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2 years ago

8

On a number line, point A has a coordinate of -6, and point B has a coordinate of 2. Which is the coordinate of point M, the mid

point of AB?
A) -3
B) -2
C) 0
D) 4

1 answer:

damaskus [11]2 years ago

5 0

In my opinion
The answer is B

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one leg of a right triangle is 5 millimeters shorter than the longer leg and the hypotneuse is 5 millimeters longer than the lon

Makovka662 [10]

The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
-----------------------------
The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².

Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5.

So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²

Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25

Now combine like terms:
2B² -10B + 25 = B² + 10B + 25

And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B

Subtract B² from each side:
B² - 10B = 10B

Add 10B to each side:
B² = 20B

And finally, divide each side by B:
B = 20

So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.

And your final answer is A = 15mm, B = 20mm, and H = 25mm

7 0

2 years ago

. The temperature fell 13°c on each of the first 2 days of the week. It rose 7°c on each of

Rina8888 [55]

Answer:

The final temperature was 9 degrees.

Step-by-step explanation:

You can first multiply 13x2, 7x2, and 9x2. Then you subtract 26 and 18 from 34. then add 14

4 0

2 years ago

DiKsa [7]

Answer:

9 books

Step-by-step explanation: 10- 1 = 9. Take away is subtract

6 0

3 years ago

The American Water Works Association reports that the per capita water use in a single-family home is 67 gallons per day. Legacy

inessss [21]

Answer:

We conclude that the null hypothesis is rejected which means residents of Legacy Ranch use less water on average.

Step-by-step explanation:

We are given that the American Water Works Association reports that the per capita water use in a single-family home is 67 gallons per day.

Twenty-three owners responded, and the sample mean water use per day was 63 gallons with a standard deviation of 8.1 gallons per day.

<u><em>Let </em></u> $\mu$ <u><em> = average water usage by residents of Legacy Ranch.</em></u>

So, Null Hypothesis, $H_0$ : $\mu \geq$ 67 gallons {means that the residents of Legacy Ranch uses more or equal to 67 gallons water on average}

Alternate Hypothesis, $H_A$ : $\mu$ < 67 gallons {means that the residents of Legacy Ranch use less water on average}

The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean water use per day = 63 gallons

s = sample standard deviation = 8.1 gallons

n = sample of responded = 23

So, <u><em>test statistics</em></u> = $\frac{63-67}{\frac{8.1}{\sqrt{23} } }$ ~ $t_2_2$

= -2.368

The value of the test statistics is -2.368.

<em>Now at 0.025 significance level, the </em><u><em>t table gives critical value of -2.074 at 22 degree of freedom for left-tailed test</em></u><em>. Since our test statistics is less than the critical values of t as -2.368 < -2.074, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to </em><u><em>which we reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the residents of Legacy Ranch use less water on average.

8 0

3 years ago

Identify at least one Hamilton path and at least one Hamilton circuit

Anna71 [15]

We will investigate how to determine Hamilton paths and circuits

Hamilton path: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex can be different.

Hamilton circuit: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex must be the same!

As the starting point we can choose any of the points. We will choose point ( F ) and trace a path as follows:

$F\to D\to E\to C\to A\to B\to F$

The above path covers all the vertices/points with the starting and ending point/vertex to be ( F ). Such a path is called a Hamilton circuit per definition.

We will choose a different point now. Lets choose ( E ) as our starting point and trace the path as follows:

$E\to D\to F\to B\to A->C$

The above path covers all the vertices/points with the starting and ending point/vertex are different with be ( E ) and ( C ), respectively. Such a path is called a Hamilton path per definition.

One more thing to note is that all Hamilton circuits can be converted into a Hamilton path like follows:

$F\to D\to E\to C\to A\to B$

The above path is a hamilton path that can be formed from the Hamilton circuit example.

But its not necessary for all Hamilton paths to form a Hamilton circuit! Unfortunately, this is not the case in the network given. Every point is in a closed loop i.e there is no loose end/vertex that is not connected by any other vertex.

4 0

6 months ago