12x - 18 = 15x Subtract 12x from both sides
-18 = 3x Divide both sides by 3
-6 = x Switch the sides to make it easier to read
x = -6
Check your answer by plugging -6 in for the x in the original problem:
So, x = -6 .
Caroline spent $41.00 on groceries after using coupons and store discounts. Without the coupons and store discounts, the groceri
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12x - 18 = 15x Subtract 12x from both sides
-18 = 3x Divide both sides by 3
-6 = x Switch the sides to make it easier to read
x = -6
Check your answer by plugging -6 in for the x in the original problem:
So, x = -6 .
Since the line is parallell to the x-axis we know the slope is zero: 
Using the point-slope formula we can substitute know values:
You could also jsut do it by inspection: since it passes through (3,4) and is horizontal it must cross at (0,4) i.e. all y=4.
Using the point-slope formula we can substitute know values:
You could also jsut do it by inspection: since it passes through (3,4) and is horizontal it must cross at (0,4) i.e. all y=4.
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Answer:
6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)
7. (a, b, C) ≈ (180.5, 238.5, 145°)
Step-by-step explanation:
My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.
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We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.
6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...
A = arccos((b² +c² -a²)/(2bc))
A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°
The other angles can be found by permuting the variables appropriately.
B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°
The third angle can be found as the supplement to the other two.
C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°
The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).
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7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.
C = 180° -A -B = 145°
a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49
b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52
The measures (a, b, C) are about (180.5, 238.5, 145°).
