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alexgriva [62]
2 years ago
12

What is the answer of this on (if 3 pieces of candy cost $2.10 how much would four pieces cost)

Mathematics
1 answer:
ale4655 [162]2 years ago
5 0

Answer:

70 hope it helps

Step-by-step explanation:

210/3=70

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What is the coefficient of x2y3 in the expansion of (2x + y)5?
Zigmanuir [339]

Option C:

The coefficient of x^{2} y^{3} is 40.

Solution:

Given expression:

(2 x+y)^{5}

Using binomial theorem:

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here a=2 x, b=y

Substitute in the binomial formula, we get

(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}

                                                            $+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}

Let us solve the term one by one.

$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}

$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y

$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}

$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}

$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}

$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}

Substitute these into the above expansion.

(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}

The coefficient of x^{2} y^{3} is 40.

Option C is the correct answer.

5 0
2 years ago
I'm studying for a test and got stuck on this problem. I took a screenshot !! Please help. I just need part C for number 5, I ge
Studentka2010 [4]
Alright, so for AB and CD to be parallel, CX and DX would have to be equal, as is with AX and BX. In addition, for CD and AB to be parallel, all sides in both triangles are either equal or not all sides in even one triangle are equal. Therefore, CD is not 3. In addition, two sides of a triangle combined must be greater than the third, so that leaves 5, 4, and 2 for CD. If it was 5, that would mean that all sides are equal, so that leaves 4 and 2. However, I don't see anything to prove either one right, sorry:/
8 0
2 years ago
At Dave's diner, 2 sandwiches and 2 drinks cost $12. You can buy 5 drinks for the cost of one sandwich.
hram777 [196]
If you’re asking for the cost of the drink, the drink would be $1. This is because 2 sandwiches would cost $10 and that means 1 sandwich would make it $5. If 2 sandwiches cost $10, the remaining $2 in the $12 dollars would be the drinks. 2 drinks for $2 would make 1 drink for $1. So the cost of 5 drinks is $5 or $1 per drink.

If confused, don’t be shy to ask :)
8 0
2 years ago
Which answers choice shows that the set of irrational numbers is not closed under addition?
babunello [35]
Problably A !!!!!!!!!!!
7 0
2 years ago
Read 2 more answers
  1) 5x-2y=4.         2) 3x-5y=13  x-2y=5<br>3x+y=9
Natali [406]
\left\{\begin{array}{ccc}5x-2y=4\\3x+y=9&/\cdot2\end{array}\right\\+\left\{\begin{array}{ccc}5x-2y=4\\6x+2y=18\end{array}\right\\----------\\.\ \ \ \ \ 11x=22\ \ \ \ /:11\\.\ \ \ \ \ \ \ x=2\\\\3\cdot2+y=9\\6+y=9\\y=9-6\\y=3\\\\Answer:x=2;\ y=3


\left\{\begin{array}{ccc}3x-5y=13\\x-2y=5\end{array}\right\\\left\{\begin{array}{ccc}3x-5y=13\\x=2y+5\end{array}\right\\\\substitute:\\\\3(2y+5)-5y=13\\6y+15-5y=13\\y=13-15\\y=-2\\\\x=2\cdot(-2)+5=-4+5=1\\\\Answer:x=1;\ y=-2.
5 0
2 years ago
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