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Marrrta [24]
3 years ago
6

Which graph represents the function y= 2x-4?sty すす0-3xits : :os : ;-32pr ftーVetーTT it tie。pttーT-it-T +--+-

Mathematics
2 answers:
liberstina [14]3 years ago
8 0
You have the y-intercept of -4. That means that the line will go through the point (0, -4). Choices B and C do that. Plug in 1 for x and find y.

y = 2x - 4

y = 2 * 1 - 4

y = 2 - 4

y = -2

In graph B, when x = 1, y = -3.5,  which is incorrect.

In graph C, when x = 1, y = -2

Graph C is the correct answer.

Sergio039 [100]3 years ago
4 0
Solutions 

You have been given the y-intercept of -4. The meaning of this is that the given line will go through the point (0, -4). Plug in 1 for x and find y.


y = 2x - 4

y = 2 * 1 - 4

y = 2 - 4

y = -2
<span>

</span>In graph C,=  x = 1, y = -2

<span>Graph C is the correct answer.</span>
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Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is
olganol [36]
<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

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