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bulgar [2K]
2 years ago
15

Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).

Mathematics
1 answer:
lions [1.4K]2 years ago
6 0

Check the picture below.  so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}

(\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill

\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}

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On a coordinate plane, a line is drawn from point a to point b. point a is at (negative 8, negative 13) and point b is at (4, 11
vladimir2022 [97]

The coordinate for point P which is one-third the length of the line segment from a to b is (-4, -5)

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Point a is at (-8, -13) and point b is at (4, 11). Hence the coordinates for point p(x, y) which is one-third the length of the line segment from a to b is:

x=\frac{1}{3}(4-(-8))+(-8)=-4\\ \\y=\frac{1}{3}(11-(-13))+(-13)=-5

The coordinate for point P which is one-third the length of the line segment from a to b is (-4, -5)

Find out more on equation at: brainly.com/question/2972832

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1 year ago
Find the interest earned: <br><br> $11,500 for 3.5 years at 7.25% annual simple interest
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Future Value, using...

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Step-by-step explanation:

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Step-by-step explanation:

Since we know that

Discrete data are those data which is countable and it is expressed in exact numerical form.

Continuous data are those data which is lie within the interval and it varies so it does not expressed in exact numerical form.

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8 0
2 years ago
The difference in age between Brita and her daughter Eva is 30 years. The sum or their ages 118. How old is Eva?
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Answer:

Eva's age is 44 years

Step-by-step explanation:

Let

x ----> Brita's age

y ----> Eva's age

we know that

The sum or their ages 118

so

x+y=118 ----> equation A

The difference in age between Brita and her daughter Eva is 30 years

so

x-y=30 ----> equation B

Solve the system by elimination

Adds equation A and equation B

x+y=118\\x-y=30\\---------\\x+x=118+30\\2x=148\\x=74

<em>Find the value of y</em>

substitute the value of x in any equation

74+y=118\\y=118-74\\y=44

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Eva's age is 44 years

3 0
3 years ago
Pls need help immediately, nd can can u explain it too
tigry1 [53]
The answer is 18...
(3 / 8 ) * 48 = 18
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2 years ago
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