For this case we can apply the Pythagorean theorem to find "x". Taking the rectangle triangle of base 5 we have:
![x = \sqrt {11 ^ 2-5 ^ 2}\\x = \sqrt {121-25}\\x = \sqrt {96}\\\x = \sqrt {4 ^ 2 * 6}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%20%7B11%20%5E%202-5%20%5E%202%7D%5C%5Cx%20%3D%20%5Csqrt%20%7B121-25%7D%5C%5Cx%20%3D%20%5Csqrt%20%7B96%7D%5C%5C%5Cx%20%3D%20%5Csqrt%20%7B4%20%5E%202%20%2A%206%7D)
By definition of power properties we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
So:
![x = 4 \sqrt {6}](https://tex.z-dn.net/?f=x%20%3D%204%20%5Csqrt%20%7B6%7D)
Answer:
![x = 4 \sqrt {6}](https://tex.z-dn.net/?f=x%20%3D%204%20%5Csqrt%20%7B6%7D)
If a graph of a system of two equations shows two lines that coincide on a coordinate plan there would be C.)Infinitely many solutions
I hope this helps, have a great day.
8 ounces = 1cup
2 cups = 1 pint
So, 16 ounces = 2 cups = 1pint
16 ounces = 1 pint
If you have 8 ounces, you would have half a pint.
If you have 20 ounces:
20 ounces/16 ounces= 5/4
So, you'd have 1 1/4 or 1.25 pints
The basic equation for interest is the investment amount(x) times the time in years(y) times the percent of interest(z).
That makes the equation:
x·y·z= amount with interest.
Lets plug in the numbers:
$900 x 1.5 x 2.4%
Now turn the percent into a decimal:
2.4% ----> .024
Now the equation is:
$900 x 1.5 x .024
Now do the math:
$900 x 1.5 = 1350
1350 x .024 = 32.4
1350 + 32.4 = 1382.4
The final answer is $1382.40
Hope this helps!
Answer:
a) (4,5)
b) (0,-3)
Step-by-step explanation:
We have to perform the following reflection over given ordered pair.
a) Reflect the ordered pair (-4,5) across the y-axis
Reflection over y-axis:
![r: (x,y)\rightarrow (-x,y)](https://tex.z-dn.net/?f=r%3A%20%28x%2Cy%29%5Crightarrow%20%28-x%2Cy%29)
Thus, (-4,5) will be reflected over y-axis as
![r: (-4,5)\rightarrow (-(-4),5) = (4.5)](https://tex.z-dn.net/?f=r%3A%20%28-4%2C5%29%5Crightarrow%20%28-%28-4%29%2C5%29%20%3D%20%284.5%29)
b) Reflect the ordered pair (0,3) across the y-axis
Reflection over x-axis:
![r: (x,y)\rightarrow (x,-y)](https://tex.z-dn.net/?f=r%3A%20%28x%2Cy%29%5Crightarrow%20%28x%2C-y%29)
Thus, (0,3) will be reflected over x-axis as
![r: (0,3)\rightarrow (0,-(3)) = (0,-3)](https://tex.z-dn.net/?f=r%3A%20%280%2C3%29%5Crightarrow%20%280%2C-%283%29%29%20%3D%20%280%2C-3%29)