<h2>
Hello!</h2>
The answer is:
The answer is the fourth option,
![f(-3)=-\frac{1}{3}](https://tex.z-dn.net/?f=f%28-3%29%3D-%5Cfrac%7B1%7D%7B3%7D)
<h2>
Why?</h2>
Piecewise functions are functions that are composed by two or more expressions, the expression to use will depend of the domain or input that we need to evaluate.
We are given the piecewise function:
![\left \{ {{\frac{1}{x}, if x](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B%5Cfrac%7B1%7D%7Bx%7D%2C%20if%20x%3C-2%7D%20%5Catop%7Bx%5E%7B2%7D%2C%20ifx%5Cgeq%202%7D%7D%20%5Cright.)
There, we know that:
We should use the first expression if the value to evaluate is less than -2.
So, for this case, the function will be:
![f(x)=\frac{1}{x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%7D)
We should use the second expression if the value to evaluate is greater or equal than 2.
So, for this case, the function will be:
![f(x)=x^{2}](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B2%7D)
Now, since we are given that the value to evaluate is -3, and its less than -2, we need to use the first expression, and evaluate it.
![-3](https://tex.z-dn.net/?f=-3%3C-2)
So, evaluating the function we have:
![f(x)=\frac{1}{x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%7D)
![f(-3)=\frac{1}{-3}](https://tex.z-dn.net/?f=f%28-3%29%3D%5Cfrac%7B1%7D%7B-3%7D)
![f(-3)=-\frac{1}{3}](https://tex.z-dn.net/?f=f%28-3%29%3D-%5Cfrac%7B1%7D%7B3%7D)
Hence, we have that the answer is the fourth option,
![f(-3)=-\frac{1}{3}](https://tex.z-dn.net/?f=f%28-3%29%3D-%5Cfrac%7B1%7D%7B3%7D)
Have a nice day!
Answer:
Roy is 10 years old at present and Joan is 5 years old at present
Step-by-step explanation:
Let
x----> Roy's age
y----> Joan's age
we know that
x=2y ----> equation A
(x+3)+(y+3)=21 ----> equation B
substitute equation A in equation B
(2y+3)+(y+3)=21
solve for y
3y+6=21
3y=21-6
3y=15
y=5 years
Find the value of x
x=2y ----> x=2(5)=10 years
therefore
Roy is 10 years old at present
Joan is 5 years old at present
Answer:
Leg of an isosceles right triangle is 7.99 long.
Step-by-step explanation:
Given:
Length of the hypotenuse =11.31
To find:
Length of the leg of an isosceles right triangle =?
Solution:
According to Pythagorean's Theorem, we have
-----------------------------(1)
Here were are given as isosceles triangle, so the two sides will be of same length
So equation 1 can be rewritten as
![a^2 +a^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2Ba%5E2%20%3D%20c%5E2)
![2a^2 = c^2](https://tex.z-dn.net/?f=2a%5E2%20%3D%20c%5E2)
Substituting the value of hypotenuse
![2a^2 = (11.31)^2](https://tex.z-dn.net/?f=2a%5E2%20%3D%20%2811.31%29%5E2)
![2a^2 = 127.91](https://tex.z-dn.net/?f=2a%5E2%20%3D%20127.91)
![a^2 = \frac{127.91}{2}](https://tex.z-dn.net/?f=a%5E2%20%3D%20%5Cfrac%7B127.91%7D%7B2%7D)
![a^2 =63.955](https://tex.z-dn.net/?f=a%5E2%20%3D63.955)
![a = \sqrt{63.955}](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7B63.955%7D)
a = 7.99
Answer:
The answer would be X=2 .
Step-by-step explanation:
Hope it helps u :)
Answer:
Input - Output
2 - $290
12 - $690
24 - $1170
Step-by-step explanation:
Cost after n months:
The cost after n months is given by the following function:
![C(n) = 40n + 210](https://tex.z-dn.net/?f=C%28n%29%20%3D%2040n%20%2B%20210)
After 2 months:
This is C(2). So
![C(2) = 40(2) + 210 = 80 + 210 = 290](https://tex.z-dn.net/?f=C%282%29%20%3D%2040%282%29%20%2B%20210%20%3D%2080%20%2B%20210%20%3D%20290)
After 12 months:
This is C(12). So
![C(12) = 40(12) + 210 = 480 + 210 = 690](https://tex.z-dn.net/?f=C%2812%29%20%3D%2040%2812%29%20%2B%20210%20%3D%20480%20%2B%20210%20%3D%20690)
After 24 months:
This is C(24). So
![C(24) = 40(24) + 210 = 960 + 210 = 1170](https://tex.z-dn.net/?f=C%2824%29%20%3D%2040%2824%29%20%2B%20210%20%3D%20960%20%2B%20210%20%3D%201170)
Table:
Input - Output
2 - $290
12 - $690
24 - $1170