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kumpel [21]
3 years ago
5

Please help me find the median to this table

Mathematics
1 answer:
ankoles [38]3 years ago
4 0
Hope this helps! feel free to clarify

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
3 years ago
What is the value of n? 9×27+2×31-28=n
gregori [183]
N=277 Hope this helps :)

4 0
3 years ago
Read 2 more answers
Which equation represents a line that is parallel to 2x-3y=9
Sever21 [200]
Two lines are parallel if they have the same slope but a different y intercept. A line with the same slope and y int as another one will be the exact same
Slope in standard form is -a/b, so your slope is 2/3 and your y int is -3
For example:
y=2/3x+1
4 0
3 years ago
The following system has a solution: x=10, y=-3, z=14
wolverine [178]
<h2>Answer:</h2><h3>False</h3>

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

In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether x=10, \ y=-3, \ z=14 is the solution to this system, that is, the ordered triple P(x,y,z) where three planes intersect.

The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:

First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \neq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation

STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the x=10, \ y=-3, \ z=14 is not the solution to the system of equations.

5 0
3 years ago
Darcy read 1 and 1⁄2 chapters in her textbook in 1⁄2 an hour. How many chapters did she read per hour?
Marina86 [1]

Answer:

She read her textbook at a speed of 3 chapters per hour.

8 0
3 years ago
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