Damian spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -6°F
1 answer:
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Answer:
Step-by-step explanation:
- First we find the slope of the line AB passing through the point (2,0)
- line AB is perpendicular to the line
, this equation is slope intercept for, which is
so our m or slope is
- Since the slope of line AB is perpendicular to
then we use the equation
, so what do we multiply
by to get -1? -4 right, so that's the slope of line AB with the point (2,0)
- Now line CD is parallel to line AB, that means it has the same slope as AB, so slope of CD is -4
- So we make the equation
so m= -4 and our point is (-1,6)
thats the equation of line side CD
Answer:
4.63 cubic yard.
Step-by-step explanation:
Given,
The length of sidewalk, l = 100 feet,
Width, w = 5 feet,
Depth, h = 3 inches = 0.25 feet,
Thus, the volume of the concrete needed for making the sidewalk,
= 125 cubic feet,
∵ 1 cubic yard = 27 cubic feet,
⇒ 1 cubic feet = cubic yard,
Thus, the quantity of concrete needed = ≈ 4.63 cubic yard.
Answer:
(x, y) = (4, -3)
Step-by-step explanation:
- x-3y=13
- 2x+4y=-4
First of all, look at the given equations. Here, we see that the second equation has coefficients that all have a factor of 2. If we divide that out, we get an equation that has an x-coefficient of 1, matching the x-coefficient in the first equation.
Here is the reduced second equation:
x +2y = -2
Now, if we subtract one equation from the other, the variable x will be eliminated. We want to choose that subtraction wisely.
We note that the y-coefficient in the first equation is less than that in the second equation. If we subtract the first equation from the second, the result will have a positive y-coefficient:
(x +2y) -(x -3y) = (-2) -(13)
5y = -15 . . . . . . . . . . . . . . . . simplify. Note that the x-variable is eliminated, which is the purpose of this exercise.
y = -3 . . . . . . . divide by 5
We can use this value in the reduced second equation to find the value of x:
x +2(-3) = -2
x = 4 . . . . . . . . . add 6 and simplify
The solution is (x, y) = (4, -3).
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I find a graphing calculator provides an easy and reliable check of the answer.
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<em>Comment on linear combination</em>
This method is often called "elimination," because the purpose of combining the equations in a particular way is to eliminate one of the variables. This requires you look at the coefficients of the variables and devise a plan to combine them so the resulting coefficient for one of the variables is zero.
In the worst case, you can combine ...
- ax +by = c
- dx +ey = f
by multiplying the second equation by <em>a</em> and the first by <em>-d</em>:
a(dx +ey) -d(ax +by) = a( f) -d(c)
y(ae -bd) = fa -cd . . . . . . simplify; x is eliminated
This sort of approach results in a formula for the solution known as Cramer's Rule.
y = (fa-cd)/(ae-bd)
The corresponding solution for x is ...
x = (ce-bf)/(ae-bd)
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The point of looking at the equations first is that you can often choose which variable to eliminate and what multiplier to use to minimize the amount of arithmetic involved—as we did above.
