Answer:
The second option: 3 (6 - 5n)/20n
Step-by-step explanation:
Make sure all fractions have a common denominator:
Step 1. Find a common multiple between all three denominators
5, 4, and 10 all have a common multiple of 20. Proof: 5 × 4 = 20, 4 × 5 = 20, and 10 × 2 = 20
Step 2. Multiply the denominators to get to 20. Whatever you do to the bottom (denominator) must be done to the top (numerator).
1/5n × 4/4 = 4/20n
3/4 × 5n/5n = 15n/20n
7/10n × 2/2 = 14/20n
Your fractions now all have a common denominator of 20n.
Rewrite the equation using the new fractions:
4/20n - 15n/20n + 14/20n
Only focus on adding/subtracting the numerators; the denominators will stay the same: 20n.
(4 - 15n + 14)/20n
Combine like terms:
(18 - 15n)/20n
Factor out any numbers possible:
3(6 - 5n)/20n
Note* 3 go into both 18 and 15, which allows us to factor 3 out. 18 ÷ 3 = 6 and 15 ÷ 3 = 5, giving us our new numbers inside the parentheses.
Answer:
B.
The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.
The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.
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Step-by-step explanation:
You can find the solution by "unfolding" the absolute value, then dividing by 2 and subtracting 4:
-6 > 2x +8 > 6 . . . . . read this as -6 is less than 2x+8 or 2x+8 is greater than 6
-3 > x +4 > 3 . . . . . . .divide by 2
-7 > x > -1 . . . . . . . . . solution to the first inequality: x is less than -7 or greater than -1.
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The solution to the other inequality is identical, except the direction of the comparison is reversed. It is read differently, because the segments overlap, rather than being disjoint.
-7 < x < -1 . . . . . . . . solution to the second inequality: x is greater than -7 and less than -1.
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These descriptions match choice B.
Well the total would be -5
Answer:
Step-by-step explanation:
<u>Complete the square</u>
<u />
<span>The two fires are about 70 feet from each other.
The assumption is that the ground is relatively level and that a right triangle will be made with the three points of the triangle being the ranger, the spot on the ground directly beneath the ranger, and the fire itself. So the distance to the first fire will be:
Calculate the angle. That will be 90° - 11.6° = 78.4°
The distance will be
tan(78.4) = X/60
60 tan(78.4) = X
60 * 4.871620136 = X
292.2972082 = X
And that's how far the 1st fire is from the ranger's station. Now for the 2nd
angle = 90° - 9.4° = 80.6°
60 tan(80.6) = X
60 * 6.040510327 = X
362.4306196 = X
And the distance between the two fires will be the difference in distance from the tower, so
362.4306196 - 292.2972082 = 70.13341146
Rounding to 2 significant figures gives 70 feet.</span>
