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2 years ago

The standard ratio of a photo's width to it's length is 2/3. what is the length of a photo that has a width of 14 inches?

Mathematics

2 answers:

ankoles [38]2 years ago

5 0

L: w

Equation

2/3 = 14/ x

Cross multiply

2xX = 14x3

2x = 42

Eliminate

2x/2 = 42/2

X = 21

AysviL [449]2 years ago

5 0

Answer:

The answer is D.21.

Step-by-step explanation:

You have to divide 14 by 2/3 and you get 21.

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Determine if the columns of the matrix form a linearly independent set. Justify your answer. [Start 3 By 4 Matrix 1st Row 1st Co

Volgvan

Answer:

Linearly Dependent for not all scalars are null.

Step-by-step explanation:

Hi there!

1)When we have vectors like $v_{1},v_{2},v_{3}, ...$ we call them linearly dependent if we have scalars $a_{1},a_{2},a_{3},...$ as scalar coefficients of those vectors, and not all are null and their sum is equal to zero.

$a_{1}\vec{v_{1}}+a_{2}\vec{v_{2}}+a_{3}\vec{v_{3}}+...a_{m}\vec{v_{m}}=0$

When all scalar coefficients are equal to zero, we can call them linearly independent

2) Now let's examine the Matrix given:

$\begin{bmatrix}1 &-2 &2 &3 \\ -2 & 4 & -4 &3 \\ 0&1 &-1 & 4\end{bmatrix}$

So each column of this Matrix is a vector. So we can write them as:

$\vec{v_{1}}=\left \langle 1,-2,1 \right \rangle,\vec{v_{2}}=\left \langle -2,4,-1 \right \rangle,\vec{v_{3}}=\left \langle 2,-4,4 \right \rangle\vec{v_{4}}=\left \langle 3,3,4 \right \rangle$ Or

Now let's rewrite it as a system of equations:

$a_{1}\begin{bmatrix}1\\ -2\\ 0\end{bmatrix}+a_{2}\begin{bmatrix}-2\\ 4\\ 1\end{bmatrix}+a_{3}\begin{bmatrix}2\\ -4\\ -1\end{bmatrix}+a_{4}\begin{bmatrix}3\\ 3\\ 4\end{bmatrix}=\begin{bmatrix}0\\ 0\\ 0\end{bmatrix}$

2.1) Since we want to try whether they are linearly independent, or dependent we'll rewrite as a Linear system so that we can find their scalar coefficients, whether all or not all are null.

Using the Gaussian Elimination Method, augmenting the matrix, then proceeding the calculations, we can see that not all scalars are equal to zero. Then it is Linearly Dependent.

$\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ -2 &4 &-4 &3 \\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )R_{1}\times2 +R_{2}\rightarrow R_{2}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &0 &9 &0\\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )\ R_{2}\Leftrightarrow R_{3}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &1 &-1 &4 \\ 0 &0 &9 &0 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )$ $\left\{\begin{matrix}1a_{1} &-2a_{2} &+2a_{3} &+3a_{4} &=0 \\ &1a_{2} &-1a_{3} &+4a_{4} &=0 \\ & & &9a_{4} &=0 \end{matrix}\right.\Rightarrow a_{1}=0, a_{2}=a_{3},a_{4}=0$

$S=\begin{bmatrix}0\\ a_{3}\\ a_{3}\\ 0\end{bmatrix}$

3 0

3 years ago

What is the Value of X?

Yakvenalex [24]

$\dfrac{x+5}{6}=\dfrac{x+5+9}{12}\\\\\dfrac{x+5}{6}=\dfrac{x+14}{12}\ \ \ \ |cross\ multiply\\\\12(x+5)=6(x+14)\\\\12\cdot x+12\cdot5=6\cdot x+6\cdot14\\\\12x+60=6x+84\ \ \ |subtract\ 6x\ from\ both\ sides\\\\6x+60=84\ \ \ \ |subtract\ 60\ from\ both\ sides\\\\6x=24\ \ \ \ |divide\ both\ sides\ by\ 6\\\\\boxed{x=4}$

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3 years ago

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How do you find the missing angle of a triangle when all other angles are there?

olya-2409 [2.1K]

All angles in a triangle add up to 180 degrees. So, if you are missing an angle, add up the degrees of the angles present and subtract that from 180. That will be the value of the missing angle in degrees.

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2 years ago

An airplane travels at a rate of 300 miles per hour in still air. one day it travels 1200 miles against the wind in the same amo

GREYUIT [131]

Wind speed: 100 miles per hour
300 times 6 = 1800 miles so it took 6 hours to travel 1800 miles. 1800 minus 1200 miles = 600 miles. you lost 600 miles over 6 hours or 100 miles per hour

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3 years ago

What is the 7th term in the sequence?

timama [110]

To determine the 7th term of a given sequence, we use the formula given above which is

an = 30 - 4n

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Therefore,

an = 30 - 4n
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3 years ago

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