, which is:

$y=mx+b \\ \\ Where: \\ \\ m: \ slope \\ \\ b: \ y-intercept$

So we just need to find $m \ and \ b$ to solve this problem.

Moreover, this problem tells us that Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. So this rate is the slope of the line, that is:

$m=-12$

Negative slope because Amir is descending. So:

$y=-12x+b$

To find $b$ , we need to use the information that tells us that he was at sea level after 30 minutes of driving, so this can be written as the point $(30,0)$ . Therefore, substituting this point into our equation:

$y=-12x+b \\ \\ 0=-12(30)+b \\ \\ 0=-360+b \\ \\ \therefore b=360$

Finally, the equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is:

$\boxed{y=-12x+360}$

Whose graph is shown bellow.

6 0

2 years ago

Read 2 more answers

Shana bought 6.2 pounds of pecans and paid $56.00. About how much per pound did the pecans cost?

bogdanovich [222]

Answer:

D. About $10

Step-by-step explanation:

To find unit price, you divide the total price by how much you're buying.

For example - $56 divided by 6.2 pounds of pecans is 9.032258064516129032258064516129‬ which can be rounded up to about $10

7 0

2 years ago

Read 2 more answers

Teo makes a necklace of x wooden beads at $0.50 each and 6 glass beads at $1.25 each. The average cost of the beads in the neckl

Ainat [17]

Answer:

0.50x + 7.50 = 0.75(x+6)

Hope this helps :)

4 0

2 years ago

Statistics In the manual “How to Have a Number One the Easy Way,” it is stated that a song “must be no longer than three minutes

dimaraw [331]

Answer:

We conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Step-by-step explanation:

We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.

Assume that the standard deviation of song lengths is 54.5 sec.

Let $\mu$ = population mean length of the songs

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}

Alternate Hypothesis, $H_A$ : $\mu$ > 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean length of songs = 252.5 seconds

$\sigma$ = population standard deviation = 54.5 seconds

n = sample of current hit songs = 40

So, the test statistics = $\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }$

= 4.932

The value of z-test statistics is 4.932.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.

4 0

2 years ago

Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a differen

Anna007 [38]

Answer:

5 miles.

Step-by-step explanation:

Consider the question: Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a different route taking 2 1/2 hours. How many miles did Jinghua hike on the return trip ?

First of all, we will find Jinghua's speed using given information as:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Convert mixed fractions into improper fractions:

$4\frac{1}{2}\Rightarrow \frac{9}{2}$

$2\frac{1}{4}\Rightarrow \frac{9}{4}$

$\text{Jinghua's speed}=\frac{\frac{9}{2}\text{ Miles}}{\frac{9}{4}\text{ Hours}}$

Using property $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$ :

$\text{Jinghua's speed}=\frac{9*4\text{ Miles}}{9*2\text{ Hours}}$

$\text{Jinghua's speed}=\frac{2\text{ Miles}}{\text{ Hour}}$

We know that distance is equal to the product of speed and time.

$\text{Distance}=\text{Speed}\times\text{Time}$

Since we have been given that Jingua hiked the return trip at the same average rate, so distance covered by her on return trip would be speed (2 miles her hour) times given time (2 1/2 hours).

$\text{Distance covered by Jingua on return trip}=\frac{2\text{ Miles}}{\text{ Hour}}\times 2\frac{1}{2}\text{ Hours}$

$\text{Distance covered by Jingua on return trip}=2\text{ Miles}\times \frac{5}{2}$

$\text{Distance covered by Jingua on return trip}=5\text{ Miles}$

Therefore, Jingua hiked 5 miles on her return trip.

8 0

2 years ago