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Mumz [18]
3 years ago
7

Where it the point of concurrency of the angle bisectors of a triangle

Mathematics
1 answer:
AlexFokin [52]3 years ago
3 0

Answer:

Incentre

Step-by-step explanation:

A triangle is a closed area in a plane bounded by three lines known as sides of a triangle.  

There will be 3 angles in a triangle.

Consider the point of concurrency of three bisectors.

Let ABC be one triangle and AI and BI are bisectors of A and B meeting at I.

Then we have since AI is angle bisector of A, I would be equidistant from sides BA and AC.  Similarly since BI is angle bisector of B, I would be equidistant form BC and BA.

It follows that I is equidistant from all the sides, and hence a centre can be drawn touching all sides of the triangle.

The circle is called in circle and the point I,  the point of concurrency of the angle bisectors of a triangle, is the incentre of the triangle.

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Let a= x2 +4 rewrite the following equation in terms of a and set it equal to zero. (X2 + 4)2 + 32 = 12x2 + 48 in the resulting
Alex73 [517]
Answer: \\ {( {x}^{2} + 4) }^{2} + 32 = 12 {x}^{2} + 48 \\ \Leftrightarrow {a}^{2} + 32 = 12( {x}^{2} + 4) \\ \Leftrightarrow {a}^{2} + 32 = 12a \\ \Leftrightarrow {a}^{2} - 12a + 32 = 0 \\ \Rightarrow Coefficients:1, \: -12. \: Constant:a
5 0
3 years ago
-4a <-32 what is the answer
Fiesta28 [93]

Answer:

a > 8

Step-by-step explanation:

Divide by the coefficient of the variable. Since it is negative, the direction of the comparison must be reversed.

(-4a)/(-4) > (-32)/(-4)

a > 8

6 0
3 years ago
You want to place a towel bar that is 10 1⁄4 inches long in the center of a door that is 26 1⁄3 inches wide. How far should you
attashe74 [19]
The bar should be 8 1/24 from the each edge of the door.

We need to subtract 10 1/4 from 26 1/3 to get the fraction of the space not covered by the towel bar. 
We also need to divide the difference by 2 because we placed the towel bar in the center of the door.

1st we need to convert the mixed fractions into fractions to perform subtraction.
26 1/3 = ((26*3)+1)/3 = 79/3
10 1/4 = ((10*4)+1)/4 = 41/4

Steps in Subtracting Fractions
Step 1. Make sure the denominator is the same. 3 and 4 are the denominators, they are not the same but they are factor of 12. So,
79/3 must be multiplied by 4 = 79 * 4 / 3 * 4 = 316 / 12
41/4 must be multiplied by 3 = 41 * 3 / 4 * 3 = 123 / 12

Step 2. Subtract the numerators and place them above the common denominator
316/12 - 123/12 = 316 - 123 / 12 = 193 / 12

Before we can simplify the fraction, we must divide it by two to get the measurement of each edge of the door.

Steps in dividing fractions.
Step 1. Get the reciprocal of the 2nd fraction.
1st fraction : 193 / 12
2nd fraction : 2 /1  ⇒ reciprocal 1/2

Step 2. Multiply the 1st fraction to the reciprocal of the 2nd fraction
193 / 12 * 1/2 = 193 * 1 / 12 * 2 = 193 / 24

Step 3. Simplify the fraction.
193 / 24 = 8 1/24
8 0
3 years ago
Last year, 400 signed up to take a virtual kickboxing class. This year, there was a 5% increase in registrations. How many peopl
ale4655 [162]

Answer:

420 people

Step-by-step explanation:

400*1.05=420

3 0
3 years ago
Can I get some help, it is due in 15 minutes and I need help. Thanks, any help appreciated
koban [17]

Well, I'm way past the 15 min mark, but here's how to do the question.


With this, you will need to use the distance formula, \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, on XY, YZ, and ZX.



XY: \sqrt{(3-1)^2+(1-6)^2}


Firstly, solve inside the parentheses: \sqrt{(2)^2+(-5)^2}


Next, solve the exponents: \sqrt{4+25}


Next, solve the addition, and XY's distance will be √29



(The process is the same with the other 2 sides, so I'll go through them real quickly)


YZ:

\sqrt{(6-3)^2+(3-1)^2}\\ \sqrt{(3)^2+(2)^2}\\ \sqrt{9+4}\\ \sqrt{13}



ZX:

\sqrt{(1-6)^2+(6-3)^2}\\ \sqrt{(-5)^2+(3)^2}\\ \sqrt{25+9}\\ \sqrt{34}



Now that we got the 3 sides, we can add them up: \sqrt{29}+\sqrt{13} +\sqrt{34} =14.8


In short, your answer is 14.8, or the second option.

8 0
3 years ago
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