To convert 2.77777777777 to a fraction:
Assume x = 2.7777777777......equation 1
Now, notice that the repeating digit is 7
multiply both sides of the equation by 10:
10x = 27.7777777777.......equation 2
Subtract equation 1 from equation 2 as follows:
10x - x = 27.7777777777 - 2.7777777777
9x = 25
Therefore x = 25/9
Based on this, 2.7 repeated can be written as a fraction = 25/9
<u>2x - 3</u> = <u>2x - 4</u>
2 - x 1 - x
(2x - 3)(1 - x) = (2x - 4)(2 - x)
2x(1 - x) - 3(1 - x) = 2x(2 - x) - 4(2 - x)
2x(1) - 2x(x) - 3(1) + 3(x) = 2x(2) - 2x(x) - 4(2) + 4(x)
2x - 2x² - 3 + 3x = 4x - 2x² - 8 + 4x
-2x² + 2x - 3 + 3x = -2x² + 4x - 8 + 4x
-2x² + 2x + 3x - 3 = -2x² + 4x + 4x - 8
-2x² + 5x - 3 = -2x² + 8x - 8
<u>+ 2x² + 2x² </u>
5x - 3 = 8x - 8
<u> - 5x - 5x </u>
-3 = 3x - 8
<u>+ 8 + 8</u>
<u>-5</u> = <u>3x</u>
3 3
-1²/₃ = x
Answer:
6
Step-by-step explanation:
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Using translation concepts, it is found that the new intercepts are given as follows:
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the function was shifted one unit right, hence the rule for the translated function is given by:
(x,y) -> (x + 1, y).
The y-intercept is given by f(0), hence for the shifted function it will be f(-1). We have that f(x) is an odd function and f(1) = 3, hence f(-1) = -f(1) = -3.
The x-intercept is given by x when f(x) = 0, hence:
(0,0) -> (0 + 1, 0) = (1,0).
More can be learned about translation concepts at brainly.com/question/4521517
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Answer:
The solution to the system of equations is
Explanation:
Giving the system of equations:
To solve this, we need to first of all eliminate one variable from any two of the equations.
Subtracting (2) from twice of (1), we have:
Subtracting (3) from 3 times (1), we have
From (4) and (5), we can solve for y and z.
Subtract 5 times (5) from 3 times (4)
Using the value of z obtained in (5), we have
Using the values obtained for y and z in (1), we have
