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Llana [10]
3 years ago
10

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes.

Each small box can hold 30 books and each large box can hold 40 books. There were twice as many large boxes sent as small boxes, which altogether can hold 330 books. Determine the number of small boxes sent and the number of large boxes sent.
Mathematics
1 answer:
jeka57 [31]3 years ago
6 0

Answer:

Step-by-step explanation:

x = small box and y = large box

30x + 40y = 330

y = 2x

30x + 40(2x) = 330

30x + 80x = 330

110x = 330

x = 330/110

x = 3 <===== 3 small boxes

y = 2x

y = 2(3)

y = 6 <=== 6 large boxes

check...

30x + 40y = 330

30(3) + 40(6) = 330

90 + 240 = 330

330 = 330 (correct)

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Given <em>YA</em> = <em>B</em>, you can solve for <em>Y</em> by multiplying by <em>A </em>⁻¹ on the right (on both sides of the equation). So we have

<em>YA</em> = <em>B</em>   ==>   (<em>YA</em>) <em>A </em>⁻¹ = <em>BA </em>⁻¹   ==>   <em>Y</em> (<em>AA </em>⁻¹) = <em>BA </em>⁻¹   ==>   <em>Y</em> = <em>BA </em>⁻¹

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A=\begin{bmatrix}-1&-4\\0&-5\end{bmatrix} \implies A^{-1}=\dfrac1{\det(A)}\begin{bmatrix}-5&0\\4&-1\end{bmatrix} = \begin{bmatrix}-1&0\\\frac45&-\frac15\end{bmatrix}

Then

Y=\begin{bmatrix}5&-5\\8&-8\end{bmatrix}A^{-1} = \begin{bmatrix}-5&5\\-8&\frac{24}5\end{bmatrix}

4 0
2 years ago
What is an equation of the line that is perpendicular to y-4=2(x-6) and passes through (-3,-5)
Nat2105 [25]

Answer:

y = -1/2 x - 13/2

Step-by-step explanation:

what is an equation of the line that is perpendicular to y-4=2(x-6) and passes through (-3,-5)

First, we need the slope of the given line.

y - 4 = 2(x - 6)

y - 4 = 2x - 12

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The slope of the given line is 2.

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We use the given point as x and y and solve for b.

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