Answer:
15 cm by 12 cm.
Step-by-step explanation:
Given:
Amanda uses a rectangular canvas for a panting.
The length is
centimeters.
The width is
centimeters, and is 4/5 of the length .
Question asked:
.What are the dimensions of the canvas ?
Solution:
<u>As given that the width is </u>
of the length.
![2x+6=\frac{4}{5} (6x-3)\\ \\ 2x+6=\frac{4}{5}\times6x-\frac{4}{5}\times3\\ \\ 2x+6=\frac{24x}{5} -\frac{12}{5} \\ \\](https://tex.z-dn.net/?f=2x%2B6%3D%5Cfrac%7B4%7D%7B5%7D%20%286x-3%29%5C%5C%20%5C%5C%202x%2B6%3D%5Cfrac%7B4%7D%7B5%7D%5Ctimes6x-%5Cfrac%7B4%7D%7B5%7D%5Ctimes3%5C%5C%20%5C%5C%202x%2B6%3D%5Cfrac%7B24x%7D%7B5%7D%20-%5Cfrac%7B12%7D%7B5%7D%20%5C%5C%20%5C%5C)
Adding both sides by ![\frac{12}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B5%7D)
![2x+6+\frac{12}{5} =\frac{24x}{5} -\frac{12}{5}+\frac{12}{5}\\ \\ 2x+\frac{42}{5} =\frac{24x}{5}](https://tex.z-dn.net/?f=2x%2B6%2B%5Cfrac%7B12%7D%7B5%7D%20%3D%5Cfrac%7B24x%7D%7B5%7D%20-%5Cfrac%7B12%7D%7B5%7D%2B%5Cfrac%7B12%7D%7B5%7D%5C%5C%20%5C%5C%202x%2B%5Cfrac%7B42%7D%7B5%7D%20%3D%5Cfrac%7B24x%7D%7B5%7D)
Subtracting both sides by ![2x](https://tex.z-dn.net/?f=2x)
![2x-2x+\frac{42}{5} =\frac{24x}{5} -2x\\ \\ \frac{42}{5} =\frac{24x-10x}{5} \\ \\ \frac{42}{5} =\frac{14x}{5} \\ \\](https://tex.z-dn.net/?f=2x-2x%2B%5Cfrac%7B42%7D%7B5%7D%20%3D%5Cfrac%7B24x%7D%7B5%7D%20-2x%5C%5C%20%5C%5C%20%5Cfrac%7B42%7D%7B5%7D%20%3D%5Cfrac%7B24x-10x%7D%7B5%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B42%7D%7B5%7D%20%3D%5Cfrac%7B14x%7D%7B5%7D%20%5C%5C%20%5C%5C)
By cross multiplication:-
![5\times14x=5\times42\\ \\ 70x=210\\ \\](https://tex.z-dn.net/?f=5%5Ctimes14x%3D5%5Ctimes42%5C%5C%20%5C%5C%2070x%3D210%5C%5C%20%5C%5C)
By diving both sides by 70
![x=3](https://tex.z-dn.net/?f=x%3D3)
<u>Now, substituting the value:-</u>
The length =
cm
= ![6\times3-3=18-3=15\ cm](https://tex.z-dn.net/?f=6%5Ctimes3-3%3D18-3%3D15%5C%20cm)
The width =
cm
= ![2\times3+6=6+6=12\ cm](https://tex.z-dn.net/?f=2%5Ctimes3%2B6%3D6%2B6%3D12%5C%20cm)
Thus, length and width of canvas are 15 cm and 12 cm.
Answer:
3. the numbers between -5 and 5
Step-by-step explanation:
Let set A=
and set
.
The solution set of A and B is the solution set of A∩B
The solution set of A is all the real number x which is greater than -5.
The solution set of B is all the real number x which is less than 5.
Therefore, the solution set of A∩B is all the real numbers between -5 and 5.
Hence, option (3) is correct.
Answer:
wouldn't be $30 all together
Step-by-step explanation:
<span>The 1/2 stretches the period from 2pi to 4pi and the amplitude stays the same. If the equation was y=2sin(x) then the amplitude would be 2.</span>
For S if the ratio is 2:7 and you use 20 drops of red paint you multiply 2 by 10 which is 20 so you also multiply 7 by ten to get 70 (So the answer for S is 70 drops) and for L you multiply 2 by 20 to get 40 so you multiply 7 by 20 and you get 140 (The answer for L is 140 drops) For T you multiply 2 by 1.5 to get 3 so you multiply 7 by 1.5 which is 10.5 ( so the answer for T is 10.5 drops)