0 or dot, depending on what course you are taking
A Trapezoid needs to have one pair of sides parallel.
Two of the points already plotted have the same Y value ( 3)
So the 4th dot, should have the same Y value as the first dot, which is 1.
The 4th dot should be plotted at C (5,1)
Answer:
x < -4 ∪ x > 4
Step-by-step explanation:
The absolute value function is shifted down 3 units. The solution space is values of x where y = |x|-3 is greater than 1. The solution is shown in red in the attachments, and the left and right (dashed) sides of the inequality are shown in blue.
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I personally prefer to rewrite the inequality so the comparison is to <em>zero</em>. That is done in the second attachment, which rewrites it to ...
|x| -4 > 0
by subtracting 1 from both sides. It is often easier to read the values of x-intercepts than it is to read the coordinate values where lines cross each other.
Answer:
the prices were $0.05 and $1.05
Step-by-step explanation:
Let 'a' and 'b' represent the costs of the two sodas. The given relations are ...
a + b = 1.10 . . . . the total cost of the sodas was $1.10
a - b = 1.00 . . . . one soda costs $1.00 more than the other one
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Adding these two equations, we get ...
2a = 2.10
a = 1.05 . . . . . divide by 2
1.05 -b = 1.00 . . . . . substitute for a in the second equation
1.05 -1.00 = b = 0.05 . . . add b-1 to both sides
The prices of the two sodas were $0.05 and $1.05.
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<em>Additional comment</em>
This is a "sum and difference" problem, in which you are given the sum and the difference of two values. As we have seen here, <em>the larger value is half the sum of the sum and difference</em>: a = (1+1.10)/2 = 1.05. If we were to subtract one equation from the other, we would find <em>the smaller value is half the difference of the sum and difference</em>: b = (1.05 -1.00)/2 = 0.05.
This result is the general solution to sum and difference problems.
Answer:
k = 5
Step-by-step explanation:
The given line is y = 4x - 14.
The given point is (k, k + 1).
For this point, x = k and y = k + 1.
You substitute these equations into the line's equation to find the value of k.
(x = k)
(y = k + 1)
y = 4x - 14
(k + 1) = 4(k) - 14
Solve for k.
k + 1 = 4k - 14
Subtract k from both sides.
1 = 3k - 14
Add 14 to both sides.
15 = 3k
Divide both sides by 3.
15/3 = k
Simplify.
5 = k
And that's the answer!
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