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liraira [26]
3 years ago
5

Write an equation in the form

Mathematics
1 answer:
elena-s [515]3 years ago
8 0

Answer:

y=4x+7

Slope m=4 with the equation y2-y1/x2-x1 with any points

y-intercept (0,7)

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Given that u =< 2,12 >, and z =< -7,5 >
swat32

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

… = √((u • u) + (u • z) + (z • u) + (z • z))

… = √(||u||² + 2 (u • z) + ||z||²)

We have

u = ⟨2, 12⟩   ⇒   ||u|| = √(2² + 12²) = 2√37

z = ⟨-7, 5⟩   ⇒   ||z|| = √((-7)² + 5²) = √74

u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46

and so

||w|| = √((2√37)² + 2•46 + (√74)²)

… = √(4•37 + 2•46 + 74)

… = √314 ≈ 17.720

Alternatively, without mentioning the dot product,

w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩

and so

||w|| = √((-5)² + 17²) = √314 ≈ 17.720

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2 years ago
Point (m, n) is transformed by the rule ​ (m−3, n) ​.
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3 years ago
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Shannon drew the line of best fit on the scatter plot shown below:
N76 [4]
Using the points (0,14) and (10,0), the gradient of the line is (14-0)/(0-5) which simplifies to -7/5.

From these points, we can also see that when the x value is zero, the y value is 14. Therefore the y-intercept is 14.

We can then put this into the equation of a straight line, y=mx+c:

y = (-7/5)x + 14
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