Answer:
-1/2
Step-by-step explanation:
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
Kimtoya is riding according to the equation y = 12.5x, which is in slope-intercept form where the slope is 12.5, so her rate is 12.5.
now, Sidney's rate... hmmm we don't know, but we have her table ahaa!, well, let's use that to get the slope or rate for Sydney let's pick two points from it hmmm say (2 , 25) and hmmm (5 , 62.5)
![(\stackrel{x_1}{2}~,~\stackrel{y_1}{25})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{62.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{62.5}-\stackrel{y1}{25}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}}\implies \cfrac{37.5}{3}\implies 12.5](https://tex.z-dn.net/?f=%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B25%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B62.5%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B62.5%7D-%5Cstackrel%7By1%7D%7B25%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B5%7D-%5Cunderset%7Bx_1%7D%7B2%7D%7D%7D%5Cimplies%20%5Ccfrac%7B37.5%7D%7B3%7D%5Cimplies%2012.5)
holy molly!, whaddaya know, they're both riding at the same rate, 12.5 km/hr
The length of the segment HI in the figure is 32.9
<h3>How to determine the length HI?</h3>
To do this, we make use of the following secant-tangent equation:
HI² = KI * JI
From the figure, we have:
KI = 21 + 24 = 45
JI = 24
So, we have:
HI² = 45 * 24
Evaluate the product
HI² = 1080
Take the square root of both sides
HI = 32.9
Hence, the length of the segment HI is 32.9
Read more about secant and tangent lines at:
brainly.com/question/14962681
#SPJ1
Answer:
a = 5
Step-by-step explanation:
Using Pythagoras' theorem in the right triangle
a² + 12² = 13²
a² + 144 = 169 ( subtract 144 from both sides )
a² = 25 ( take the square root of both sides )
a =
= 5
Answer:
The answer is 41%.
Step-by-step explanation:
First, you have to find the total volume of the cylindrical flask using the formula. Then, you have to substitute the following values into the formula :
![v = \pi \times {r}^{2} \times h](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5Ctimes%20%20%7Br%7D%5E%7B2%7D%20%20%20%5Ctimes%20h)
![let \: \pi = 3.14 \\ let \: r = 3 \\ let \: h = 12](https://tex.z-dn.net/?f=let%20%5C%3A%20%5Cpi%20%3D%203.14%20%5C%5C%20let%20%5C%3A%20r%20%3D%203%20%5C%5C%20let%20%5C%3A%20h%20%3D%2012)
![v = 3.14 \times {3}^{2} \times 12](https://tex.z-dn.net/?f=v%20%3D%203.14%20%5Ctimes%20%20%7B3%7D%5E%7B2%7D%20%20%5Ctimes%2012)
![v = 3.14 \times 108](https://tex.z-dn.net/?f=v%20%3D%203.14%20%5Ctimes%20108)
![v = 339.12 {cm}^{3}](https://tex.z-dn.net/?f=v%20%3D%20339.12%20%7Bcm%7D%5E%7B3%7D%20)
Next, given that 200cm³ of liquid is poured into the cylinder. So in order to find the volume of flask that is not filled by liquid, you have to subtract :
![v = 339.12 - 200 = 139.12 {cm}^{3}](https://tex.z-dn.net/?f=v%20%3D%20339.12%20-%20200%20%3D%20139.12%20%7Bcm%7D%5E%7B3%7D%20)
Lastly, you have to find the percentage :
![\frac{139.12}{339.12} \times 100 = 41\% \: (near. \: whole \: number)](https://tex.z-dn.net/?f=%20%5Cfrac%7B139.12%7D%7B339.12%7D%20%20%5Ctimes%20100%20%3D%2041%5C%25%20%5C%3A%20%28near.%20%5C%3A%20whole%20%5C%3A%20number%29)