Answer:
1.) 16/20
2.) 15/35
3.) 12/9
4.) 52/60
5.) 9 inches
6.) 24 centimeters
7.) 16 logs
8.) $15.40
9.) 10 miles
10.) 1.5 inches
I hope this is good enough:
Answer:
a= 1%
b= 0.1%
c= 0.1875% probably have to round
Step-by-step explanation:
a= 2/2= 1
B= 1/10=0.1
c= 1.5/8= 0.1875
Step-by-step explanation:
1. No: angles add to more than 180 deg.
2. Yes: each side's length is between the sum and difference of the lengths of the other two sides.
3. No: not every side's length is between the sum and difference of the lengths of the other two sides.
4. Yes: for example, place the 50 deg angle between the two given sides. Another side will then make the triangle.
5. Yes: for example, use 3 cm as the short leg in a 30-60-90 right triangle.
Answer:
(a) The slope of f(x) is greater than the slope of g(x)
(b) f(x) has a greater y intercept
Step-by-step explanation:
Given
![\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcc%7Dx%20%26%20%7Bf%28x%29%7D%20%26%20-1%26-9%260%26-1%261%267%20%5C%20%5Cend%7Barray%7D)
![g(x) = 3x - 2](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20-%202)
Solving (a): Compare the slopes
The slope (m) of f(x) is calculated as;
![m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bf%28x_2%29%20-%20f%28x_1%29%7D%7Bx_2%20-%20x_1%7D)
This gives:
![m = \frac{f(0) - f(1)}{0 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bf%280%29%20-%20f%281%29%7D%7B0%20-%201%7D)
![m = \frac{f(0) - f(1)}{- 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bf%280%29%20-%20f%281%29%7D%7B-%201%7D)
Substitute values for f(0) and f(1)
![m = \frac{-1 - 7}{- 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1%20-%207%7D%7B-%201%7D)
![m = \frac{-8}{- 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-8%7D%7B-%201%7D)
![m = 8](https://tex.z-dn.net/?f=m%20%3D%208)
The slope of g(x) can be gotten using the following comparison
![g(x) = mx + b](https://tex.z-dn.net/?f=g%28x%29%20%3D%20mx%20%2B%20b)
![m \to slope](https://tex.z-dn.net/?f=m%20%5Cto%20slope)
So:
![g(x) = 3x -2](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20-2)
![m = 3](https://tex.z-dn.net/?f=m%20%3D%203)
![m_{f(x)} > m_{g(x)}](https://tex.z-dn.net/?f=m_%7Bf%28x%29%7D%20%3E%20m_%7Bg%28x%29%7D)
Solving (b): Compare the y intercept
y intercept is when ![x = 0](https://tex.z-dn.net/?f=x%20%3D%200)
From the table of f(x)
![f(0) = -1](https://tex.z-dn.net/?f=f%280%29%20%3D%20-1)
From the equation of g(x)
![g(x) = 3x -2](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20-2)
![g(0) = 3*0-2](https://tex.z-dn.net/?f=g%280%29%20%3D%203%2A0-2)
![g(0) =-2](https://tex.z-dn.net/?f=g%280%29%20%3D-2)
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