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ale4655 [162]
2 years ago
13

Which equation represents the linear relationship shown on the graph below?

Mathematics
1 answer:
jek_recluse [69]2 years ago
4 0

To find the linear relationship we need

  • two points on the line: (0,3), (2,4)
  • and the slope = \frac{y2-y1}{x2-x1} =\frac{4-3}{2-0} =\frac{1}{2}

Now lets put any one point on the line such as (0,3) and the slope into the point-slope form:

      y - 3 = (\frac{1}{2} )(x-0)\\y = \frac{1}{2}x + 3

Hope that helps!

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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
120 members are going to pass a resolution to select a team leader. If 1 over 6 of the members voted in favor and 2 over 5 of th
____ [38]

Answer:

52 did not vote.

Step-by-step explanation:

120 * 1/6 = 20

120 * 2/5 = 240/5 = 48.

NUMBER who did not vote = 120 - 20 - 48

= 52.

5 0
2 years ago
PLEASE HELP! WILL UPVOTE!
bagirrra123 [75]
Just "plug n chug" as my teacher would say. In other words, replace the letters with the values. 

Choice A is (7,19) which means x = 7 and y = 19. Let's replace the x and y value with these numbers in both equations. If we get a true equation, then we found the answer. 

2x-y = -5
2*7-19 = -5
14-19 = -5
-5 = -5 ... true
So that works. Let's try the other equation
x+3y = 22
7+3*19 = 22
7+57 = 22
64 = 22 ... false 
So choice A is NOT the answer because of this. Let's try out choice B
2x-y = -5
2*4-9 = -5
-1 = -5 ... false
so B doesn't work either. How about C? 
2x-y = -5
2*8-21 = -5
-5 = -5 ... that works
x+3y = 22
8+3*21 = 22
71 = 22 ... but this is false
So D has to be the answer. Let's check to confirm or not
2x-y = -5
2*1-7 = -5
-5 = -5 ... true
x+3y = 22
1+3*7 = 22
22 = 22 ... true
BOTH equations are true at the same time so (1,7) is definitely the final answer


6 0
3 years ago
70 POINTS PLEASE HELP GIVING BRAINLIEST
aivan3 [116]

Answer:

the answer would be 40%.

5 0
2 years ago
Read 2 more answers
Find the distance between (–3, –5) and (3, 4).
zhenek [66]

Answer:(6,9)

Step-by-step explanation:

4 0
2 years ago
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