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Evgen [1.6K]
3 years ago
7

(b) Given that p = 6n + 1, show that p2 + 2 is divisible by 3.

Mathematics
1 answer:
Alona [7]3 years ago
3 0

Answer:

See below.

Step-by-step explanation:

p^2 + 2

= (6n + 1)^2 + 2

= 36n^2 + 12n + 1 + 2

=  36n^3 + 12n + 3

= 3(12n^2 + 4n + 1).

- which is divisible by 3.

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25+25= so first u want to add 5+5so that equals 10 so u put the one on the top of 2 then u add2+2+1 so that equals 5 so ur answe
goblinko [34]

Answer:

So you pretty much just solved your math by yourself :)

Step-by-step explanation:

7 0
3 years ago
Which equation has the solution x=4. A) 4x= 20<br> B) x/2= 8<br> C) x + 8 = 3x<br> D) x= x+5/2
ivolga24 [154]

Answer:

A I believe

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Can someone please explain the Pythagorean theorem to me?
Leona [35]

Answer:

Pythagoras theorem is is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.

Step-by-step explanation:

The hypotenuse is the side opposite to the right angle and so the equation for finding the hypotenuse would be:

a^2+^b^2=c^2

7 0
3 years ago
1/2+6 over 3 = x-3 over 2
Amanda [17]

Answer:

x = 7 1/3

Step-by-step explanation:

First, add 1/2 and 6

1/2 + 12/2 = 13/2 = 6 1/2

Our equation now:

13/2 over 3 - x - 3 over 2 = 0

Next, divide 13/2 by 3

13/2 divided by 3 = 13/6

Our equation now:

13/6 over 3 - (x - 3) over 2 = 0

Now, find common denominators and simplify

13/6 - ((x - 3) times 3) over 6 = 0

22 - 3x over 6 = 0

Multiply by six on both sides

22 - 3x = 0

Subtract 22 from both sides

-3x = -22

Divide by -1

3x = 22

Divide both sides of the equation by 3

x = 22/3

x = 7 1/3

Hope this helps!

8 0
3 years ago
Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –y equals negative StartFraction one-third EndFr
DiKsa [7]

Answer:

y=-\frac{1}{3} x+5

Step-by-step explanation:

Notice that the answers they give you to choose from are all lines in slope y-intercept form, it would be very simple to just find the answer finding yourself the slope and y-intercept of the line in question.

Since they give you two points (x_1,y_1) and  (x_2,y_2) for the line, use them to find the slope of the line that goes through them, with the formula:  slope=\frac{y_2-y_1}{x_2-x_1} =\frac{7-6}{-6-(-3)} =\frac{1}{-3} =-\frac{1}{3}

Therefore, the slope of the line must be -\frac{1}{3}

Now, find the y-intercept (b) using the general form of a line with the given slope:

y=-\frac{1}{3}x +b

Use one of the given coordinate points to request that the line passes through it. For example, through the point (-3,6) (when x = -3, y must be 6):

y=-\frac{1}{3} x+b\\6=-\frac{1}{3}(-3)+b\\6=1+b\\b=6-1=5

then the y-intercept must be 5. Therefore our line is : y=-\frac{1}{3}x +5 which appears listed as your second choice.

8 0
4 years ago
Read 2 more answers
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