You need to go up 5 units
Answer:
5.83 miles
Step-by-step explanation:
Bill's net distance west of his starting point is -4+7 = 3 miles. His net distance north of his starting point is 5 miles. The straight-line distance will be the hypotenuse of a right triangle with legs 3 miles and 5 miles. That distance is given by the Pythagorean theorem:
d² = (3 mi)² +(5 mi)² = 34 mi²
d = √34 mi ≈ 5.83 mi
Bill is 5.83 miles on a direct line from his starting point.
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The attached calculator screenshot shows the sum of the travel distances. The angles are bearings measured clockwise from north. The angle of the sum indicates Bill is about 31° west of north relative to his starting point.
Answer:
CD = 14 cm; DE = 21 cm
Step-by-step explanation:
The perimeter is the sum of side lengths (in centimeters), so ...
CD + DE + CF + EF = 55
CD + DE + 8 + 12 = 55 . . . . . . . substittute for CF and EF
CD + DE = 35 . . . . . . . . . . . . . . subtract 20
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The segment DF is a diagonal of the rhombus, so bisects angle D. That angle bisector divides ΔCDE into segments that are proportional. That is, ...
CD/DE = CF/EF = 8/12 = 2/3
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So, we have two segments whose sum is 35 (cm) and whose ratio is 2 : 3. The total of "ratio units is 2+3=5, so each must stand for a length unit of 35/5 = 7 (cm). The sides are ...
CD = 2·7 cm = 14 cm
DE = 3·7 cm = 21 cm
<em>Check</em>
CD + DE = (14 +21) cm = 35 cm . . . . . matches requirements
The only way to think about this is that the $158 Alberto paid is 70% of the original price. If you save 30% you pay 70% (30% + 70% = 100%)
I will put that into math language
$158 = 70% of n or $158 = .7n Solve by dividing both sides of the equation by .7
(note that when you divide by a decimal less than 1, the answer will be larger than the starting number - $158 - which is exactly what we want.
To the nearest penny the cost of the phone is $225.71
Many people will try to find 30% of $158 and add it onto $158 but that will not work because the 30% came off the unknown price you are looking for and not the $158. You can't find 30% of a price you don't know. You must talk about it in terms of what you a paying - reread the first thing I wrote at the top of this page. You can try the wrong way yourself (finding 30% and adding it on) and when you check it, it won't work.