Given g(x) = 3x + 3, find g(-6).

Simplify: (2x-3)(4x+1)

mixas84 [53]

Answer:

$8x^2-10x-3$

Step-by-step explanation:

$(2x-3)(4x+1)$

$2x(4x+1)-3(4x+1)$

$8x^2+2x-12x-3$

$8x^2-10x-3$

3 0

3 years ago

What is the slope of the graph ? Leave your answer as a reduced fraction ?

Juliette [100K]

Answer:

-3/4

Step-by-step explanation:

(-8,4),(0,-2)

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\ \\\\\\\frac{-2-4}{0-(-8)} \\\\\\\frac{-2-4}{0+8}\\\\ \\\frac{-6}{8} or \frac{-3}{4}\\$

6 0

3 years ago

Ten samples were taken from a plating bath used in an electronics manufacturing process, and the bath pH was determined. The sam

Korolek [52]

Answer:

There is no sufficient evidence to support the claim.

Step-by-step explanation:

Given the data:

7.91, 7.85, 6.82, 8.01, 7.46, 6.95, 7.05, 7.35, 7.25, 7.42

Sample size, n = 10

The sample mean, xbar = ΣX/ n = 74.07 / 10 = 7.407

The sample standard deviation, s = 0.41158 ( from calculator)

The hypothesis :

H0 : μ = 7

H0 : μ ≠ 7

The test statistic :

(xbar - μ) ÷ (s/√(n))

(7.047 - 7) ÷ (0.41158/√(10))

0.047 / 0.1301530

Test statistic = 0.361

Testing the hypothesis at α = 0.05

The Pvalue ;

df = n - 1 ; 10 - 1 = 9

Two tailed test

Pvalue(0.361, 9) = 0.7263

Since the Pvalue > α ; we fail to reject the Null and conclude that there isn't sufficient evidence to support the claim.

4 0

2 years ago

Which do you think is easier to understand and why do you think so, multiplying radicals or multiplying polynomials?

Vera_Pavlovna [14]

I believe that its easier to understand the multiplication of a radical than that of a polynomial.

<h3>How to illustrate the information?</h3>

In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.

A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.

When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:

= 3✓2 × 4✓2

= 12✓4

= 12 × 2

= 24

The multiplication of a radical is easier.

Learn more about polynomial on:

brainly.com/question/2833285

#SPJ1

3 0

2 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 <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