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NemiM [27]
3 years ago
9

How does anyone know how to prove parallel lines, especially when there are two pairs of them?

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0

Answer:

Step-by-step explanation:

If two lines are cut by a transversal so that any pair of alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so that any pair of corresponding angles are congruent, then the lines are parallel. You can use these converses to decide whether two lines are parallel.

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3.141562.... And it goes on and on and on
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Solve the following system by any method -8x-8y=0 -8x+2y=-20
iVinArrow [24]
                     \fbox{Solution by using Matrix} 

\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20

\text{Rewrite the linear equations above as a matrix} 

\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right] 

\text{Apply to Row2 : Row2 + Row1} 

\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right] 

\text{ Simplify rows} 

\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right] 

\text{Note: The matrix is now in echelon form.}\text{The steps below are for back substitution.} 

\text{Apply to Row1 : Row1 + 8 Row2} 

\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right] 

\text{ Simplify rows}  

\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right] 

\text{Therefore, the solution is} 

x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}
7 0
3 years ago
What is the theoretical probability that the dial will land on the number 5? Enter your answer in all forms
Sedbober [7]

Answer:

1/3

Step-by-step explanation:

There are <u>four</u>  5's on the dial out of 12 possible stops

    4/12 = 1/3   theoretical

5 0
2 years ago
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Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x − 4y − 6z = 22
madam [21]

The equation x^{2} +y^{2} +z^{2} +2x-4y-6z=22  in standard form looks like (x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}.

Given equation of sphere be x^{2} +y^{2} +z^{2} +2x-4y-6z=22.

We are required to express the given equation in the standard form of the equation of sphere.

Equation is basically relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation,quadratic equation, cubic equation or many more depending on the powers of variables. The standard form of the equation of sphere looks like  x^{2} +y^{2} +z^{2} =r^{2}.

The given equation is x^{2} +y^{2} +z^{2} +2x-4y-6z=22.

We have to break 22 which is in right side into various parts according to the left side of the equation.

x^{2} +y^{2} +z^{2} +2x-4y-6z=-1-4-9+36

x^{2} +y^{2} +z^{2} +2x-4y-6z+1+4+9=36

x^{2} +1+2x+y^{2}+4-4y+z^{2} +9-6z=36

x^{2} +(1)^{2} +2*1*x+y^{2} +(2)^{2} -2*2y+z^{2} +(3)^{2} -2*3z=36

(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}

Hence the equation x^{2} +y^{2} +z^{2} +2x-4y-6z=22  in standard form looks like (x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}.

Learn more about equations at brainly.com/question/2972832

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Y = –x + 4<br> x + 2y = –8<br> How many solutions does this linear system have?
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It only has one solution. x= 16 and y = -12
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