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Volgvan
3 years ago
12

Prove that the sum of three successive even integers is always a multiple of 6.​

Mathematics
1 answer:
zlopas [31]3 years ago
5 0

Answer:

if you see three consecutive numbers you can figure out that at least one of them is divisible by 6

Step-by-step explanation:

you can use mathematical induction by proving it mathematically. for a number to be divisible by 6, it should be divisible by 2. Since all are even numbers the number will be divisible by 2.

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Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12
miskamm [114]

keeping in mind that parallel lines have the same exact slope, hmmmm what's the slope of the line above anyway?

\bf 3y-x=-12\implies 3y=x-12\implies y=\cfrac{x-12}{3}\implies y = \cfrac{x}{3}-\cfrac{12}{3} \\\\\\ y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

so we're really looking for the equation of a line whose slope is 1/3 and runs through (18,2)

\bf (\stackrel{x_1}{18}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{1}{3} \\\\\\ \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-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{18}) \\\\\\ y-2=\cfrac{1}{3}x-6\implies y=\cfrac{1}{3}x-4

3 0
3 years ago
HELPPPP FIND THE AREA
GuDViN [60]

you can just split the figure in 2 separate figures and them add the areas:

area rec. 1:

3m×3m= 9m²

area rec. 2:

3m× (2m+3m)

= 3m×5m

=15m²

total area:

9m²+15m²= 24m²

5 0
2 years ago
Read 2 more answers
Tina observes the points on the plane of a paper. What is the minimum number of points required to make a plane?
Ymorist [56]
Isnt it 3? because hes making a plane 
3 0
3 years ago
Help its really easy but i need help.Which calculation would result in the decimal point moving two spaces to the right in a dec
aliya0001 [1]

Answer:

The decimal number is multiplied by 100

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is 128.439 rounded to the nearest tenth??
irga5000 [103]

Answer:

the answer is 128.4

Step-by-step explanation:

To round up a number to the nearest tenth if the hundredth is more than or 5 you add 1 to the tenth but if it less than 5 you remove the other numbers and leave the number like that which will give you 128.4.

6 0
3 years ago
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