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podryga [215]
2 years ago
11

8) The sum of the first n consecutive even numbers can be found using S= n^2= n, where n > 2

Mathematics
2 answers:
muminat2 years ago
8 0

Answer:

D

Step-by-step explanation:

oee [108]2 years ago
4 0
D 6 ……….………………………………..……
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Determine if its possible to form a triangle using the set of segments with the given measurement. explain please! 7 in., 8.7.,
mafiozo [28]

Start by adding together the shortest two sides, 7 and 8.7 inches.  Result:  15.7 inches.  Because this sum is greater than the longest side, 15.4 inches, it's possible to construct a triangle, whose largest angle will be close to 180 degrees.

8 0
3 years ago
What is the distance between the points (4, -8) and (10,8)?
schepotkina [342]

Answer:

Standard Form:

2√ 73

Decimal form:

17.08800749...

Step-by-step explanation:

5 0
2 years ago
Caden states that n^2 +3n + 2n is an equivalent expression to 6n. Why is Caden's statement incorrect?
malfutka [58]
\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}

Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}

Hence, the correct options that apply are options A, D, E and F

7 0
9 months ago
Louise's family traveled 3 10 of the distance to her grandmother's house on Saturday. They traveled 4 7 of the remaining distanc
Ludmilka [50]

Answer:

4/10

Step-by-step explanation:

Louise's family traveled 3/10 of the distance to her grandmother's house on Saturday.

Let us represent total distance = 1

The remaining distance left is calculated as:

1 - 3/10

Lowest common denominator = 10

= 10 - 3/10 = 7/10

They traveled 4/7 of the remaining distance on Sunday.

This is calculated as:

= 4/7 × 7/10

= 4/10

What fraction of the total distance to her grandmother's house was traveled on Sunday?

7 0
2 years ago
Discrete Mathematics I
faust18 [17]

ANSWER



The general solution is 86+280n, where n is an  integer



<u>EXPLANATION</u>



In order  to solve the linear congruence;



33x \equiv 38(mod\:280)



We need to determine the inverse of 33 (which is a Bézout coefficient for 33).



To do that we must first use  the Euclidean Algorithm to verify the existence of the inverse by showing that;



gcd(33,\:280)=1



Now, here we go;



280=8\times33+16



33=2\times 16+1



16=2\times 8+0



The greatest common divisor is the last remainder before the remainder of zero.



Hence, the gcd(33,\:280)=1.



We now express this gcd of 1 as a linear combination of  33 and 280.



We can achieve this by making all the non zero remainders the subject and making a backward substitution.



1=33-2\times 16--(1)



16=280-33\times8--(2)



Equation (2) in equation (1) gives,



1=33-2\times (280-8\times33)



1=33-2\times 280+16\times33



1=17\times33-2\times 280



The above linear combination tells us that  17 is the inverse of 33.



Now we multiply both sides of our congruence relation by 17.



17\times 33x \equiv 17\times 38(mod\:280)



This implies that;



x \equiv 646(mod\:280)



x \equiv 86.



Since this is modulo, the solution is not unique because any integral addition or subtraction of the modulo (280 in this case) produces an equivalent solution.



Therefore the general solution is,



86+280n, where n is an  integer

6 0
3 years ago
Read 2 more answers
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