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kodGreya [7K]
3 years ago
6

Without graphing, is the system independent, dependent, inconsistent? {12x=3y=12 y=-4x+5

Mathematics
1 answer:
Alla [95]3 years ago
7 0
Okay so you out them into the form of y=mx+b. since equation 2 is already like that you need to do it to equation 1. which is y=-4x+4. graph both equations. if it has a solution (1 point where the two lines meet) it is consistantly and independent. if they are parallel lines and the solution is 0 the system is inconsistent and the lines are dependent. if it's the same line they are consistent and dependent. the line is not the same since the y intercept is different. the slope is the same though which tells us its parallel. so the system has a solution of 0 and is inconsistent and the lines are independent.
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find the x-intercepts of the parabola with vertex(6,27) and y-intercept (0,-81). write answer in form (x1,y1)(x2,y2). if necessa
sergey [27]
The vertex form of the equation is:
y = a ( x - h )² + k
- 81 = a ( 0 - 6 )² + 27
- 81 = 36 a + 27
- 108 = 36 a
a = - 108 : 36
a = - 3
y = - 3 ( x - 6 )² + 27
y = - 3 ( x² - 12 x + 36 ) + 27
y = - 3 x² + 36 x - 108 + 27
y = - 3 x² + 36 x - 81
y = - 3 ( x² - 12 x + 27 )
x² - 12 x + 27 = 0
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x ( x - 9 ) - 3 ( x - 9 ) = 0
( x - 9 ) ( x - 3 ) = 0
x 1 = 3,  x 2 = 9
Answer:
The x-intercepts are ( 3, 0 ) and ( 9, 0 ).
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3 years ago
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Step-by-step explanation:

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A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfill
gavmur [86]

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John and Robyn promised their three sons that they will each get to pick one spot within 500 miles of their home in City A to vi
Ray Of Light [21]

Answer:

A) Weighted graph is attached

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1. A → C → B → D → A

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Step-by-step explanation:

A) We are told their home is in City A. So that's where any journey will begin from.

Furthermore we are told that;

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City A to City C = 206 ​miles

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City C to City D = 281 miles.

I have attached an image of the weighted graph showing the distances on the appropriate edges.

B) We want to find the shortest route using Brute force method. The brute force method is by solving a particular problem by checking all the possible cases/routes to get the desired result we are looking for.

In this case, the desired result is the shortest route for the family to complete their vacation. So, i have attached a diagram showing the different routes via brute force method.

From the brute force method, the shortest length route is 1023 miles and this routes are from Cities;

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