Which of the following is a true statement?

Which statement is valid when a circumscribed circle of an acute triangle is

Anni [7]

<h3>There are two answers: Choice C, Choice D</h3>

Explanation:

For any acute triangle, the center of the circle is always inside the triangle.

For any right triangle, the center of the circle is the midpoint of the hypotenuse. The hypotenuse is the diameter of the circle.

For any obtuse triangle, the center of the circle is outside the triangle.

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Let's look at the answer choices more closely

A. False. This is only true if we have a right triangle as mentioned earlier.

B. False. This describes an inscribed circle.

C. True. As stated earlier.

D. True. This is based on how the circumscribed triangle is defined. It is set up to be the circle that goes through all three vertex points of a triangle. In other words, it is the smallest circle to completely enclose the given triangle.

4 0

2 years ago

Given a line with slope m = -3/2 and a point (5, -6), what's the y-coordinate of the y- intercept?

Svetlanka [38]

Answer:

3/2

Step-by-step explanation:

y = mx + b

-6 = -3/2(5/1) + b

-12/2 = -15/2 + b

b = 3/2

3 0

2 years ago

Easy geometric shapes question!

Evgen [1.6K]

Answer:

Cylinder

Step-by-step explanation:

The given geometric shape is of a cylinder.

8 0

2 years ago

Read 2 more answers

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.

Let $\mu$ = average water usage by residents of Legacy Ranch.

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 One-sample t test statistics 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, test statistics = $\frac{63-67}{\frac{8.1}{\sqrt{23} } }$ ~ $t_2_2$

= -2.368

The value of the test statistics is -2.368.

Now at 0.025 significance level, the t table gives critical value of -2.074 at 22 degree of freedom for left-tailed test. 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 which we reject our null hypothesis.

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

8 0

3 years ago

The list below gives the location of friends who are scuba diving together.

Marianna [84]

According to the information, it can be inferred that the correct inequality is Mallory > Eva (option D).

<h3>How to identify who is closer to the surface of the water?</h3>

To identify who is closer to the surface of the water we must read the distance that each of the characters is.

In this case, the person closest to the surface is Eva, who is 5 feet from the surface.

Now we must identify which inequality corresponds to reality. In this case the inequality that is correct is:

Mallory > Eva

This inequality is correct because Mallory is further from the surface than Eva.

Learn more about inequality in: brainly.com/question/20383699

#SPJ1

6 0

1 year ago