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Aleonysh [2.5K]
3 years ago
5

Find the lengths of two segments whose sum is 45 and whose ratio is 2:3

Mathematics
1 answer:
ohaa [14]3 years ago
8 0
Let the two segments be x and y
x+y=45...1
X/y = 2/3...2
From1, y=45-x
Sub this into 2
x/(45-x)=2/3
3x=90-2X
5x=90
x=18
y=45-18=27
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The product of two consecutive even integers is 14 more than their sum. Find the integers
sukhopar [10]
4 and 6! 

4*6 = 24

24 - 14 = 10

4 + 6 = 10
5 0
3 years ago
Which statement about the simplified binomial expansion of (a + b)", where n is a positive integer, is true?
Alja [10]

Answer:

(a+b)^n  ={n \choose 0}a^{(n)}b^{(0)} + {n \choose 1}a^{(n-1)}b^{(1)} + {n \choose 2}a^{(n-2)}b^{(2)} + .....  +{n \choose n}a^{(0)}b^{(n)}

Step-by-step explanation:

The Given question is INCOMPLETE as the statements are not provided.

Now, let us try and solve the given expression here:

The given expression is: (a +b)^n, n > 0

Now, the BINOMIAL EXPANSION is the expansion which  describes the algebraic expansion of powers of a binomial.

Here, (a+b)^n  = \sum_{k=0}^{n}{n \choose k}a^{(n-k)}b^{(k)}

or, on simplification, the terms of the expansion are:

(a+b)^n  ={n \choose 0}a^{(n)}b^{(0)} + {n \choose 1}a^{(n-1)}b^{(1)} + {n \choose 2}a^{(n-2)}b^{(2)} + .....  +{n \choose n}a^{(0)}b^{(n)}

The above statement holds for each  n > 0

Hence, the complete expansion for the given expression is given as above.

4 0
3 years ago
Read 2 more answers
The length of a rectangle is three more than its width. The perimeter is 86cm. Find the length and width of the rectangle. Write
elena-s [515]
P=2(l+w)
Substitute width plus 3 for length
Remember order of operations: multiply before adding

86=2((w+3) + w)
86=2w+6+2w
86=4w+6
80=4w
20=w
23=w+3=l

Check the answer
86=2((w+3) + w)
86=2((20+3)+20
86=2(23+20)
86=46+40
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5 0
3 years ago
During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs be
Ratling [72]

Answer:a

 a

    m  = 57.5

b

   \= x  = 50.14

Step-by-step explanation:

From the question we told that

  The stem plots for American League is

                  2\\3\ \ \ \ \ 5\\4 \ \ \ \ \ 0\  3 \ 9\\5 \ \ \ \ \ 1\ 4\ 7\ 8\ 8\\6 \ \ \ \ \ 4\ 8\ 8\\7 \ \ \ \ \ 5\ 7

Here the first column  is the tens while each digit in the in the second column is the unit of the first column

  For example row 3 means

      40 , 43, 49

The  sample  size is  n = 14  

Generally the median is mathematically represented as

         m  =  \frac{ K  +  Z}{2}

Here  K is the (\frac{n}{2}) th  \  term \ in \ the \  data \  given i.e  \frac{14}{2}  =  7th \  term

 From the stem plot the 7th term is  57

And

       K is the (\frac{n}{2} + 1) th  \  term \ in \ the \  data \  given i.e  \frac{14}{2} + 1 =  8th \  term

 From the stem plot the 8th term is  58

Thus the median is  

          m  =  \frac{ 57  +  58}{2}

=>       m  = 57.5

The stem plots for National League is

            2\ \ \  9\\3\ \ \ \ 1\\4 \ \ \ \ 2\ 6\ 7\ 8\ 8\\5 \ \ \ \  3\ 5\ 5\ 5\\6 \ \ \ \  3\ 3\ 7\\7\\

Generally the mean is mathematically evaluated as

           \= x  =  \frac{\sum x_i}{n}

           \= x  =  \frac{29 + 31 + 42 + 46 + 47 + 48 + 48 + 53 + 55+ 55+ 55+ 63+ 63+ 67}{14}

         \= x  = 50.14

5 0
3 years ago
Solve and identify the solution. 10+1.5x=3.5x
julia-pushkina [17]

Answer:

x=5

Step-by-step explanation:

hope this is correct have a wonderful day! <3

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