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4 years ago

Which of the following is a step in constructing a circle circumscribed about a triangle?

Mathematics

1 answer:

zaharov [31]4 years ago

8 0

Answer:

<u><em>Use the perpendicular bisectors to find the center of the circle</em></u>.

Explanation:

A <em>circle circumscribed about a triangle</em> passes through the three vertices of the triangle.

The distance from each vertex to the center of the <em>circle</em> is the radius of the circle: each vertex of the triangle is at the same distance from the center of the circle.

All the points on the <em>perpendicular bisector</em> of a side of the triangle are at the same distance from the two vertices that define that side.

Thus, where the three perpedicular bisectors intersect each other is a point (the only one) at the same distance from the three vertices of the triangle, i.e. the center of the circle.

Hence, once the center of the circle is found, you can use a compass to draw the circle that passes through the three vertices of the triangle to construct the circle circumscribed about the triangle.

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Please help i dont understand it<br>30 POINTS

IceJOKER [234]

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

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3 years ago

What does > −1 indicate about the positions of and −1 on the number line? (4 points) Select one: a. is located on the right o

aksik [14]

>-1 means 'Greater than -1'. So, the numbers like 0,1,2,3,.... and so on are signified by '>-1'. So, >-1 signifies all the numbers to the right of -1. That is, Option (d). Also, 0 is located to the right of -1.

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4 years ago

After stepping into a room with unusual lighting, Reagan's pupil has a radius of 1 millimeter. What is the pupil's area?

Alexeev081 [22]

Answer: The formula is PI * RADUIS²
So, multiplying the radius by itself is 1, and then multiplying 1 by PI is the same as 3.14 .

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2 years ago

Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the ques

Ganezh [65]

<h2>a. What is your equation?</h2>

This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:

$h(t)=-\frac{1}{2}gt^2+v_{0}t+h_{0}$

Where:

$h(t): \ height \ at \ any \ time \\ \\ g: \ acceleration \ due \ to \ gravity \ 9.8m/s^2 \ or \ 32.16ft/s^2 \\ \\ v_{0}= \ Initial \ velocity$

So:

$v_{0}=64ft/s \\ \\ h_{0}=3ft$

Finally, the equation is:

$h(t)=-\frac{1}{2}(32.16)t^2+(64)t+3 \\ \\ \boxed{h(t)=-16.08t^2+64t+3}$

<h2>b. How long will it take the rocket to reach its maximum height?</h2>

The rocket will reach the maximum height at the vertex of the parabola described by the equation $h(t)=-16.08t^2+64t+3$ . Therefore, our goal is to find $t$ at this point. In math, a parabola is described by the quadratic function:

$f(x)=ax^2+bx+c$

So the x-coordinate of the vertex can be calculated as:

$x=-\frac{b}{2a}$

From our equation:

$a=-16.08 \\ \\ b=64 \\ \\ c=3$

So:

$t=-\frac{64}{2(-16.08)} \\ \\ \boxed{t=1.99s}$

So the rocket will take its maximum value after 1.99 seconds.

<h2>c. What is the maximum height the rocket will reach?</h2>

From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by $h(1.99)$ . Thus, we can find this as follows:

$H_{max}=h(1.99)=-16.08(1.99)^2+64(1.99)+3 \\ \\ \boxed{H_{max}=66.68ft}$

So the maximum height the rocket will reach is 66.68ft

<h2>d. How long is the rocket in the air?</h2>

The rocket is in the air until it hits the ground. This can be found setting $h(t)=0$ , so:

$0=-16.08t^2+64t+3 \\ \\ Applying \ quadratic \ formula: \\ \\ t_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=-16.08 \\ \\ b=64 \\ \\ c=3 \\ \\ t_{12}=\frac{-64 \pm \sqrt{64^2-4(-16.08)(3)}}{2(-16.08)} \\ \\ t_{1}=4.0264 \\ \\ t_{2}=-0.046$

We can't have negative value of time, so the only correct option is $t_{1}=4.0264$ and rounding to the nearest hundredth we have definitively:

$\boxed{t=4.03s}$

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4 years ago

Rory has 3 pounds of ground beef to make meatballs. He uses 3/8 pound per meatball to make 7 meatballs. How many 1/8-pound meatb

olga55 [171]

Answer:

Step-by-step explanation:

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