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antoniya [11.8K]
2 years ago
12

George had 1 sheet of paper. He cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. What were the dimensions and total

area of his original sheet of paper?
Mathematics
2 answers:
grandymaker [24]2 years ago
7 0

Answer:

The area is 48 square inches and the original dimensions are 6 by 8 inches.

Step-by-step explanation:

Total area = (6 x 5 + 3 x 6) sq.in. = 48 sq. in.

The original size of the (rectangular) paper must have been 6 by 8 inches. The two pieces share a side of length 6, so that's the first dimension. The sum of their other sides gives the second dimension: 3+5=8 inches.

Neporo4naja [7]2 years ago
5 0
The answer is 48 inches ^2
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Find a matrix representation of the transformation L(x, y) = (3x + 4y, x − 2y).
mario62 [17]

Answer:

\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}3&1\\4&-2\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]

Step-by-step explanation:

The general matrix representation for this transformation would be:

\left[\begin{array}{cc}x&y\end{array}\right] * A = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]

As the matrix A should have the same amount of rows as columns in the firs matrix and the same amount of columns as the result matrix it should be a 2x2 matrix.

\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]

Solving the matrix product you have that the members of the result matrix are:

3x+4y = a*x + c*y

x - 2y = b*x + d*y

So the matrix A should be:

\left[\begin{array}{cc}3&1\\4&-2\end{array}\right]

8 0
2 years ago
Which represents the solution set of the inequality 5 x minus 9 less-than-or-equal-to 21
Whitepunk [10]

Answer:

x less than or equal to 6

Step-by-step explanation:

5x-9 ≤ 21 ===> 5x ≤ 21+9 ===> 5x ≤ 30 ===> x ≤ 30/5 ===> x ≤ 6

5 0
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Since we are multiplying an exponential number to a fraction the answer is going to be

\frac{7 {}^{11} }{4 {}^{11} }

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2 years ago
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The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism. Find the volume of each
Art [367]

Answer:

Step-by-step explanation:

Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT

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