How do I solve this problem and check all the solutions?
2 answers:
Answer:
x = 10
Step-by-step explanation:
Given
x - = 5 ( subtract x from both sides )
- = 5 - x ( divide all terms by - 1 )
= x - 5 ( square both sides )
2x + 5 = (x - 5)²
2x + 5 = x² - 10x + 25 ( subtract 2x + 5 from both sides )
0 = x² - 12x + 20 ← in standard form
0 = (x - 2)(x - 10) ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 10 = 0 ⇒ x = 10
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 2
2 - = 2 -
= 2 - 3 = - 1 ≠ 5
Thus x = 2 is an extraneous solution
x = 10
10 - = 10 -
= 10 - 5 = 5 = right side
Thus x = 10 is the solution
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Answer:
y = - x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3x - y = 9 into this form by subtracting 3x from both sides
- y = - 3x + 9 ( divide all terms by - 1 )
y = 3x - 9 ← in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
, thus
y = - x + c ← is the partial equation
To find c substitute (6, 6) into the partial equation
6 = - 2 + c ⇒ c = 6 + 2 = 8
y = - x + 8 ← equation of perpendicular line
Point-slope form: y-y1 = m(x-x1)
Standard form: ax + by = c
Slope-intercept form: y = mx+b
Start by finding the slope. We know it is negative since the line is decreasing. The slope is -4/3.
To create point-slope form, we need to get one point from the graph. Let's use (3,0).
To create slope-intercept form, we need the slope and the y-intercept. The y-intercept is the point where our equation crosses the y-axis. For this equation, it is 4.
To get standard form, solve the equation in terms of C.
Point-slope form: y = -4/3(x-3)
Slope-intercept form: y = -4/3x + 4
Standard form: 4/3x + y = 4