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2 years ago

Point P is the incenter of triangle ABC, PZ = 7 units, and PA = 12 units.

Mathematics

1 answer:

cestrela7 [59]2 years ago

4 0

The complete question is

"Point P is the incenter of triangle ABC, PZ = 7 units, and PA = 12 units.

The radius of the incircle centered at point P is ? units."

The radius of the incircle centered at point P is 7 units.

We are given that point P is the incenter of the triangle, and is the center point of the incircle of the triangle.

<h3>What is incircle?</h3>

The incircle is defined as the largest circle that can be made in a triangle and is tangent to each side of the triangle.

Here, The radius of the circle is going to be a perpendicular line from point P to any side of the triangle.

In the triangle ,

PZ = PY = PX,

Each measure of value is equal to the radius of the circle.

Therefore, we already know that PZ = 7 units making the radius, r = 7 units.

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Just need help on #7 thru 8(a), b and c

Stella [2.4K]

a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

c. The midpoint of the R(3, 5) and H(-1,2) is (2, 4)

a. The transformation rule is (x,y) → (x + 1, y - 1)

The x-coordinate is shifted 1 unit to the left and

The y - coordinate is shifted 1 unit downwards.

c. The image of B' the pre-image of B(5, 6) is (6, 5)

<h3 /><h3>7 a. How to find the slope of the line?</h3>

The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

So, m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 5)/(-1 - 3)

m = -3/-4

m = -3/4

So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

<h3>b. The distance between the points</h3>

The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

d = √[(2 - 5)² + (-1 - 3)²]

d = √[(-3)² + (-4)²]

d = √[9 + 16]

d = √25

d = 5 units

So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>

The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

So, the midpoint (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x, y) = [(3 + (-1))/2, (5 + 3)/2]

(x, y) = [(3 - 1)/2, (5 + 3)/2]

(x, y) = [4/2, 8/2]

(x, y) = (2, 4)

So, the midpoint of the R(3, 5) and H(-1,2) is (2, 4)

<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>

Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).

Let pont A be (x,y).

So, point B = (x + 1, y - 1)

So, the transformation rule is (x,y) → (x + 1, y - 1)

<h3>b. Describe the transformation</h3>

Since the transformation rule is (x,y) → (x + 1, y - 1), we see that

the x-coordinate is shifted 1 unit to the left and
the y - coordinate is shifted 1 unit downwards.

<h3>c. The image of B' the pre-image of B(5, 6)</h3>

Since the transformation rule is (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is

(x,y) → (x + 1, y - 1)

(5,6) → (5 + 1, 6 - 1)

(5,6) → (6, 5)

So, the image of B' the pre-image of B(5, 6) is (6, 5)

Learn more about slope of a line here:

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3 0

2 years ago

The table shows the ages and weights of babies at a hospital.

zzz [600]

I believe the answer is B) positive

8 0

3 years ago

Read 2 more answers

Please help me match this

Setler [38]

4/5=0.8
0.35=7/20
3/8=0.375
0.775=31/40

You could have use a calculator for this but you’re welcome

8 0

3 years ago

A die is rolled. If you roll a 1, 2 or 3, you will toss 10 coins. If you roll a 4, 5 or 6, you will toss 20 coins. Let X denote

trasher [3.6K]

Answer:

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the <em>behavior</em> of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.

5 0

3 years ago

What is the solution to the equation 2/3a-1/6=1/3

Vsevolod [243]

Answer:

a = $\frac{3}{4}$

Step-by-step explanation:

$\frac{2a}{3} -\frac{1}{6} =\frac{1}{3}$

$\frac{4a}{6}-\frac{1}{6} =\frac{2}{6}$

(now you can multiply the whole equation by 6 to remove the fractions

4a - 1 = 2

4a = 2+1

4a = 3

a = $\frac{3}{4}$

4 0

2 years ago