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Nana76 [90]
3 years ago
5

Graph the function -2x+5y=10

Mathematics
1 answer:
loris [4]3 years ago
6 0
An equation of the form ax+by+c=0, where x, y are variable, and a, b, c are numbers, is called a "linear equation"

the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.

To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.

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

-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)


to find 2 solutions, we set x or y any value we want, and solve for the other

for example: 

let x=0, 

then

-2x+5y-10=0 becomes 5y-10=0, so y=2

this gives us the solution (0, 2)

another example; set y=0

then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5

thus another solution is (-5, 0)



Draw these 2 points, and join them with a line, as shown in the figure.

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Twelve pounds less than twice janes weight is 270 pounds. What is Janes weight?
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Janes weight = x
Twelve pounds less than twice janes weight is 270 pounds
12 less than 2x is 270 

2x -12 = 270   (add 12 to each side)
2x = 270 + 12
2x = 282   (divide 2 from each side)
x = 282/2
x = 141

The answer is 141 pounds
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Consider the following set of vectors. v1 = 0 0 0 1 , v2 = 0 0 3 1 , v3 = 0 4 3 1 , v4 = 8 4 3 1 Let v1, v2, v3, and v4 be (colu
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Answer:

We have the equation

c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]

Then, the augmented matrix of the system is

\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]

We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:

\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]

This matrix is in echelon form. Then, now we apply backward substitution:

1.

8c_4=0\\c_4=0

2.

4c_3+4c_4=0\\4c_3+4*0=0\\c_3=0

3.

3c_2+3c_3+3c_4=0\\3c_2+3*0+3*0=0\\c_2=0

4.

c_1+c_2+c_3+c_4=0\\c_1+0+0+0=0\\c_1=0

Then the system has unique solution that is (c_1,c_2c_3,c_4)=(0,0,0,0) and this imply that the vectors v_1,v_2,v_3,v_4 are linear independent.

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Step-by-step explanation:

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Answer:

10.77

Step-by-step explanation:

by using Pythagoras theorem we can find the distance between the points,

so...

distance between the points, which is the hypotenuse will be xy

difference between the y coordinates will be dy

difference between the x coordinates will be dx

according to pythagoras theorem,

xy^{2} = dx^{2} +  dy^{2} \\xy^{2} = (-6-(-2))^{2} + (-5-5)^{2}\\xy^{2} =(-4)^{2} +(-10)^{2} \\xy^{2} =16+100\\xy^{2} =116\\xy =\sqrt{116} \\xy=10.77

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2 years ago
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