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Viefleur [7K]
2 years ago
5

The verticle of a triangle are (2, 18) (-2, -4), and (6,12.

Mathematics
1 answer:
Sergeu [11.5K]2 years ago
6 0

so the triangle has the vertices of  (2, 18) (-2, -4), and (6,12), that gives us the endpoints for each line of

(2, 18) , (-2, -4)

(-2, -4) , (6,12)

(6,12) , (2, 18)


\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-18}{-2-2}\implies \cfrac{-22}{-4}\implies \cfrac{11}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-18=\cfrac{11}{2}(x-2) \\\\\\ y-18=\cfrac{11}{2}x-11 \implies \blacktriangleright y=\cfrac{11}{2}x+7 \blacktriangleleft


\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{12}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{12-(-4)}{6-(-2)}\implies \cfrac{12+4}{6+2}\implies \cfrac{16}{8}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=2[x-(-2)] \\\\\\ y+4=2(x+2)\implies y+4=2x+4\implies \blacktriangleright y=2x \blacktriangleleft


\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{18}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{18-12}{2-6}\implies \cfrac{6}{-3}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-12=-2(x-6) \\\\\\ y-12=-2x+12\implies \blacktriangleright y=-2x+24 \blacktriangleleft

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The reduced row-echelon forms of the augmented matrices of four systems are given below. How many solutions does each system hav
vagabundo [1.1K]

Answer:

A. Infinitely many solutions.

Step-by-step explanation:

The row and column numbers are equal in the echelon. This rows have 0001 numbers which indicates that there is free variable at the end. The reduced row echelon has equal number of rows and columns. There are infinitely many solution as the numbers in the rows are zero ending of the free variable 1. If there is no free variable then there will be no solution.

8 0
3 years ago
Please I need help on this question, A line passes through (6,3), (8,4), and (n,-2). Find the value of n.
Vika [28.1K]

Answer:

n= -4

Step-by-step explanation:

First we have to find the equation of line which passes through (6,3) and (8,4).

Then we have to pass this line through the point (n , -2).

we know, equation of line passing through (x1,y1) and (x2,y2) is

\frac{x-x1}{x1-x2}=\frac{y-y1}{y1-y2}

So, the equation of line passing through (6,3) and (8,4) is

\frac{x-6}{6-8}=\frac{y-3}{3-4}

or, \frac{x-6}{-2} =\frac{y-3}{-1}

multiplying both sides by  -2

x-6=2(y-3)

or, x-6=2y-6

or, x-2y=6-6

or, x-2y=0


Now, we have to pass this line through  (n,-2)

So, using the point in the line, that is using  x=n  , y=-2

we get

n-2(-2)=0

or, n+4=0

or, n=-4

6 0
3 years ago
Read 2 more answers
I need help attachment below will give brainliest
Veronika [31]

Answer:

see explanation

Step-by-step explanation:

(1)

Calculate the circumference (C) of the wheel

C = πd (d is the diameter )

   = 3.14 × 8 = 25.12 cm

Now divide the distance travelled by the circumference.

times rotated = 12560 ÷ 25.12 ≈ 500

----------------------------------------------------------------

(2)

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Find r by using the circumference (C)

2πr = 50.24 ( divide both sides by 2π )

r = 50.24 ÷ 6.28 = 8 , then

A = 3.14 × 8² = 3.14 × 64 ≈ 200.96 ft² ( student 3 )

-----------------------------------------------------------------

(3)

C = πd = 3.14 × 30 = 94.2 ≈ 94 m

7 0
2 years ago
The ordered pair (1, -2) is a solution to the system of linear equations.
vesna_86 [32]

Answer:

False

Step-by-step explanation:

2x + y = 0

Try (1, -2)

2(1) + (-2) = 0

2 + (-2) = 0

0 = 0

The solution works on the first equation.

-x + 2y = 5

-(1) + 2(-2) = 5

-1 - 4 = 5

-5 = 5

The solution does not work in the second equation.

Answer: False

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2 years ago
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2³-4²

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Hopefully this helps! Good luck! :)

6 0
3 years ago
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