2/3 of $48 is $32. (48 / 3 = 16 x 2 =3)
7/8 of $22 is $19.25.
3/4 of 60 is 45.
By applying <em>radical</em>, <em>power</em> and <em>rational</em> properties we have the following results after simplifying expressions:
- x
- x
<h3>How to reduce radical and rational expressions into a single power expression with rational exponent</h3>
In this question we need to simplify four given expressions by using the following <em>radical</em> and <em>power</em> properties:
![\sqrt[n]{x} = x^{\frac{1}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D)
(1)
(2)
(3)
(4)
Now we proceed to simplify each of the four expressions:
![\sqrt[4]{x^{3}} = x^{3/4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E%7B3%7D%7D%20%3D%20x%5E%7B3%2F4%7D)
![\sqrt[10]{x^{5}\cdot x^{4}\cdot x^{2}} = \sqrt[10]{x^{11}} = x^{\frac{11}{10} }](https://tex.z-dn.net/?f=%5Csqrt%5B10%5D%7Bx%5E%7B5%7D%5Ccdot%20x%5E%7B4%7D%5Ccdot%20x%5E%7B2%7D%7D%20%3D%20%5Csqrt%5B10%5D%7Bx%5E%7B11%7D%7D%20%3D%20x%5E%7B%5Cfrac%7B11%7D%7B10%7D%20%7D)
To learn more on power functions: brainly.com/question/18719083
#SPJ1
<span>3.01419753086 or approximately 3
</span>
Answer:
(−1, –1.25), (5, –2.75)
Step-by-step explanation:
If "slope-intercept form" is mentioned, then we already know that the function rule is that of a straight line with slope m and y-intercept b.
As we go from (−1, –1.25) to (5, –2.75), x increases by 6 and y decreases by 1.50. Thus, the slope, m, is m = rise / run = -1.50 / 6, or m = -0.25 or -1/4.
Choosing one of the given points at random: (8, -3.5), we start with the slope-intercept form y = mx + b and substitute -1/4 for m, 8 for x and -3.5 for y: y = mx + b becomes -3.5 = (-1/4)(8) + b. Then -3.5 + 2 = b, or b = -1.5.
The desired equation is y = (-1/4)x - 3/2, or y = -0.25x - 1.5
