Can you get the same sum when you use 12 rather than 6 as a common denominator for the fractions 2\3 and 2\1? Explains

Mathematics

1 answer:

sashaice [31]4 years ago

5 0

Lets see...
The answer is yes! This is because when you solve for a common denominator, you need to multiply the numerator by what you multiplied to get the denominator. I solved the problem for you, which is displayed in the picture below:

You can see that the answer in improper form is 8/3 and in proper form is 2 2/3. If you look at the work, I believe you can draw conclusions from there. I am not good at explaining and I apologize. Good luck on your homework, common denominators are not hard to solve and I bet you will do a wonderful job in solving questions like these! You will soon become a Master at solving these kinds of questions in about a day from now and/or when you get to the upper grades like me! :)

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lukranit [14]

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4 years ago

A parabolà can be drawn given a focus of (7,9) and a

NeTakaya

from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".

keeping in mind the vertex is half-way between these two fellows, Check the picture below.

$\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}$

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4 years ago

dan is building a circular swimming pool and wants the circumference to be no more than 95 feet what is the largest radius possi

sleet_krkn [62]

The largest radius for the swimming pool is 15.1 feet

Step-by-step explanation:

Step 1:

Circumference of the circular swimming pool built by Dan = 95 feet

We need to determine the largest radius for the pool.

Step 2 :

Circle's circumference is given by 2πr

Where r represents the radius

This shows that the radius is in direct proportion to the circumference. Hence the radius corresponding to the maximum circumference will be the largest possible radius

So we have 2πr = 95

=> r = $\frac{95}{2\pi }$