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melamori03 [73]
3 years ago
9

Determine whether each equation defines y as function of x, 2x+y=8​

Mathematics
1 answer:
solong [7]3 years ago
6 0

Answer:

Yes. This equation defines y as function of x.

Step-by-step explanation:

Step 1:

Solve the equation for y (this puts the equations in terms of y)

2x+y=8​     becomes

 y = 2x - 8    

This is a linear equation, which is a funtion.  


*Another way to solve this is to look at the graph.  Graphing this equation gives us a line.  Use the vertical line test to see if it's a function.  

To pass the vertical line test (VLT), there can only be one y value to each x value along the graph.  If it passes the VLT, the equation is a function.

If it fails the VRT, the equation is not a function.

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Which of the equations below represents
Ray Of Light [21]

The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

<h3>What is the equation of the ellipse represented in the graph?</h3>

Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following <em>standard</em> formula:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

  • (h, k) - Coordinates of the center
  • a, b - Lengths of the semiaxes

Please notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a <em>vertical</em> ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

To learn more on ellipses: brainly.com/question/14281133

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7 0
1 year ago
Suppose you are the manager of a firm the accounting department has provided cost estimates in the sales department sales estima
wlad13 [49]

Answer:

gfcfg

Step-by-step explanation:

8 0
3 years ago
Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t
Marat540 [252]

Answer:

The location of the new cell phone tower is (h,k) = (3,4), and the equation of the circle is x^{2}+y^{2} -6\cdot x - 8\cdot y = 0.

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0 (1)

Where:

x - Independent variable.

y - Dependent variable.

A, B, C - Circunference constants.

Given the number of variable, we need the location of three distinct points:

(x_{1},y_{1}) = (6,0)

36 +6\cdot A + C = 0

(x_{2},y_{2}) = (8,4)

80 + 8\cdot A + 4\cdot B + C = 0

(x_{3},y_{3}) = (3,9)

90 + 3\cdot A + 9\cdot B + C = 0

Then, we have the following system of linear equations:

6\cdot A + C = -36 (2)

8\cdot A +4\cdot B + C = -80 (3)

3\cdot A + 9\cdot B + C = -90 (4)

The solution of this system is:

A = -6, B = -8, C = 0

By comparing the general form with the standard form of the equation of the circunference is:

A = -2\cdot h (5)

B = -2\cdot k (6)

C = h^{2}+k^{2}-r^{2} (7)

Where:

h, k - Coordinates of the center of the circle.

r - Radius of the circle.

If we know that A = -6, B = -8 and C = 0, then coordinates of the center of the circle and its radius are, respectively:

h = -\frac{A}{2}

k = -\frac{B}{2}

r = \sqrt{h^{2}+k^{2}-C}

h = 3, k = 4, r = 5

The location of the new cell phone tower is (h,k) = (3,4), and the equation of the circle is x^{2}+y^{2} -6\cdot x - 8\cdot y = 0.

3 0
2 years ago
CAN SOMEONE GIVE ME THE REAL ASNWER TO THIS IM IN A RUSH
rosijanka [135]

Answer:

145 degrees

Explanation:

A straight line is 180 degrees so minus 180 by 35 to get 145 degrees.

8 0
2 years ago
Read 2 more answers
What is the area of the figure below? PLEASE HELP ​
viktelen [127]

Answer:

Step-by-step explanation:

This can be broken down into a square and a rectangle.

A=5(5)+(12)(8-5)

A=25+12(3)

A=25+36

A=61 u^2

6 0
2 years ago
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