How much chocolate will each person get if 5 people share ½ lb of chocolate equally? (6NS1)
2 answers:
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Answer:
Step-by-step explanation:
So we have the function:
To find the inverse function, switch x and f(x), change f(x) to f⁻¹(x), and solve for f⁻¹(x). Therefore:
Switch:
Add 1 to both sides:
Divide both sides by 6:
And that's our answer :)
Answer:
- (x, y) = (3, 5)
- (x, y) = (1, 2)
Step-by-step explanation:
A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.
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The usual methods of solving a system of equations involve <em>elimination</em> or <em>substitution</em>.
There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to <em>elimination</em>. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.
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1. In standard form, your equations are ...
- 2x -3y = -9
- 5x +2y = 25
Then the solution is ...
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2. In standard form, your equations are ...
- 3x +2y = 7
- 2x +5y = 12
Then the solution is ...
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<em>Note on Cramer's Rule</em>
The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.
The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.
Answer:
D) y = -4/5x – 47/10
Step-by-step explanation:
Step 1. Find the <em>midpoint of the segmen</em>t.
The two end points are (-6, -4) and (-2, 1).
The midpoint is at the average of the coordinates.
(xₚ, yₚ) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
(xₚ, yₚ) = ((-6 - 2)/2, (-4 + 1)/2)
(xₚ, yₚ) = (-8/2, -3/2)
(xₚ, yₚ) = (-4, -3/2)
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Step 2. Find the <em>slope (m₁) of the segment</em>
m₁ = (y₂ - y₁)/(x₂ - x₁)
m₁ = (1 - (-4))/(-2 - (-6))
m₁ = (1 + 4)/(-2 + 6)
m₁ = 5/4
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Step 3. Find the <em>slope (m₂) of the perpendicular bisector </em>
m₂ = -1/m₁
m₂ = -4/5
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Step 4. Find the <em>intercept of the perpendicular bisector</em>
y = mx + b
y = -(4/5)x + b
The line passes through (-4, -3/2).
-3/2 = -(4/5)(-4) + b
-3/2 = 16/5 + b Multiply each side by 10
-15 = 32 + 10 b Subtract 32 from each side
-47 = 10b Divide each side by 10
b = -47/10
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Step 5. Write the <em>equation for the perpendicular bisector</em>
y = -4/5x – 47/10
The graph shows the midpoint of your segment at (-4, -3/2) and the perpendicular bisector passing through the midpoint and (0, -47/10).
