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love history [14]
1 year ago
8

The lines y1 = 2x - 6, y2 = -3x + 4, y3 = -1/2x + 4 intersect to form the sides of a right triangle. Find the perimeter and area

of the triangle.
Mathematics
1 answer:
tino4ka555 [31]1 year ago
3 0

The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

<h3>Determining the perimeter and area of the triangle giving line equation</h3>

In order to determine the area and perimeter of the lines, we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.

The points of intersection of the line are;

(x₁, y₁) = (- 0.4, 5.2),

(x₂, y₂) = (-0.8, 4.4),

(x₃, y₃) = (0, 4)

Determine the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

Determine the height

h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²

height = 2√5 / 5

For the hypotenuse

r = √2 · b

r = 2√10 / 5

<h3>Determine the Perimeter and area</h3>

Perimeter = s1+s2+s3

Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5

Perimeter = (2√10 + 4√5) / 5 units

<u>For the area</u>

area = 1/2* base * height

A = 0.5 · (2√5 / 5) · (2√5 / 5)

A = 2/5 square units

Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Learn more on area and perimeter of triangles here: brainly.com/question/12010318

#SPJ1

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29. Find the height of the trapezoid. Use this height to find the area. (A =
harkovskaia [24]

Answer:

<em>The area of the trapezium is 168</em>

Step-by-step explanation:

<u>Area of a Trapezoid</u>

Given a trapezoid of parallel bases b1 and b2, and height h, the area is calculated with the formula:

\displaystyle A=\frac{b_1+b_2}{2}h

The trapezoid in the figure has b1=15 and b2=27. We need to find the height. If we focus on triangle BCD, we can calculate the height as the distance EC by using the Pythagora's Theorem:

10^2=EC^2+BC^2

The side BC can be found as half the difference of the bases:

BC=\frac{27-15}{2}=6

Solving for EC:

EC^2=10^2-6^2=100-36=64

EC=\sqrt{64}=8

Now we have the height, calculate the area:

\displaystyle A=\frac{15+27}{2}*8

\displaystyle A=\frac{42}{2}*8

A = 168

The area of the trapezium is 168

5 0
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The sum of two consecutive integers is 23. what are the integers?
Zepler [3.9K]

Let the consecutive integers be x and x+1.

Then,

x + (x + 1) = 23

=> x + x + 1 = 23

=> 2x + 1 = 23

=> 2x = 23 - 1

=> 2x = 22

=> x = 22/2

=> x = 11

So, the integers are:

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Answer:

\hat y(2)=2 +3(2) =8

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Step-by-step explanation:

Assuming the linear model y=mx+b where m is the slope and b the intercept.

For this case the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

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If we see our linear model we have the equation in terms of y and x. So we can replace directly the value of x=2 into the equation and see what we got:

\hat y(2)=2 +3(2) =8

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