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2 years ago

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Explain how slope is used to determine if a triangle is a right triangle.

2 answers:

Bond [772]2 years ago

5 0

A right triangle contains a right angle, so it must have two sides that are perpendicular. If the slopes of two sides can be shown to be negative reciprocals of each other, then it can be concluded that a right angle is formed. If a triangle contains a right angle, then it is a right triangle.

zysi [14]2 years ago

4 0

Do determine if a triangle is a right triangle using slopes, you have to understand perpendicular slopes/negative reciprocals.

You can calculate the slope of all 3 sides of the triangle and if two of the slopes are negative reciprocals, then those two lines intersect creating a right angle/right triangle.

Let's say there's triangle ABC.

If the slope of AB is 1/2
and the slope of BC is 2/5
and the slope of CA is -2/1
then AB and CA intersect resulting in a right angle (triangle).

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Solve each system of equations by graphing.<br> y = 2x<br> y = x + 1

yawa3891 [41]

Step-by-step explanation:

The system of linear equations are , (i) y = 2x and (ii) y = x + 1 . We will find some coordinates and then we will plot its graph. The point where both Graphs will meet will be the solution of the graph .

<u>•</u><u> </u><u>Findin</u><u>g</u><u> </u><u>coordinates</u><u> </u><u>of </u><u>Equ</u><u>ⁿ</u><u> </u><u>(</u><u>i</u><u>)</u><u> </u><u>:</u><u>-</u>

Step 1 : <u>Put</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>0</u><u> </u><u>:</u><u>-</u>

$\tt y = 2x = 2(0) = \red{0}$

Step 2: <u>Put</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>1</u><u> </u><u>:</u><u>-</u><u> </u>

$\tt y = 2x = 2(1) = \red{2}$

$\boxed{\begin{array}{c|c|c} \bf x & \tt 0 &\tt 1 \\ \bf y &\tt 0 & \tt 2 \end{array}}$

<u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u>

<u>•</u><u> </u><u>Finding</u><u> </u><u>coord</u><u>inates</u><u> </u><u>of</u><u> </u><u>equⁿ</u><u> </u><u>(</u><u>ii</u><u>)</u><u> </u><u>:</u><u>-</u>

Step 1 : Put x = 0 :-

$\tt y = x + 1 = 1 + 0 = \red{1}$

Step 2: Put x = 1 :-

$\tt y = x + 1 = 1 + 1 = \red{2}$

$\boxed{\begin{array}{c|c|c} \bf x & \tt 0 &\tt 1 \\ \bf y &\tt 1 & \tt 2\end{array}}$

Now plot these points on the graph Taking appropriate scale . Refer to the attachment in graph . From graph the Solution is (1,2) .

8 0

2 years ago

What is the logarithmic form of the solution to 102t = 9?

Harman [31]

Equivalent equations are equations that have the same value

The equation in logarithmic form is $t = \frac{\log(9)}{2}$

<h3>How to rewrite the equation</h3>

The expression is given as:

$10^{2t} = 9$

Take the logarithm of both sides

$\log(10^{2t}) = \log(9)$

Apply the power rule of logarithm

$2t\log(10) = \log(9)$

Divide both sides by log(10)

$2t = \frac{\log(9)}{\log(10)}$

Apply change of base rule

$2t = \log_{10}(9)$

Divide both sides by 2

$t = \frac{\log_{10}(9)}{2}$

Rewrite as:

$t = \frac{\log(9)}{2}$

Hence, the equation in logarithmic form is $t = \frac{\log(9)}{2}$

Read more about logarithms at:

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