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3 years ago

13

Can somebody help with #11.

1 answer:

Gelneren [198K]3 years ago

5 0

6, 8, 10
9, 12, 15
30, 40, 50
(note that all of these are multiples of 3,4, and 5)

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Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

7 0

4 years ago

A new surgical procedure is said to be successful 60% of the time. Suppose the operation is performed five times and the results

USPshnik [31]

Answer:

0.07776, 0.3456,0.08704

Step-by-step explanation:

Given that a new surgical procedure is said to be successful 60% of the time

Let X be the no of successes

Then X has only two outcomes and each trial is independent of the other

Hence X is binomial with p = prob of success in a single trial = 0.60

n = Number of operations performed = 5

Prob that

a) all five operations are successful =

$P(X=5)\\= (0.6)^5\\=0.07776$

(b) exactly three are successful

= $P(X=3) = 5C3 (0.6)^3(0.4)^2\\= 0.3456$

(c) less than two are successful

$==P(X$

3 0

3 years ago

Summarize the process of solving a two-step equation.

Alenkinab [10]

Answer:

Solving Two-Step Equations

1) First, add or subtract both sides of the linear equation by the same number.

2) Secondly, multiply or divide both sides of the linear equation by the same number.

3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable

3 0

3 years ago

A ^-56<br> a^72 a^2<br><br><br> i need help now

AlekseyPX

Answer:

a to the -56th power, a to the 72nd power, and a squared.

Step-by-step explanation:

4 0

4 years ago

The total price of $35.5 haircut with 10% tip is $_______________ .

Lera25 [3.4K]

Answer:

39.5

Step-by-step explanation:

1.10 * 35.5 = 39.5

8 0

3 years ago

Read 2 more answers