Answer: The fabric costs $7.60 per yard.
Step-by-step explanation: First we can divide it by 106 then multiply it by 100 to get rid of the 6% sales tax, which now the cost of the stuff is $17.50.
Next, we subtract 8 from this to represent the clothing pattern cost. Now it is $9.50.
The last stap to this is to divide it by 1 1/4 to get the final cost per yard:
The fabric costs $7.60 per yard.
The area of a rectangle is A=LW, the area of a square is A=S^2.
W=S-2 and L=2S-3
And we are told that the areas of each figure are the same.
S^2=LW, using L and W found above we have:
S^2=(2S-3)(S-2) perform indicated multiplication on right side
S^2=2S^2-4S-3S+6 combine like terms on right side
S^2=2S^2-7S+6 subtract S^2 from both sides
S^2-7S+6=0 factor:
S^2-S-6S+6=0
S(S-1)-6(S-1)=0
(S-6)(S-1)=0, since W=S-2, and W>0, S>2 so:
S=6 is the only valid value for S. Now we can find the dimensions of the rectangle...
W=S-2 and L=2S-3 given that S=6 in
W=4 in and L=9 in
So the width of the rectangle is 4 inches and the length of the rectangle is 9 inches.
If the 3 points are collinear, then the slopes of all line segments connecting the points are the same.
Thus,
-6 - (-8) 2
m = ------------- = -------- = -1/2
-7 - (-3) -4
Then the following must be true:
4-(-6) 10
-1/2 = ------------ = ---------
c - (-7) c + 7
Cross multiplying, -(c+7) = 20, and c+7 = -20, so that c = -27
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Answer:
After 4 days, the number of people attending both conferences be the same.
Step-by-step explanation:
We are given the following in the question:
Maths conference:
Number of people already signed = 7
Number of people who sign up each day = 2
Thus, the number of people who will sign up for maths conference in x days will be given by the linear function:
History conference:
Number of people already signed =11
Number of people who sign up each day = 1
Thus, the number of people who will sign up for maths conference in x days will be given by the linear function:
Both conference will have same number of people when
Thus, after 4 days, the number of people attending both conferences be the same.
