(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.
Answer: D. 41 cm
There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,
a^2+b^2 = (b+1)^2
a^2 + b^2 = b^2 + 2b +1
a^2=2b+1
So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.
b = (a^2 - 1)/2
a=3, b=(3^2-1)/2=4, c=b+1=5
a=5, b=(5^2-1)/2 =12, c = 13
a=7, b=24, c=25
a=9, b=40, c=41
a=11, b=60, c=61
a=13, b=84, c=85
It's good to be able to recognize Pythagorean Triples when we see them.
Otherwise we'd have to work the calculator:
√(9² + 40²) = √1681 = 41
Answer:
Graph A
Step-by-step explanation:
Say that the car rental rate stands for c dollars ( $ ). We know that Jamal's trip lasts for 4 days, paying $ 24 in expenses for gas, and $ 128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality.
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The big key here is the part " which graph shows the range of car rental rates that would be cheaper than the taxi service. " Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( $ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,
24 + 4c < 128 - Subtract 24 from either side,
4c < 104 - Divide by 4 on either side, isolating c,
c < 26
The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.
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The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.
Answer:
There are probably more than this but here
$12 for pens would give you 6
$12 for notepads would give you 4
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$18 for notepads would give you 6
$6 for pens would give you 3
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$21 for for notepads would give you 7
$2 or pens would give you 1
and $1 left
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$6 for notepads would give you 2
$18 for pens would give you 9
For this case we have:
Polynomial 1: 
Polynomial 2: 
Sorting the polynomials:
Polynomial 1: 
Polynomial 2:
Adding term to term (similar) we have:
Answer:
An observation of the Moon was conducted from Friday, November 8, 2013 to Thursday, November 14, 2013. The study of the Moon during this period occurred consistently between the hours of 8 and 9 p.m. EST within the Northern Hemisphere at 37.3346° N, 79.5228° W (Bedford, V.A.). The Moon was noted to be illuminated on the right side and had a dark shadow on the left side indicating a waxing phase. The light region grew over the surface of the Moon with each subsequent night. The first night’s phase was waxing crescent with over 25 percent of the Moon lit up. The next night, the light had grown to cover more of the Moon as it continued through its waxing crescent phase. On November 10th, the Moon exhibited traits of being at first-quarter or …show more content…
An observation of the Moon was conducted from Friday, November 8, 2013 to Thursday, November 14, 2013. The study of the Moon during this period occurred consistently between the hours of 8 and 9 p.m. EST within the Northern Hemisphere at 37.3346° N, 79.5228° W (Bedford, V.A.). The Moon was noted to be illuminated on the right side and had a dark shadow on the left side indicating a waxing phase. The light region grew over the surface of the Moon with each subsequent night. The first night’s phase was waxing crescent with over 25 percent of the Moon lit up. The next night, the light had grown to cover more of the Moon as it continued through its waxing crescent phase. On November 10th, the Moon exhibited traits of being at first-quarter or half-moon status because at least 50 percent of its surface was illuminated. In the following nights, the Moon displayed characteristics of waxing gibbous as the light continued to grow across the moon’s surface from right to left. The Moon was nearing closer to the full moon phase on November 14th as only a very small dark shadow was visible on the left side.
The Moon takes 27.3 days (sidereal month) to complete its actual orbit around the Earth. Like the Sun, the Moon rises in the east and sets in the west each day.
