The sum of two non-zero numbers a and b equals the sum of their reciprocals. If a+b≠0, what is the product of the two numbers?
1 answer:
Answer:
ab = 1
Step-by-step explanation:
A Reciprocal of a number is a number which when multiplied by the original number yields the multiplicative number, 1.
So the reciprocal of x would be x⁻¹ or ¹⁄ₓ
The information we are given states that the sum of the two non-zero numbers a and b equals the sum of their reciprocals.
So we can write this into an equation and solve,
(See image)
Once we solve, we get the equation (ab-1)(a+b) = 0
We are given info that a+b≠0
So for the above equation to be true, ab-1 has to equal 0
For <em>this</em> to be true, the product ab must equal 1
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the equation of a line perpendicular to and passes through the point (-6,8) is
Step-by-step explanation:
We need to write equation of line perpendicular to and passes through the point (-6,8)
Since the line is in slope-inetercept form
the slope of line m = 0.25
As, the new line is perpendicular to the given line so, slopes of lines that are perpendicular are: slope = -1/slope1
So, slope will be -1/0.25 = -4
Now, finding y-intercept.
So, value of y-intercept b = 30
Now the equation of the required line having slope m= -4 and b =30 will be:
So, the equation of a line perpendicular to and passes through the point (-6,8) is
Keywords: Equation of line, slope-intercept form
Learn more about slope-intercept form at:
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Answer:
(2, 7)
Step-by-step explanation:
represents the reflection of a point P about the y-axis.
If a point (x, y) is reflected across y-axis, rule for the reflection is,
(x, y) → (-x, y)
If a point (-2, 7) follows the same rule, coordinates of the image point will be,
P(-2, 7) → P'(2, 7)
Therefore, answer is (2, 7).