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3 years ago

Six times a number minus two all over eight

Mathematics

1 answer:

Elis [28]3 years ago

8 0

Answer: 6(x)-2/8

Step-by-step explanation:

6 parentheses to represent multiplying,and unknown number inside you would use a variable, and then subtract 2 and use the slash sign ( / ) to represent the fraction bar and write 8 next to it

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Kyleigh invested $2800 in an account paying an interest rate of 5 1/2% compounded annually Ariana invested $2800 in an account p

shutvik [7]

Answer:

Step-by-step explanation:

Kyleigh invested $2800 in an account paying an interest rate of 5 1/2% compounded annually Ariana invested $2800 in an account paying in interest rate of 5 3/4%compounded continuously after 12 years how much more money with Ariana having her account then Kylie to the nearest dollar?

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3 years ago

Read 2 more answers

Only male crickets chirp. They chirp at different rates depending on their species and the temperature of their environment. Sup

bezimeni [28]

Answer:

4920

7084800

2585952000

Step-by-step explanation:

82 chirps = 1 minute

We have 60 minutes in one hour, so 82 x 60 =4920 chirps in one hour

In 24 hours we have 60x24 = 1440 minutes and in one minutes we have 4920 chirps,

Therefore 4920 x 1440 mins =7084800 chirps in one day .

There are 365 days in a year and in one day the cricket chirps 7084800, so 365 days x 7084800 = 258595200 chirps in a year

6 0

3 years ago

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 $\neq$ 0.

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

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

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

(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 consistent and has 2 solutions for the 2 unknown ( $X_{1}$ and $X_{2}$ ).

Summary:

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

How many different pizza's can be ordered if the restaurant offers 15 different toppings and there is not limit to the number of

RSB [31]

225 different pizzas can be ordered

4 0

3 years ago

What is GE ? Enter your answer in the box.

Flura [38]

The length of GE is 10 units

Explanation:

Given that the length of XY = 5 units and YZ = 4.6 units

The length of GE:

We need to determine the length of GE

From the figure, we can see that ZY bisects GE and XY bisects EF.

The lines ZY and XY both bisect GF.

The midpoint theorem states that "the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side".

Since, we have,

EX = XF and X is the midpoint of EF

GY = YF and Y is the midpoint of GF

Since, XY is the line segment that connects the midpoints of the two sides of the triangle.

Applying the midpoint theorem, we have,

$GE = 2XY$

$GE = 2(5)=10 \ units$

Thus, the length of GE is 10 units.

6 0

3 years ago