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Olegator [25]
3 years ago
11

(08.03) Consider the following pair of equations:

Mathematics
1 answer:
Luba_88 [7]3 years ago
6 0

Substitution method is used to solve the linear system of equations for one or more variables.

Consider the first equation y = 3x + 3 -----(1)

In equation (1) plug in y=x-1, we get

x -1 = 3x + 3

Add -3x on both side , we get

x-3x -1 = 3x-3x +3

-2x-1=0 + 3

Now add +1 on both sides, we get

-2x-1+1= 3+1

-2x + 0 =4

Now divide both side by -2

-2x/-2= 4/-2

X= -2

Now put x=-2 in the the second equation,

y=x-1

y=(-2)-1

y=-3

Solution(-2,-3)

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In this exercise, T: R2 → R2 is a function. For each of the following parts, state why T is not linear. (a) T(a1, a2)= (1, a2) (
DENIUS [597]

Answer:

  • a) T is not homogeneous
  • b) T is not additive
  • c) T is not homogeneous
  • d) T is not additive
  • e) T is not additive

Step-by-step explanation:

In each case there is an example where one property of linear functions fails.

  • a) T(2(1,0))=T((2,0))=(1,0); 2T((1,0))=2(1,0)=(2,0). These vectors are not equal, then T doesn't satisfy the condition of scalar multiplication (homogeneity).
  • b) T((1,2)+(2,3))=T(3,5)=(3,9); T((1,2))+T((2,3))=(1,1)+(2,4)=(3,5). Because these vectors are not equal, T doesn't satisfy the property of vector addition (additivity).
  • c) T(\frac{1}{2}(\pi,0))=T((\frac{\pi}{2},0))=(\sin(\frac{\pi}{2}),0)=(1,0); \frac{1}{2}T((\pi,0))=\frac{1}{2}(0,0)=(0,0) so T is not homogeneous.
  • d) T((-1,0)+(1,0))=T(0,0)=(0,0); T((-1,0))+T((1,0))=(1,0)+(1,0)=(2,0) then T is not additive.
  • e) T((0,0)+(1,0))=T(1,0)=(2,0); T((0,0))+T((1,0))=(1,0)+(2,0)=(3,0) then T is not additive.
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The x values are the
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The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"
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Convert 8.132132132 ... to a rational expression in the form of a over b , where b ≠ 0.
bezimeni [28]

Let <em>x</em> = 8.132132132...

Then 1000<em>x</em> = 8132.132132132...

Subtract <em>x</em> from 1000<em>x</em> to eliminate the fractional part:

1000<em>x</em> - <em>x</em> = 8132.132132132... - 8.132132132...

999<em>x</em> = 8132 - 8 = 8124

<em>x</em> = 8124/999 = 2708/333

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Easiest math problem giving brainlist and points!!!!
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Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^x + 2 intersect are the
torisob [31]

Answer:

Step-by-step explanation:

Part A:

We have two equations in the given question:

y=8x and y=2x+2

Then these two equations will intersect at a point where y is same fro both the equations:

In equation y=8x we will exchange y with the other equation which is y=2x+2 then we would have  8x=2x+2..

Part B:

8x = 2x + 2. Take the integer values of x between −3 and 3

x= -3

8(-3)=2(-3)+2

-24=-6+2

-24= -4

It is false

Now plug x= -2

8(-2)=2(-2)+2

-16 = -4+2

-16 = -2

This is false

Now plug x= -1

8(-1)=2(-1)+2

-8 = -2+2

-8=0

It is false

Now plug x= 0

8(0)=2(0)+2

0=0+2

0=2

It is false

Now plug x= 1

8(1)=2(1)+2

8=2+2

8=4

False

Now plug x= 2

8(2)=2(2)+2

16=4+2

16=6

False

Now plug x=3

8(3)=2(3)+2

24=6+2

24=8

It is false

It means there is no solution to 8x=2x+2 for the integers values of x between −3 and 3

Part C:

Plot the two given functions on a coordinate plane and identifying the point of intersection(values of the variables which satisfy both equations at a particular point) of the two graphs.

The graph is attached. The point of intersection at x =0.333 and value of y = 2.667....

7 0
3 years ago
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