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3 years ago

Which point is the incenter of △DEF ?

Mathematics

2 answers:

stellarik [79]3 years ago

7 0

It is point G, because that is where the 3 angle bisectors meet.

charle [14.2K]3 years ago

4 0

Answer:- G is the point which is the incenter of Δ DEF.

Explanation:-

Incenter of a triangle is defined as a point occurred by the intersection of the internal angle bisectors of the three vertices of the triangle.

In the given picture ΔDEF has three angle bisectors ,bisecting vertices of triangle D,E and F and intersect at point G.

Thus point G is the incenter of Δ DEF.

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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

$s$ : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

Ben:

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

Josh:

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ Eqn. (4).

Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at $h(t)=0$ . Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.

Thus we have for Ben, Eqn. (3) gives:

$h(t)=0-16t^2+60t+40=0$

Using the quadratic expression to find the roots of the quadratic we have:

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$

Since time can only be positive we reject the $t_{2}$ solution and we keep that Ben's book took $t=4.3276$ seconds to reach the ground.

Similarly solving for Josh we obtain

$t_{1}=3.6794sec\\t_{2}=-0.6794sec$

Thus again we reject the negative and keep the positive solution, so Josh's book took $t=3.6794$ seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

$t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482$

So to answer the original question:

Whose textbook reaches the ground first and by how many seconds?

Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of $t=0.6482$

3 0

3 years ago

Alexandra and Austin applied to the same university. They looked up the average SAT score of students admitted to that universit

Deffense [45]

Answer:

x= (y+40)-(y-330)

Step-by-step explanation:

According to the information provided, the difference in their scores would be the result of subtracting Austin's SAT score from Alexandra's SAT score.

Then, as Alexandra's SAT score was 40 points above the average score this means that you have to add 40 to the average score to get her result. Also, as Austin's SAT score was 330 points below the average score, this means that you have to subtract 330 from the average score. With this you can write the expression:

x= difference in their scores

y= average score

x= (y+40)-(y-330)

7 0

3 years ago

The three sides of a triangle are: 16, 12 and 22. Is the triangle Acute, Right, or Obtuse?

tamaranim1 [39]

I know it’s not right, I think it’s obtuse

7 0

3 years ago

Find the area of a sector with a central angle of 125 degrees and a radius of 11cm. Express the approximate answer to the neares

White raven [17]

The answer is c I’m pretty aure

5 0

3 years ago

If you know any of these could yoy hep me out :D

Mekhanik [1.2K]

7. X=5
8. X=6
9. B=-3
10. G=3.4

5 0

2 years ago

Which point is the incenter of ​ △DEF ​ ?

Which point is the incenter of △DEF ?