Describe this pattern. Then see if you can think of another Pythagorean triple that doesn't follow the pattern you just described and that can't be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings. x-value Pythagorean Triple 7 (14,48,50) 8 (16,63,65) 9 (18,80,82) 10 (20,99,101)

Answers

Answer 1

Answer:

Answer:

See explanation

Step-by-step explanation:

A Pythagorean triple is a set of 3 positive integer numbers, a, b, and c which satisfies the Pythagorean theorem: $c^2=a^2+b^2$

Given the identity: $(x^2 - 1)^2 + (2x)^2 = (x^2 + 1)^2.$

We verify that the numbers given table are Pythagorean triples.

$14^2+48^2=2500=50^2\n16^2+63^2=4225=65^2\n18^2+80^2=6724=82^2\n20^2+99^2=10201=101^2$

Next, we examine the pattern:

$\left|\begin{array}{c|c|c|c|c}x-value&x^2-1&2x&x^2 + 1&$Triple\n--&--&--&--&----\n7&48&14&50&(14,48,50)\n8&63&16&65&(16,63,65)\n9&80&18&82&(18,80,82)\n10&99&20&101&(20,99,101)\end{array}\right|$

From the pattern, our first number is 2x, the second number is x² - 1, and the third number(hypotenuse) is x² + 1

Next, we show that (x² - 1)² + (2x)² = (x² + 1)² is an identity

$LHS: (x^2 - 1)^2 + (2x)^2 \n= (x^2-1)(x^2-1)+2x^2\n=x^4-2x^2+1+4x^2\n=x^4+2x^2+1$

$RHS: (x^2+1)^2\n= (x^2+1) (x^2+1)\n=x^4+2x^2+1$

Since Left Hand Side=Right hand Side. For all x, the equation is always true.

Therefore, the pattern is true for any Pythagorean triple.

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During the month of February, Fabulous Feet Shoe Mart sold 30 pairs of red loafers. After an ad campaign to boost sales, they sold 39 pairs in March. Find the percent of increase in sales.

Answers

between 30-33 % good luck what is this for?

32.5? that could be an accuret answer

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What is the period of the sinusoidal function?

Answers

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James paddles upstream in a canoe at 2mph (relative to the shore), and when he paddles down-stream, he goes 9mph. Find the speed of the current and the speed James can paddle in still water and come up with an equation.

Answers

Let x represent James's speed and y represent the speed of the current. Since upstream the current goes against him, $x-y=2$ describes the speed upstream, and since downstream the current goes with him, $x+y=9$ describes the speed downstream.

Use elimination to solve for x: $x-y=2 \n -(x+y=9) \n =-2y=-7 \n y=7/2$ or 3.5 miles per hour for James in still water. Substitute y into either original equation: $x-(7/2)=2 \n x=11/2$ or 5.5 miles per hour for the current. As far as an equation, you can use $y=(11/2)x$ , where x is the number of hours James has paddled in still water and y is the distance he has traveled (in miles).

Not sure what equation you're looking for, but against the current he goes 2 mph and with he goes 9mph, so 9-2=7mph difference between them, divided by 2 = 3.5 mph of the current. So in this case, James can paddle 2+3.5= 5.5 mph in still water and the current moves at 3.5 mph.

James can paddle 5.5 mph
The current moves at 3.5 mph
Equation: speed = 5.5 + 3.5x where x can equal -1, 0, or 1 depending on whether James is going with the current (x = 1), without the current (x = 0), or against the current (x = -1)

Solve using order of operations.
16 + (4 ∙ 2) – 3

Answers

Answer: 21

Order of operations, multiply first

16 + (4 x 2) - 3

= 16 + (8) - 3

Then add/subtract as needed from left to right

24 - 3

= 21

Answer:

The answer would be 21.

Step-by-step explanation: First, you would multiply what is in the parentheses, 4 x 2 = 8.

Next, you add. 16 + 8 = 24

Then, you subtract. 24 - 3 = 21.

Video club A charged $10 for membership and $3 for movie rental. Video Club B charges $15 for membership and $2 per movie rental. For how many movie rentals will the cost be the same at both video clubs? What is that cost?

Answers

write an equation

10 + 3x = 15 +2x
-2x -2x
-----------------------
10 + x (1x) = 15
-10 -10
----------------------
x = 5

cost= 25 (10 + 15)

Sam will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of 57 and costs an additional 0.13 per mile driven. The second plan has an initial fee of 46 and costs an additional 0.15 per mile driven.For what amount of driving do the two plans cost the same?

What is the cost when the two plans cost the same?

Answers

Answer:

550 miles and 128.50

Step-by-step explanation:

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x = 11 / 0.02 = 1100 / 2 = 550 miles

cost = 57 + 0.13 . 550 = 128.50

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