Answer:
|-8|=8
|10|=10
Step-by-step explanation:
any negative number between the two slashes '||' equals to always a positive number
and a positive number between the two slashes '||' remains the same
Answer:
The second option
x ==> f(x)
-1 ==> 0
0 ==> 3
3 ==> 36
Step-by-step explanation:
Given:
f(x) = 2x² + 5x + 3
{-1, 0, 3}
Required:
Determine the best mapping representing the function
SOLUTION:
First, find f(x) each domain value.
To find f(x), plug in the domain value into the function.
For -1, we have:
f(-1) = 2(-1)² + 5(-1) + 3
f(-1) = 2 - 5 + 3
f(-1) = 0
For 0, we have:
f(0) = 2(0)² + 5(0) + 3
f(0) = 0 + 0 + 3
f(0) = 3
For 3, we have:
f(3) = 2(3)² + 5(3) + 3
f(3) = 18 + 15 + 3
f(3) = 36
The mapping that best represents the function would be:
x (domain) ==> f(x) (range)
-1 ==> 0
0 ==> 3
3 ==> 36
The second option is the answer.
Answer:
To empty the aquarium it takes 26 minutes
Step-by-step explanation:
step 1
Find the volume of the aquarium
The volume of rectangular prism is
![V=LWH](https://tex.z-dn.net/?f=V%3DLWH)
we have
![L=33\ in\\W=26\ in\\H=12\ in](https://tex.z-dn.net/?f=L%3D33%5C%20in%5C%5CW%3D26%5C%20in%5C%5CH%3D12%5C%20in)
substitute the given values
![V=(33)(26)(12)=10,296\ in^3](https://tex.z-dn.net/?f=V%3D%2833%29%2826%29%2812%29%3D10%2C296%5C%20in%5E3)
step 2
Divide the volume by the rate of 396 in^3 per minute
![10,296/(396)=26\ minutes](https://tex.z-dn.net/?f=10%2C296%2F%28396%29%3D26%5C%20minutes)
therefore
To empty the aquarium it takes 26 minutes
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36