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Which 3 side lengths from the list below make a Pythagorean Triple?

6,9,12,14,15
Type the numbers that form the Pythagorean Triple in order from smallest to largest:
qquad

qquad

qquad

Which $3$ side lengths from the list below make a Pythagorean Triple? $\newline$ $6,9,12,14,15$ $\newline$ Type the numbers that form the Pythagorean Triple in order from smallest to largest: $\qquad$ $\newline$ $\qquad$ $\newline$ $\qquad$

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Reflections of functions

Full solution

Q. Which

3

side lengths from the list below make a Pythagorean Triple?

\newline

6,9,12,14,15

\newline

Type the numbers that form the Pythagorean Triple in order from smallest to largest:

\qquad

\newline

\qquad

\newline

\qquad

Introduction: A Pythagorean Triple consists of three positive integers $a$ , $b$ , and $c$ , such that $a^2 + b^2 = c^2$ . We need to check each combination of three numbers to see if they satisfy this condition.
Check $6$ , $9$ , $12$ : First, let's try the smallest three numbers: $6$ , $9$ , and $12$ . $\newline$ Check if $6^2 + 9^2 = 12^2$ . $\newline$ $6^2 = 36$ , $9^2 = 81$ , $12^2 = 144$ . $\newline$ $36 + 81 = 117$ , which is not equal to $144$ . $\newline$ So, $6$ , $9$ , and $12$ do not form a Pythagorean Triple.
Check $6$ , $9$ , $15$ : Next, let's try $6$ , $9$ , and $15$ . $\newline$ Check if $6^2 + 9^2 = 15^2$ . $\newline$ $6^2 = 36$ , $9^2 = 81$ , $15^2 = 225$ . $\newline$ $36 + 81 = 117$ , which is not equal to $225$ . $\newline$ So, $6$ , $9$ , and $15$ do not form a Pythagorean Triple.
Check $6$ , $12$ , $15$ : Now, let's try $6$ , $12$ , and $15$ . $\newline$ Check if $6^2 + 12^2 = 15^2$ . $\newline$ $6^2 = 36$ , $12^2 = 144$ , $15^2 = 225$ . $\newline$ $36 + 144 = 180$ , which is not equal to $225$ . $\newline$ So, $6$ , $12$ , and $15$ do not form a Pythagorean Triple.
Check $9$ , $12$ , $15$ : Let's try $9$ , $12$ , and $15$ . $\newline$ Check if $9^2 + 12^2 = 15^2$ . $\newline$ $9^2 = 81$ , $12^2 = 144$ , $15^2 = 225$ . $\newline$ $81 + 144 = 225$ , which is equal to $225$ . $\newline$ So, $9$ , $12$ , and $15$ do form a Pythagorean Triple.
Final Verification: Finally, let's check if there's a mistake in our calculations. $\newline$ Recheck the calculation for $9$ , $12$ , and $15$ . $\newline$ $9^2 + 12^2 = 81 + 144 = 225$ , which is indeed equal to $15^2$ . $\newline$ No mistake found, so $9$ , $12$ , and $15$ is the correct Pythagorean Triple.

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Tess tried to solve the differential equation

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\newline

\frac{d y}{d x}=2 x y-6 x

\newline

1

\quad \frac{d y}{d x}=(y-3) 2 x

\newline

2

\quad \int \frac{1}{y-3} d y=\int 2 x d x

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5

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7

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\newline

(A) Tess's work is correct.

\newline

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is incorrect. We're not allowed to factor an expression when solving differential equations.

\newline

4

is incorrect. The right-hand side of the equation should be

e^{x^{2}+C_{1}}

\newline

7

is incorrect. Tess didn't account for adding

3

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Aditya tried to solve the differential equation

\frac{d y}{d x}=6 x-30

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\newline

\frac{d y}{d x}=6 x-30

\newline

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\quad \int 30 d y=\int 6 x d x

\newline

2

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3

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of the following expressions represents the distance between the sandbag and the target?

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\newline

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\newline

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\newline

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f(x)

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