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Igoryamba
3 years ago
14

The length of the sides of a triangle are 2x +y/2, 5x/3+y + ½ and 2/3x +2y +5/2. If the triangle is equilateral, find its perime

ter.
Mathematics
1 answer:
Sav [38]3 years ago
6 0

Answer:

Step-by-step explanation:

If the triangle is equilateral :

2x +y/2 =  5x/3+y + ½  = 2/3x +2y +5/2

so the perimeter is : P = 3(2x +y/2) or 3(5x/3+y + ½) or 3(2/3x +2y +5/2)

the simplest is :  P = 3(2x +y/2)

                            P = 6x + (3y)/2

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A popular online music store allowed shoppers to listen to an entire album before buying it. Of the people who listened to the w
katrin2010 [14]

Answer:

IDK this stuff is confusing

Step-by-step explanation:

Plz like and follow

4 0
3 years ago
If a car travels at an average speed of x miles per hour, how far would the car travel in 90 minutes ?
antiseptic1488 [7]

Answer:

(1.5)x

Step-by-step explanation:

90 minutes = 1.5 hours therefore

if car travels x miles in 1 hour

then the care has to travel (1.5)x miles in 90 minutes

6 0
3 years ago
Read 2 more answers
Ruby plans to make 3 quilts per month until she makes 15 quilts. She figures this will take 1/5 month. Which is NOT a reason why
pashok25 [27]

Answer: c)She should have multiplied 15 by 3 instead of dividing.


Step-by-step explanation:

Number of quilts Ruby plan to make in one month= 3

which means if Ruby makes more than 3 quilts, the time will be more than 1 month.

To find the number of months to make 15 quilts, she need to divide 15 by 3

Thus, the number of months to make 15 quilts=5

Her answer was 1/5 which was absolutely wrong as if she is making 3 quilt in 1 month then in 1/5  month she would make fewer than 3 quilts.

She divides 3 by 15 instead of 15 by 3, thus but the unit is quilts not months.

Thus the only wrong option is c)She should have multiplied 15 by 3 instead of dividing.


4 0
3 years ago
Read 2 more answers
Consider the transpose of Your matrix A, that is, the matrix whose first column is the first row of A, the second column is the
Zarrin [17]

Answer:The system could have no solution or n number of solution where n is the number of unknown in the n linear equations.

Step-by-step explanation:

To determine if solution exist or not, you test the equation for consistency.

A system is said to be consistent if the rank of a matrix (say B ) is equal to the rank of the matrix formed by adding the constant terms(in this case the zeros) as a third column to the matrix B.

Consider the following scenarios:

(1) For example:Given the matrix A=\left[\begin{array}{ccc}1&2\\3&4\end{array}\right], to transpose A, exchange rows with columns i.e take first column as first row and second column as second row as follows:

Let A transpose be B.

∵B=\left[\begin{array}{ccc}1&3\\2&4\end{array}\right]

the system Bx=0 can be represented in matrix form as:

\left[\begin{array}{ccc}1&3\\2&4\end{array}\right]\left[\begin{array}{ccc}x_{1} \\x_{2} \end{array}\right]=\left[\begin{array}{ccc}0\\0\end{array}\right] ................................eq(1)

Now, to determine the rank of B, we work the determinant of the maximum sub-square matrix of B. In this case, B is a 2 x 2 matrix, therefore, the maximum sub-square matrix of B is itself B. Hence,

|B|=(1*4)-(3*2)= 4-6 = -2 i.e, B is a non-singular matrix with rank of order (-2).

Again, adding the constant terms of equation 1(in this case zeros) as a third column to B, we have B_{0}:      

B_{0}=\left[\begin{array}{ccc}1&3&0\\4&2&0\end{array}\right]. The rank of B_{0} can be found by using the second column and third column pair as follows:

|B_{0}|=(3*0)-(0*2)=0 i.e, B_{0} is a singular matrix with rank of order 1.

Note: a matrix is singular if its determinant is = 0 and non-singular if it is \neq0.

Comparing the rank of both B and B_{0}, it is obvious that

Rank of B\neqRank of B_{0} since (-2)<1.

Therefore, we can conclude that equation(1) is <em>inconsistent and thus has no solution.     </em>

(2) If B=\left[\begin{array}{ccc}-4&5\\-8&10&\end{array}\right] is the transpose of matrix A=\left[\begin{array}{ccc}-4&-8\\5&10\end{array}\right], then

Then the equation Bx=0 is represented as:

\left[\begin{array}{ccc}-4&5\\-8&10&\end{array}\right]\left[\begin{array}{ccc}x_{1} \\x_{2} \end{array}\right]=\left[\begin{array}{ccc}0\\0\end{array}\right]..................................eq(2)

|B|= (-4*10)-(5*(-8))= -40+40 = 0  i.e B has a rank of order 1.

B_{0}=\left[\begin{array}{ccc}-4&5&0\\-8&10&0\end{array}\right],

|B_{0}|=(5*0)-(0*10)=0-0=0   i.e B_{0} has a rank of order 1.

we can therefor conclude that since

rank B=rank B_{0}=1,  equation(2) is <em>consistent</em> and has 2 solutions for the 2 unknown (X_{1} and X_{2}).

<u>Summary:</u>

  • Given an equation Bx=0, transform the set of linear equations into matrix form as shown in equations(1 and 2).
  • Determine the rank of both the coefficients matrix B and B_{0} which is formed by adding a column with the constant elements of the equation to the coefficient matrix.
  • If the rank of both matrix is same, then the equation is consistent and there exists n number of solutions(n is based on the number of unknown) but if they are not equal, then the equation is not consistent and there is no number of solution.
5 0
3 years ago
Is the function represented by the table non-linear?
Vladimir79 [104]

Answer:

Step-by-step explanation:

Yes because it has a constant rate of change

3 0
3 years ago
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