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r-ruslan [8.4K]

3 years ago

7

PLEASE HELP!! NOTE: Angles not necessarily drawn to scale.

1 answer:

UkoKoshka [18]3 years ago

8 0

Answer:

35 degrees

Step-by-step explanation:

They give you AGE is 55. AGD is a right angle, so 90-55 = 35 fr angle DGE. Since DGE and BGF are vertical angles, they are congruent.

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The area of a rectangular outdoor stage has been

jeyben [28]

Answer:

c is right i think

Step-by-step explanation:

hope this helps you

3 0

3 years ago

Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

Molodets [167]

Notice that

$(n+1)^4-n^4=4n^3+6n^2+4n+1$

so that

$\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

We have

$\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)$

$\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1$

so that

$\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

You might already know that

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

so from these formulas we get

$\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n$

$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

4 years ago

Can you answer and explain how to do this?<br><br> 1x-4-3x=2x-3-1

OverLord2011 [107]

Here is what you have to do first, combine like terms. On the left side do x-3x (you can do 1x-3x because x is just 1 variable, so I can see why you put 1x instead of x). Then combine -3-1. Then add the x answer on the left side to the 2x on the other side then you can figure out the rest. The reason why I want you to figure out the rest is because I'm just helping you and you need to get the answer yourself.

8 0

3 years ago

Scatter plots & trend lines is there a easier way to do this?

ira [324]

Answer:

23

Step-by-step explanation:

Using the best fit equation y = 1.5x - 1

with x = 16 ( number of years since 2000 ), then

y = (1.5 × 16) - 1 = 24 - 1 = 23

7 0

3 years ago

Can someone help me

zzz [600]

The answer is B (-1,3) hope this helped u

7 0

4 years ago