Hiring the bus will cost $25 a day for the driver, $2 per mile traveled, and $3 for gas per mile traveled. The field trip will total 8 miles round trip.

Mrs. Garcia needs to calculate the cost of the bus. Which expression could she write that uses the distributive property?

Answer:

AE and BE

Step-by-step explanation:

Please refer to the image attached with this.

Here in we have made a diagram a per the conditions given in the question. If  we observe ΔABE, We see

AG=GE ( CD is perpendicular bisector of AB , Hence G is mid point)

∠AGE = ∠BGE = 90°

GE = GE

Hence

ΔAGE ≅ ΔBGE

Therefore the theorem of congruent triangles  ,

AE ≅ BE

To answer the question, let's break down what we know from the given information:
1. CD is the perpendicular bisector of AB: This means that CD intersects AB at a 90-degree angle (perpendicular) and divides AB into two equal parts (bisector).
2. G is the midpoint of AB: This means that point G is exactly in the middle of AB, which implies that AG is equal in length to GB.
3. Points E and F lie on CD: Without additional information, we cannot determine any specific relationships between E and F and the other points. However, since E and F are on CD, they are somewhere along the line that includes the perpendicular bisector.
The question asks which pair of line segments must be congruent.
Since G is the midpoint of AB and CD is the perpendicular bisector of AB, by definition of the perpendicular bisector, AG must be congruent to GB. This is because a perpendicular bisector not only intersects a segment at a right angle but also cuts the segment into two congruent parts.
Therefore, the pair of line segments that must be congruent are AG and GB.

Answer:

10.5

Step-by-step explanation:

tan(55°)=15/b

b=15/tan(55°)

=10.5

Answer:

AC ≈ 10.5

Step-by-step explanation:

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{15}{b}[/tex]

Multiply both sides by b

b × tan55° = 15 ( divide both sides by tan55° )

b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5

Hence b = AC ≈ 10.5 ( to the nearest tenth )

Answer:

D

Step-by-step explanation:

Given the 2 equations

2x + 3y = 11 → I(1)

y = x - 3 → (2)

Substitute y = x - 3 into (1)

2x + 3(x - 3) = 11 ← distribute parenthesis and simplify left side

2x + 3x - 9 = 11

5x - 9 = 11 ( add 9 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Substitute x = 4 into (2) for corresponding value of y

y = 4 - 3 = 1

Solution is (4, 1 ) → D

The correct ordered pairs for the equations 2x+3y=11, y=x-3 is (4,1)

In the substitution method we have to calculate the value of one variable by  putting the value of another variable in terms of first variable.

We are having two equations

2x+3y=11.......1

y=x-3........2

Put the value of y from2 in 1

2x+3(x-3)=11

2x+3x-9=11

5x=20

x=4

put the value of x=4 in 2

y=4-3

y=1

Hence the ordered pairs becomes (4,1)

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pretty much about the same as before.

a = weight of a large box

b = weight of a small box.

we know their combined weight is 65 lbs, thus a + b = 65.

we also know that the truck has 60 large ones, and 55 small ones, thus 60*a is the total weight for the large ones and 55*b is the total weight for the small ones, and we know that is a total of 3775, 60a + 55b = 3775.

[tex]\bf \begin{cases} a+b=65\\ \boxed{b}=65-a\\ \cline{1-1} 60a+55b=3775 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{60a+55\left( \boxed{65-a} \right)=3775} \\\\\\ 60a+3575-55a=3775\implies 5a+3575=3775\implies 5a=200 \\\\\\ a=\cfrac{200}{5}\implies \blacktriangleright a = 40 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=65-a\implies }b=65-40\implies \blacktriangleright b=25\blacktriangleleft[/tex]

h = 800

In this question, we're trying to find the value of h.

Lets set up an equation:

[tex]1.5/100 * h = 12[/tex]

With the equation above, we can solve it to find the answer.

[tex]1.5/100h = 12\\\\\text{We would first divide 1.5 by 100}\\\\0.015h=12\\\\\text{Now, we would simply divide}\\\\h=800[/tex]

When you're done solving, you should get 800.

This means that h = 800

To check if it's correct, we could multiply 800 by 0.015 (1.5%) to see if it gives us 12.

[tex]800*0.015=12[/tex]

Now, we can confirm that the answer is h = 800

Answer:

The solution is

[tex]x=\frac{9}{11}[/tex]

[tex]y=\frac{17}{11}[/tex]

Step-by-step explanation:

We have the system:

-4x+6y=6

-7x+5y=2

I would like to solve this by elimination because I don't feel like rearranging both equations and they both have the same form which is crucial in elimination. The only thing is I will need opposites in a column (where the variable are).

So I'm going to focus on the x's.  I want the x part to be opposites.

I know if I multiply the first equation by 7 I will get -28x plus... and if I multiply the last equation by -4 I will get 28x plus... .

28x and -28 are opposites and we all know what happens to opposites when you add them. They zero out; cancel out.  That is -28x+28x=0.

So let's multiply first equation by 7 and

multiply bottom equation by -4:

-28x+42y=42

28x-20y=-8

----------------------We are ready to add the equations:

  0+22y=34

      22y=34

Divide both sides by 22:

          y=34/22

Reduce the fraction:

         y=17/11              (I divided top and bottom by 2.)

Now if y=17/11 and -4x+6y=6, we can find x by inserting 17/11 for y in the second equation I wrote in this sentence.

[tex]-4x+6\cdot \frac{17}{11}=6[/tex]

Perform the simplification/multiplication of 6 and 17/11:

[tex]-4x+\frac{102}{11}=6[/tex]

Subtact 102/11 on both sides:

[tex]-4x=6-\frac{102}{11}[/tex]

Find a common denominator:

[tex]-4x=\frac{66}{11}-\frac{102}{11}[/tex]

[tex]-4x=\frac{-102+66}{11}[/tex]

[tex]-4x=\frac{-36}{11}[/tex]

Divide both sides by -4:

[tex]x=\frac{-36}{-4(11)}[/tex]

Reduce 36/4 to 9:

[tex]x=\frac{9}{11}[/tex]

[tex]x=\frac{9}{11}[/tex]

The solution is

[tex]x=\frac{9}{11}[/tex]

[tex]y=\frac{17}{11}[/tex]

Answer:

6

Step-by-step explanation:

54=2x3x3x3

12=2x2x3

common factors are 2 and 3 so 2x3=6

Answer:

25 nickels and 23 quarters

Step-by-step explanation:

The smallest possible integer solution is 23 nickels and 25 quarters.

23×0.05 + 25×0.25 = 1.15 + 6.25 = $7.40.

That's already over $7.00.

We can't solve the problem as stated unless we use fractional numbers of coins, and that's impossible.

Assume the correct ratio is 25/23

Let n = number of nickels

and q = number of quarters. Then we have two conditions.

(1)                                n/q = 25/23

(2)             0.05n + 0.25q = 7

(3)                                    n = (25/23)q     Multiplied (1) by q

(4) 0.05(25/23)q + 0.25q = 7                  Substituted (3) into (1)

          0.05435q + 0.25q = 7                  Simplified

                          0.3043q = 7                  Combined like terms

(5)                                   q = 23              Divided each side by 0.3043

                                 n/23 = 25/23         Substituted (5) into (1)

                                       n = 25              Divided each side by 23

There are 25 nickels and 23 quarters.

Check:

(1) 25/23 = 25/23     (2) 0.05×25 + 0.25×23 = 7

                                                     1.25 + 5.75 = 7

                                                                     7 = 7

OK.  

The salesman earned $280 in commission last month, which was calculated by taking 40% of the $700 worth of merchandise he sold.

This question is about calculating commission which falls under the topic of percentage calculations in math. The salesman earns a 40% commission on the merchandise he sells. So, to find out how much he earned in commission last month, we need to calculate 40% of the total value of merchandise he sold, which is $700.

To do this, multiply $700 by 40% (or 0.4 in decimal form). That would give you $280. So, the salesman earned $280 in commission last month.

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To find out how much commission the salesman earned, we need to calculate 40% of the $700 worth of merchandise that he sold. The commission rate is expressed as a percentage, which we can also write as a decimal for the purpose of calculation.
First, let's convert the commission rate from a percentage to a decimal. To do this, we divide the percentage by 100:
40% / 100 = 0.40
Now that we have the commission rate as a decimal, we can calculate the commission by multiplying the sales amount by the commission rate.
The calculation is as follows:
Commission = Sales Amount × Commission Rate
Commission = $700 × 0.40
Calculating this gives us:
Commission = $280
Therefore, the salesman earned $280 in commission last month.

Step-by-step explanation:

Let the number be x

ATQ,

-200+x =45

x=45+200

x=245

The other integer is equal to 245.

We know that [tex]x+y=45[/tex].  We also know that [tex]x=-200[/tex].

Substitute the value into the equation.  [tex]-200+y=45[/tex]

Add 200 to both sides of the equation.  [tex]y=45+200=245[/tex]

Now, you have the answer.  [tex]y=245[/tex]

Answer:

15

Step-by-step explanation:

Population size= 2107+903+1505+1499

                        = 6014

Calculating the sample of ward B by using the stratified random sampling formula:

Stratified Random Sample, np= ( Np / N ) * n

where

np= pth stratum  sample size

Np= pth stratum  population size

N = population  size

n = sample size

Stratified Sample (ward B) = 100 / 6014 * 903 = 15 !

The values of x for which A U B = ø (empty set) are x > 3 AND x < 2, but no number can satisfy both inequalities simultaneously.

To find the values of x for which A U B = ø (empty set), we need to find the values that make both inequalities false. Let's solve each inequality separately:

Inequality 1: 3x + 4 > 13

Subtracting 4 from both sides, we get 3x > 9. Dividing both sides by 3, we have x > 3.

Inequality 2: 1/2x + 3 < 4

Subtracting 3 from both sides, we get 1/2x < 1. Multiplying both sides by 2, we have x < 2.

Therefore, the values of x that satisfy both inequalities are x > 3 AND x < 2.

However, no number can be greater than 3 and less than 2 at the same time, so the solution for A U B = ø (empty set).

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Answer:

[tex]\sqrt[5]{13^3} = 13^{\frac{3}{5}}[/tex]

Step-by-step explanation:

Answer:

D on EDGE

Step-by-step explanation:

Answer:

Step-by-step explanation:

She has 1 in 11 chances of getting the purple one

One of her choices is gone after she takes out the purple one. She has a 1 in 10 chance of taking out the gray one.

1/11 * 1/10 = 1/110

The probability that Gloria will draw the purple marker first and then the gray marker from her backpack on consecutive tries without replacement is 1/110.

The question asks to find the probability that Gloria will pull the purple marker and then the gray marker out of the backpack on consecutive tries without replacement. To calculate the combined probability of two independent events happening in succession, you multiply the probability of each event occurring separately.

On the first draw, the probability of selecting the purple marker is 1 out of 11 markers, or 1/11. After drawing the purple marker, it is not replaced, so there are now only 10 markers left, one of which is gray. The probability of drawing the gray marker on the second draw is then 1 out of the remaining 10 markers, or 1/10.

To find the overall probability of both events happening, multiply the two probabilities: (1/11) x (1/10) = 1/110.

The probability that Gloria will draw the purple marker first and then the gray marker is 1/110.

Answer:

See below.

Step-by-step explanation:

Increases by 25% :- it is 80 * 1.25 = 100.

100 decreased by 25% = 100 * 0.75

= 75.

Answer:

75

Step-by-step explanation:

We are given that 80 is increased by 25% and then decreased by 25% so we are to find the final value.

Increase of 25% in 80 = 25% of 80

= 25/100 × 80

= 20

So our new value after 25% increase = 80 + 20 = 100

Now this new value is decreased by 25% = (100 - 25)% of 100

= 75/100 × 100

= 75

Answer:

the answer is A

Step-by-step explanation:

always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to

start with the 950 * .018 = 171.00

950 + 171.00 = 1121.00

then you follow this process

1121.00 * .018 = 201.78

1121.00 + 201.78 = 1322.78

The answer is A

Always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to

Start with the 950 *.018 = 171.00

950 + 171.00 = 1121.00

Then you follow this process

1121.00 * .018 = 201.78

1121.00 + 201.78 = 1322.78

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

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Answer:

One side is 10

Step-by-step explanation:

10*10 is equal to 100

Answer:

8.55 inches

Step-by-step explanation:

We can use the slope intercept form to write this equation

y = mx+b where m is the lope and b is the y intercept

The y intercept, b, is how tall the candle is when we start, 12 inches

The slope is the rate at which it is burning or -.75  (the negative is because it is burning or getting smaller)

y = -.75x+12

or rewriting

t = 12-.75h  where h is the hours and t is how tall

We are burning for 4.6 hours

t = 12-.75(4.6)

t = 12 -3.45

t= 8.55

Answer:

4\pm\sqrt{19}

Step-by-step explanation:

Move everything to left side

[tex]x^{2} -8x -3 =0[/tex]

Now to solve this square equation we need to find Descriminant

[tex]D=b^{2} -4ac=64+12=76[/tex]

As Descriminant D is greater than 0 then we have 2 solutions which we can calculate by this formula

[tex]x_{1,2}=\frac{-b\pm\sqrt{D}}{2a} =\frac{8\pm2\sqrt{19}}{2}=4\pm\sqrt{19}[/tex]

Completing the square in mathematics is a technique used to solve quadratic equations by transforming them into a perfect square trinomial form. It helps in finding the roots of the equation more efficiently.

Completing the square involves transforming a quadratic equation into a perfect square trinomial form to solve it. In the case of x^2 - 8x = 3, the steps would include halving the coefficient of x, squaring that value, and adding/subtracting it to both sides of the equation to complete the square.

The solution set for the equation x^2 - 8x = 3 would be {4 + √19, 4 - √19}, as completing the square helps in finding the roots of the quadratic equation.

Completing the square is a helpful technique in mathematics for solving quadratic equations more easily and efficiently.

Answer:

Step-by-step explanation:

The point-slope form of an equation:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation of a line:

[tex]y=5x-3[/tex]

therefore the slope m = 5.

Put the value of the slope and the coordinates of the given point (-2, -13) to the equation of a line:

[tex]y-(-13)=5(x-(-2))\\\\y+13=5(x+2)[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y-1=\frac{2}{3}(x-3)[/tex]

This is the equation of the line into point slope form

The slope is m=2/3

The point is (3.1)

To easily identify the graph look for the intercepts of the line

The y-intercept is the value of y when the value of x is equal to zero

For x=0

[tex]y-1=\frac{2}{3}(0-3)[/tex]

[tex]y=-2+1=-1[/tex]

The y-intercept is the point (0,-1)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0-1=\frac{2}{3}(x-3)[/tex]

[tex]-3=2x-6[/tex]

[tex]2x=3[/tex]

[tex]x=1.5[/tex]

The x-intercept is the point (1.5,0)

Plot the intercepts and join the points to identify the graph

using a graphing tool

The graph in the attached figure

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side  to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

[tex]x^2 +(x+7)^2=(x+9)^2\\\\[/tex]

Expand the terms in brackets

[tex]x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81[/tex]

collect like terms

[tex]x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0[/tex]

solve for x in the quadratic equation by factorization

[tex]x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8[/tex]

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Answer:

Step-by-step explanation:

distribute the first part of each term

(21/5x+12)+(-3+5/2x)

combine the xs and the numbers

9+6.7x

For this case we must simplify the following expression:

[tex]3(\frac{7}{5}x+4)-2(\frac{3}{2}-\frac{5}{4}x)=\\\frac{3*7}{5}x+ 3*4-\frac{2*3}{2} +\frac{2*5}{4}x=\\\frac{21}{5}x +12-\frac{6}{2} +\frac{10}{4}x=\\\frac{21}{5}x +12-3+ \frac{10}{4}x=[/tex]

We add similar terms:

[tex]\frac{21}{5}x+ \frac{10}{4}x+ 9=\\(\frac{21}{5} +\frac{10}{4})x +9=\\\frac{67}{10}x +9[/tex]

ANswer:

[tex]\frac{67}{10}x+9[/tex]

Answer:

2nd choice

Step-by-step explanation:

How you have to is multiply the coordinates by 2 since the scale factor you want to dilate image at is at 2.

That is the pre-image is (x,y) and the image is (2x,2y) per each point.

A(3,5) becomes A'(3*2,5*2)=A'(6,10)

B(6,1) becomes B'(6*2,1*2)=B'(12,2)

C(5,9) becomes C'(5*2,9*2)=C'(10,18)

So 2nd choice.

The coordinates of the dilated triangle are (6,10) , (12,2) and (10,18)

The scale factor is a measure for similar figures, who look the same but have different scales or measures

A' = (3 x 2, 5 x 2) = (6, 10)

B' = (6 x 2, 1x 2) = (12,2)

Similarly C' will be (10 , 18)

So the coordinates of the dilated triangle are (6,10) , (12,2) and (10,18)

So option B is correct.

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[tex]3x^2(2x+1)=6x^3+3x^2[/tex]

Answer:

(9,7)

Step-by-step explanation:

The goal is to write in standard form for a circle.

That is write in this form: [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.

So you have

[tex]x^2+y^2-18x-14y+124=0[/tex]

Reorder so you have your x's together, your y's together, and the constant on the other side:

[tex]x^2-18x+y^2-14y=-124[/tex]

Now we are going to complete the square using

[tex]x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex].

This means we are going to add something in next to the x's and something in next to y's.  Keep in mind whatever you add on one side you must add to the other.

[tex]x^2-18x+(\frac{-18}{2})^2+y^2-14y+(\frac{-14}{2})^2=-124+(\frac{-18}{2})^2+(\frac{-14}{2})^2[/tex]

The whole reason we did is so we can write x^2-18x+(-9)^2 as (x-9)^2 and y^2-14y+(-7)^2 as (y-7)^2.  We are just using this lovely thing I have I already mentioned: [tex]x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex].

[tex](x-9)^2+(y-7)^2=-124+81+49[/tex]

[tex](x-9)^2+(y-7)^2=6[/tex]

Comparing this to [tex](x-h)^2+(y-k)^2=r^2[/tex] tells us

[tex]h=9,k=7,r^2=6[/tex]

So the center is (9,7) while the radius is [tex]\sqrt{6}[/tex].

Answer: (9,7)

Step-by-step explanation:

The equation of the circle in Center-radius form is:

 [tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

To rewrite the given equation in Center-radius form, we need to complete the square:

1. Move 124 to the other side of the equation:

[tex]x^2+y^2-18x-14y+124=0\\\\x^2+y^2-18x-14y=-124[/tex]

2. Group terms:

[tex](x^2-18x)+(y^2-14y)=-124[/tex]

3. Add [tex](\frac{-18}{2})^2=81[/tex] to the group of the variable "x" and to the right side of the equation.

4. Add [tex](\frac{-14}{2})^2=49[/tex] to  the group of the variable "y" and to the right side of the equation.

Then:

[tex](x^2-18x+81)+(y^2-14y+49)=-124+81+49[/tex]

5. Finally,  simplify and convert the left side to squared form:

[tex](x-9)^2+(y-7)^2=6[/tex]

You can identify that the center of the circle is at:

[tex](h,k)=(9,7)[/tex]

Answer:

8ft sq is your area.

Step-by-step explanation:

Solve the area of a triangle by using the following equation:

Area (of a triangle) = 1/2(base * height)

Note:

Height = 4 feet

Base = 4 feet

Plug in the corresponding numbers to the corresponding variables.

Area = 1/2(base * height)

Area = 1/2(4 * 4)

Solve. Follow PEMDAS. First, solve the parenthesis, then divide:

Area = 1/2(4 * 4)

Area = 1/2(16)

Area = 16/2

Area = 8

8ft sq is your area.

~

Answer:

Third option: [tex]8\ ft^2[/tex]

Step-by-step explanation:

The area of a triangle can be calculated with the following formula:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height of the triangle.

In this case you know that this triangle has a base of 4 feet and a height of 4 feet, then:

[tex]b=4\ ft\\h=4\ ft[/tex]

Therefore, you can substitute these values into the formula, getting that the area of this triangle is:

[tex]A=\frac{(4\ ft)(4\ ft)}{2}\\\\A=8\ ft^2[/tex]

Answer:

D. about 8.5 mi

Step-by-step explanation:

To go from Aesha to Josh, you go 6 units right and 6 units up.

Each unit is a mile, so you go 6 miles right and 6 miles up.

Think of each 6 mile distance as a leg of a right triangle, and the direct distance from one place to the other as the hypotenuse of the right triangle. Use the Pythagorean theorem to find the length of the hypotenuse.

a^2 + b^2 = c^2

The 6-mile legs are a and b. c is the hypotenuse.

(6 mi)^2 + (6 mi)^2 = c^2

c^2 = 36 mi^2 + 36 mi^2

c^2 = 72 mi^2

c = sqrt(72) mi

c = sqrt(36 * 2) mi

c = 6sqrt(2) mi

c = 6(1.4142) mi

c = 8.5 mi

Answer:

56.0650

Step-by-step explanation:

here is your answer

i hope this is what u want

In this question the number that is in the 4th decimal place is...

56.0649702307

Nine is the 4th decimal, so this is the number that you will determine if it gets rounded or not.

This question wants you to have four decimal places left after you finish rounding

To determine if you round up or stay the same you must look at the number after the asked decimal place. In this case the number after the 4th decimal is 7. A number will round up if this number (7) is 5 or greater. If it is smaller then 5 then the decimal will not round up.

In this case 7 is bigger then 5. This means that the 4th decimal place (9) will round up

56.0650

^^^Since the fourth decimal is 9 when you round up the next number is ten. This means that the rounding will be bumped to the number in front of the 9 and the 9 will simply become zero.

Let me know if this makes sense!

~Just a girl in love with Shawn Mendes

Answer:  A . The point where the three angle bisector intersect.

Step-by-step explanation:

The incenter of a triangle is a point constructing the origin of a circle inscribed inside it. The incenter of a triangle is created by taking the intersection of the angle bisectors of the three vertices of the triangle such that it is equidistant from all the vertices of the triangle.

Therefore, the statement which best describes the incenter of a triangle is " the point where the three angle bisector intersect"

Answer:

The point where the three angle bisector intersect.

Step-by-step explanation: