2 years ago

Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.

Mathematics

1 answer:

ICE Princess25 [194]2 years ago

5 0

Answer:

Step-by-step explanation:

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Select all the statements that are true about the linear equation. y = 4x - 3

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The answer is B. Have a nice day

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4 years ago

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The temperature is -4 it increases to 8 how many degrees did the temperature increase

Oliga [24]

Answer:

12 degrees.

Step-by-step explanation:

8 - (-4) = 12. So, the temperature increased by 12 degrees.

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3 years ago

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Step-by-step explanation:

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3 years ago

Write an equation in slope intercept form for the line that passes through (5, -8) and (11, 10)

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$\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-8})\qquad
(\stackrel{x_2}{11}~,~\stackrel{y_2}{10})
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-(-8)}{11-5}\implies \cfrac{10+8}{11-5}\implies \cfrac{18}{16}\implies \cfrac{9}{8}$

$\bf \begin{array}{|c|ll}
\cline{1-1}
\textit{point-slope form}\\
\cline{1-1}
\\
y-y_1=m(x-x_1)
\\\\
\cline{1-1}
\end{array}\implies y-(-8)=\cfrac{9}{8}(x-5)\implies y+8=\cfrac{9}{8}(x-5)
\\\\\\
y+8=\cfrac{9}{8}x-\cfrac{45}{8}\implies y=\cfrac{9}{8}x-\cfrac{45}{8}-8\implies y=\cfrac{9}{8}x-\cfrac{109}{8}$

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4 years ago

In a 30cm by 25cm rectangle, a quadrant of a circle of radius 7cm has been cut away from each corner. What is the perimeter of t

Anton [14]

Answer:

97.96 cm

596.14 cm²

Step-by-step explanation:

sides become:

30 cm ⇒ 16 cm
25 cm ⇒ 11 cm

and added corners:

4*2πr/4= 2πr = 2*3.14*7 cm= 43.96 cm

then perimeter is:

P= 2*16+2*11+43.96= 97.96 cm

the area left is:

A= 30*25- 4*1/4*3.14*7²= 596.14 cm²

5 0

3 years ago