Write the equation 12=3x + 6 in the form ax + b = c with c=12 what are the values of a & b?
2 answers:
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Answer:
The tables are given below and
since,
so, Noah's mixture will taste more like orange, than Andre's mixture.
Step-by-step explanation:
To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water, Andre mixes 5 scoops of powder with 8 cups of water.
so, can construct the following tables -
A) table that shows different amounts of powder and water that taste the same as Noah's mixture :-
Serial no. Powder in scoops cups of water
1 8 12
2 12 18
3 16 24
4. 20 30
5. 24 36
B) table that shows different amounts of powder and water that taste the same as Andre 's mixture :-
Serial no. Powder in scoops cups of water
1 10 16
2 15 24
3 20 32
4. 25 40
5. 30 48
C) Since,
so, Noah's mixture wili taste more like orange, than Andre's mixture.
9514 1404 393
Answer:
34 square units.
Step-by-step explanation:
The figure can be decomposed into a trapezoid and a triangle. The point of intersection of the two lines is (6, 4), so a horizontal line at y=4 will create ...
- a triangle of height 2 and base 6
- a trapezoid with bases 6 and 8, and height 4.
Using the relevant area formulas, we find ...
triangle area = 1/2bh = 1/2(6)(2) = 6
trapezoid area = 1/2(b1 +b2)h = 1/2(6+8)(4) = 28
Total shaded area = 6 + 28 = 34 square units.
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The equations of the lines can be written as ...
y = -2x +16
y = -1/3x +6
Equating y, we get
-2x +16 = -1/3x +6
10 = 5/3x . . . . . . . . . add 2x-6
6 = x . . . . . . . . . multiply by 3/5
y = -2(6) +16 = 4
The point of intersection is (6, 4).
_____
<em>Alternate solution</em>
Once we know the vertices of the shaded area:
- (0, 0)
- (0, 6)
- (6, 4)
- (8, 0)
- (0, 0)
we can form pairwise "determinants" of the form x1y2 -x2y1. Note the first point is repeated at the bottom of the list, and the points are listed in order around the boundary of the area. The points (0, 0) contribute nothing, so we have left them out of the computation below. The area is half the absolute value of the sum of these "determinants".
1/2|(0·4 -6·6) +(6·0)-(8·4)|
= 1/2|-36 -32| = 1/2(68) = 34
_____
In the attachment, the equations of the lines are written in intercept form, since the problem statement gives the intercepts of the lines.
