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zepelin [54]
3 years ago
5

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?

Mathematics
1 answer:
Aneli [31]3 years ago
7 0

Answer: 5x + 2y = -2

Step-by-step explanation:

Change 5x+2y=12 to slope intercept: 2y = 12 - 5x, y = -5x/2 + 6

A parallel line has the same slope, so the line we try to find is y = -5x/2 + b.

Substitute (-2, 4) in and get 4=5+b, so b = -1.

Therefore the answer is y = -5x/2 - 1, or if you want it in the original form it would be 2y = -5x - 2 ---> 5x+2y = -2.

Hope that helped,

-sirswagger21

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The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (
kow [346]

Answer:

\|a\| = 5\sqrt{13}.

\|b\| = 3\sqrt{29}.

Step-by-step explanation:

Let m,n, and k be scalars such that:

\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}.

\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}.

\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}.

The question states that \| a + b \| = 34. In other words:

k\, \sqrt{8^{2} + 15^{2}} = 34.

k^{2} \, (8^{2} + 15^{2}) = 34^{2}.

289\, k^{2} = 34^{2}.

Make use of the fact that 289 = 17^{2} whereas 34 = 2 \times 17.

\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}.

k^{2} = 2^{2}.

The question also states that the scalar multiple here is positive. Hence, k = 2.

Therefore:

\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}.

(a + b) could also be expressed in terms of m and n:

\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}.

\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}.

Equate the two expressions and solve for m and n:

\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}.

\begin{cases}m = 5 \\ n = 3\end{cases}.

Hence:

\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}.

\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}.

6 0
3 years ago
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MissTica

Answer:

x = -3

Step-by-step explanation:

6x - 9 = -27 (Given)

6x = -18 (Add 9 on both sides.)

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Answer:

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Step-by-step explanation:

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£b = charge for booking online

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