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3 years ago

I REALLY NEED HELP

Mathematics

1 answer:

irga5000 [103]3 years ago

8 0

Answer:

6x + 3y = 3846

x + y = 846

Step-by-step explanation:

(value of adult ticket [6] * number of adult tickets [x]) + (value of student ticket [3] * number of student tickets [y]) = total value (3846)

6x + 3y = 3846

(number of adult tickets [x]) + (number of student tickets [y]) = total number of tickets (846)

x + y =846

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You can factor a quadratic function using the completing the square method for any coefficient of the a term. True or false

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Step-by-step explanation:

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4 years ago

At a furniture manufacturer, worker A can assemble a shelving unit in 5 hours. Worker B can assemble the same shelving unit in 3

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Let's define the following variable:
t = total time it takes to assemble a shelving unit together.
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3 years ago

Read 2 more answers

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Kazeer [188]

Answer:

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Step-by-step explanation:

30=2r+r would be the answer for the first question because the red line, 30, is equal to the line 2r and r.

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4 years ago

Round to the nearest tenth. x= y=

11111nata11111 [884]

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3 years ago

Using the definition of inverse (Definition 1, on Page 43) and nothing more, show that if A is an invertible matrix and c is a n

elena-s [515]

Answer:

The matrix $cA$ is invertible and its inverse is $\frac{1}{c}\cdot A^{-1}$ .

Step-by-step explanation:

Since the definition of the inverse matrix states that the inverse of matrix $A$ is a matrix B such that:

$A\cdot B=B\cdot A=I$

we have to assume the form of such matrix. In our case we have the matrix $cA, c\neq 0$ and so, the constant $c$ must be somehow eliminated from the equation. The most logical way to do so is to include $\frac{1}{c}$ in the inverse. If we choose matrix B to be $B=\frac{1}{c}\cdot A^{-1}$ , we will have this:

$cA\cdot \frac{1}{c}\cdot A^{-1}=c\cdot \frac{1}{c}\cdot A\cdot A^{-1}=1\cdot I=I$ and

$\frac{1}{c}\cdot A^{-1}\cdot cA=\frac{1}{c}\cdot c\cdot A^{-1}\cdot A=1\cdot I=I$ .

We can form the matrix B like this because we know from the text of the problem that the inverse matrix of A exists and that c is a nonzero number.

Here is another way to solve this using the formula of the inverse matrix

Since we know that the matrix $A$ is invertible, it follows that its determinant is different from zero. Using the formula for the inverse matrix:

$A^{-1}=\frac{1}{\det (A)}\cdot \text{Adj} (A)$

we will assume the form of an inverse matrix of $cA$ . We need to obtain the formula for the inverse of $cA$ , so we first need to find $\det (cA)\ \text{and}\ \text{Adj} (cA)$ . Since the matrix $cA$ is obtained from matrix $A$ by multiplying every term with $c$ , while calculating determinant we have a constant $c$ that can be extracted from every column (or row) in front. Therefore, we have that

$\det (cA)=c^n\cdot \det (A)$ .

On the other hand, $\text{Adj} (cA)$ consists of minors of the matrix $cA$ . Therefore, when we extract the constant in front of such ( $n-1 \times n-1$ ) determinants, we have $c^{n-1}$ in each column (row). Including all this into the formula we have that:

$(cA)^{-1}=\frac{1}{c^n\cdot \det (A)}\cdot c^{n-1} \text{Adj } (A)=\frac{1}{c\cdot \det (A)} \cdot \text{Adj} A=\frac{1}{c}\cdot A^{-1}$ .

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4 years ago