To find the original number, you'll have to work backwards from your final number, 5.
1) June's last step was adding 6 to a number to get 5. To find that number, undo the addition by subtracting 6 from 5:
5 - 6 = -1
2) Her first step was dividing some number by 3 to get -1 (the number from our last step). Undo that division by multiplying 3 by -1:
3 x -1 = -3
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The original number was -3.
Answer:
The extraneous solution is 4.
Step-by-step explanation:
First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:
-5 = 3x - 7
Collect like terms
-5 + 7 = 3x
2 = 3x
Divide both side by 3
x = 2/3.
Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:
(-5)^2 = (3x - 7)^2
25 = (3x - 7)(3x - 7)
25 = 9x^2 - 21x - 21x + 49
9x^2 - 42x + 49 - 25 = 0
9x^2 - 42x + 24 = 0
Solving by factorisation:
Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.
Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x
Now we can write the above equation as:
9x^2 - 42x + 24 = 0
9x^2 - 6x - 36x + 24 = 0
3x(3x - 2) - 12(3x - 2) = 0
(3x - 12)(3x - 2) = 0
3x - 12 = 0 or 3x - 2 = 0
3x = 12 or 3x = 2
x = 12/3 or x = 2/3
x = 4 or 2/3.
We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.
Therefore, the extraneous solution to the question is 4.
Answer:
y = 3x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y-intercept )
here m = 3 and b = 2, hence
y = 3x + 2 ← equation of line in slope-intercept form
Answer:
28.4 degrees
Step-by-step explanation:
sin(theta) = 20/42. theta=arcsin(10/21)=28.43
Answer:
No; x=1.6
Step-by-step explanation: