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3 years ago

Which must be true? Select two options. Point H is the center of the circle that passes through points D, E, and F.

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Answer:

A. Point H is the center of the circle that passes through points D, E, and F.

C. Line segment H E is-congruent-to line segment H D

Step-by-step explanation:

The center of a circle is a point within it that has the same distance to all other points on its circumference.

Constructing a circle with center H would pass through the points D, E and F at the three vertices of the given triangle. Thus producing a circumscribed circle to the triangle. A circumscribed circle is one that can is constructed outside a given figure.

It can also be observed that, DH ≅ EH ≅ FH. So that, the line segment HE is congruent to line segment HD.

The correct options in the given question are: A and C.

You might be interested in

Which is equivalent to 4 square root 9 1/2x?

motikmotik

I believe the correct answer is B. I really hope this was the correct answer and helped you out.

8 0

3 years ago

Read 2 more answers

the speed of a stream is 4mph. If a boat travels 92 miles downstream in the same time that it takes to travel 46 miles upstream,

Elanso [62]

Answer:

12 miles per hour

Step-by-step explanation:

Let speed of boat in still water be "x"

and speed of current be "c"

So, downstream rate would be "x + c"

And, upstream rate would be "x - c"

Now, given c = 4

We can use the distance formula, D = RT, where

D is distance, R is rate, and T is time

to solve this.

Downstream:

D = RT

92 = (x+4)(t)

Upstream:

D = RT

46 = (x-4)(t)

Both the times are same, we can equate both the times. Lets simplify first:

t = 92/(x+4)

and

t = 46/(x-4)

Equate:

$\frac{92}{x+4}=\frac{46}{x-4}$

Now, cross multiply and solve for x to get our answer:

$\frac{92}{x+4}=\frac{46}{x-4}\\92(x-4)=46(x+4)\\92x-368=46x+184\\46x=552\\x=12$

Speed of Boat (in still water) = 12 mph

6 0

3 years ago

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

zhannawk [14.2K]

Answer:

a) 0.6032

Lower limit: 0.48

Upper limit: 0.72

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.