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Varvara68 [4.7K]
3 years ago
10

5x + 2y = 8

Mathematics
2 answers:
Mrrafil [7]3 years ago
8 0
Mult the 2nd by 2 then add. this eliminates one of the variables (y) and allows you to solve the other one x
vitfil [10]3 years ago
5 0

Answer:

So it's b.) right

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Use the Binomial Theorem/Pascal's Triangle to expand (2a + 2b)^5
pochemuha

Answer:  

32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5

============================================================

Explanation:

Let's use Pascal's Triangle

In the row that starts with 1,5,... we have the values 1,5,10,10,5,1

These will be the coefficients of the terms.

Let x = 2a and y = 2b

We want to expand out (x+y)^5

Using pascals triangle, we get the following expansion

(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5

The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.

Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.

At this point, we plug in x = 2a and y = 2b

Since this will clutter things a bit, I'll do it term by term

  • 1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5
  • 5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b
  • 10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2
  • 10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3
  • 5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4
  • 1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5

So in the end, the expression (2a+2b)^5 expands out to

32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5

The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.

8 0
3 years ago
Meanwhile, at the ballpark Juan was practicing his hitting while talking to the girls standing around watching. He started telli
Naddik [55]

Answer:

5.2 seconds

Step-by-step explanation:

We want to determine the value of x when h(x) = 0

:

-16x^2 +83x + 4 = 0

:

use quadratic formula to determine the value for x

:

x = ( -83 + sqrt(83^2 - 4*(-16)*4) ) / (2*(-16) = −0.047753182

:

x = ( -83 - sqrt(83^2 - 4*(-16)*4) ) / (2*(-16) = 5.235253182

:

we want the positive value for x since time runs forward

:

the ball hung in the air for approx 5.2 seconds

7 0
3 years ago
On the coordinate plane below, triangle ABC was rotated
agasfer [191]

Answer: AB/y = BC/z = AC/x

Step-by-step explanation:

Side AB corresponds to side y, side BC corresponds to side z, and side AC corresponds to side x.

7 0
2 years ago
Solve the following equation. then place the correct number in the box provided. 2x + 1 < 9
allsm [11]
I think the answer is 4
8 0
2 years ago
Suppose the probabilities for the letters on a spinner are known to be: p(A)=1/4 p(B)=1/3 p(C)=5/12 predict the number of times
svlad2 [7]

Answer:

You will end up on A 3 times, B 4 times, and C 5 times.

Step-by-step explanation:

Just divide 12 by each value and you get your answer.

7 0
2 years ago
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