Answer:
1). x = 81
2). x = 84
Step-by-step explanation:
1). By applying geometric mean theorem in the given triangle,
![\frac{x}{18\sqrt{14}}= \frac{18\sqrt{14}}{56}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B18%5Csqrt%7B14%7D%7D%3D%20%5Cfrac%7B18%5Csqrt%7B14%7D%7D%7B56%7D)
56x = (18√14)²
56x = 4536
x = ![\frac{4536}{56}](https://tex.z-dn.net/?f=%5Cfrac%7B4536%7D%7B56%7D)
x = 81
2). By applying geometric mean theorem,
![\frac{x}{8\sqrt{21}}= \frac{8\sqrt{21} }{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B8%5Csqrt%7B21%7D%7D%3D%20%5Cfrac%7B8%5Csqrt%7B21%7D%20%7D%7B16%7D)
16x = (8√21)²
16x = 1344
x = ![\frac{1344}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1344%7D%7B16%7D)
x = 84
The expression for which you want to find an equivalent form is:
Answer:
Here there are 3 equivalent expressions:
Explanation:
There are many equivalent forms that you can find, so I will show some of the most important.
The first step that you should do is to put the radicand number (the number inside the root, i.e. 3) as a product of its prime factors. Thus the first equivalent expression is:
Now you can simplify the root index, 4, with the exponent of the radicand, 2, an you get a new equivalent:
Another equivalent form is obtained if you convert the 1/2 index (before the x) into a root index:
The main properties used to find those equivalent expressions are:
And:
Step-by-step explanation:
The slope-intercept form of an equation of a line:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
- slope
- y-intercept
![11)\ m=-1,\ b=2\\\\y=-x+2\\\\12)\ m=-\dfrac{3}{2},\ b=3\\\\y=-\dfrac{3}{2}x+3\\\\13)\ m=3,\ y=-2\\\\y=3x-2\\\\14)\ y=\dfrac{3}{4},\ b=1\\\\y=\dfrac{3}{4}x+1\\\\15)\ m=\dfrac{1}{2},\ b=1\\\\y=\dfrac{1}{2}x+1\\\\16)\ m=-\dfrac{2}{5},\ b=0\\\\y=-\dfrac{2}{5}x\\\\17)\ m=-7,\ b=2\\\\y=-7x+2\\\\18)\ m=\dfrac{4}{3},\ b=-4\\\\y=\dfrac{4}{3}x-4](https://tex.z-dn.net/?f=11%29%5C%20m%3D-1%2C%5C%20b%3D2%5C%5C%5C%5Cy%3D-x%2B2%5C%5C%5C%5C12%29%5C%20m%3D-%5Cdfrac%7B3%7D%7B2%7D%2C%5C%20b%3D3%5C%5C%5C%5Cy%3D-%5Cdfrac%7B3%7D%7B2%7Dx%2B3%5C%5C%5C%5C13%29%5C%20m%3D3%2C%5C%20y%3D-2%5C%5C%5C%5Cy%3D3x-2%5C%5C%5C%5C14%29%5C%20y%3D%5Cdfrac%7B3%7D%7B4%7D%2C%5C%20b%3D1%5C%5C%5C%5Cy%3D%5Cdfrac%7B3%7D%7B4%7Dx%2B1%5C%5C%5C%5C15%29%5C%20m%3D%5Cdfrac%7B1%7D%7B2%7D%2C%5C%20b%3D1%5C%5C%5C%5Cy%3D%5Cdfrac%7B1%7D%7B2%7Dx%2B1%5C%5C%5C%5C16%29%5C%20m%3D-%5Cdfrac%7B2%7D%7B5%7D%2C%5C%20b%3D0%5C%5C%5C%5Cy%3D-%5Cdfrac%7B2%7D%7B5%7Dx%5C%5C%5C%5C17%29%5C%20m%3D-7%2C%5C%20b%3D2%5C%5C%5C%5Cy%3D-7x%2B2%5C%5C%5C%5C18%29%5C%20m%3D%5Cdfrac%7B4%7D%7B3%7D%2C%5C%20b%3D-4%5C%5C%5C%5Cy%3D%5Cdfrac%7B4%7D%7B3%7Dx-4)
19) and 20) you have in other your question.
Answer:she will earn $200 in 5 weeks
Step-by-step explanation:
Susan takes care of a child for 2 hours after school each weekday and 6 hours on Saturday. There are 5 school days in a week. Total number of hours that she spends in taking care of the child during the weekdays would be 5×2 = 10 hours.
Total hours for the week would be
10 + 6 = 16 hours
Total amount of hours in 5 weeks would be
5 × 16 = 80
If she earns 2.50 per hour, it means that in 80 hours, she would earn
2.5 × 80 = $200
Answer:
y = -3 + 6ˣ
Step-by-step explanation:
-3 is the lowest it goes, and the more you increase the base, the more it its stretch will become. Now, although it passes through -2, we are not dealing with y-intercept here because this is NOT a linear function. This is called a horizontal asymptote. This is an exponential function, from the parent function of <em>y</em><em> </em><em>=</em><em> </em><em>abˣ</em><em>,</em><em> </em>if I can recall correctly. Anyway, you understand?