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2 years ago

What is the simplified form of 3 StartRoot 135 EndRoot?

Mathematics

2 answers:

jek_recluse [69]2 years ago

5 0

Answer:

$9 \sqrt{135}$

Step-by-step explanation:

Express 135 as a product of 15 and 9:

$135=15*9$

So:

$3\sqrt{15*9}$

Now, use the following property:

$\sqrt[n]{a*b} =\sqrt[n]{a}\hspace{3} \sqrt[n]{b}$

Therefore:

$3\sqrt{15} \sqrt{9}$

Since the square root of 9 is 3, the simplified form of $3\sqrt{135}$ :

$3\sqrt{15} \sqrt{9}=3*3\sqrt{15} =9\sqrt{15}$

svetoff [14.1K]2 years ago

3 0

$\bf 3\sqrt{135}~~ \begin{cases} 135=&3\cdot 3\cdot 15\\ &3^2\cdot 15 \end{cases}\implies 3\sqrt{3^2\cdot 15}\implies 9\sqrt{15}$

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At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least

attashe74 [19]

Answer:

Step-by-step explanation:

Here let the number of ride tickets be r, and the number of food tickets be f.

Hence

$r+f\ge16\\4r+2f\le40$

We first plot the two inequalities on graph as shown in attachment. From the graph we see that the two in-equation meet at (4,12)

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2 years ago

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Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

VLD [36.1K]

<h2>Answer:</h2>

The average speed of car is:

0.75 miles per minutes.

The equation of line is:

$n=\dfrac{3}{4}t$

<h2>Step-by-step solution:</h2>

The table that describes the time and number of miles marked is given by:

Time Miles

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4 3

8 6

Clearly we could observe that with the increase in time by every 4 minutes the number of mile increases by 3.

i.e. the average speed is calculated as the ratio of change in miles to the change in time.

Hence,

$Average\ Speed=\dfrac{3-0}{4-0}\\\\\\i.e.\\\\\\Average\ Speed=\dfrac{3}{4}=0.75$

Hence, the average speed=0.75 miles per minutes.

Also we will find the equation of the lines that related the miles and time by using the two-point formula.

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$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here (a,b)=(0,0) and (c,d)=(4,3)

i.e. the equation is given by:

$n-0=\dfrac{3-0}{4-0}\times (t-0)\\\\i.e.\\\\n=\dfrac{3}{4}t$

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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

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So the matrix A should be:

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

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