Given:
The equations are
To find:
Which function is changing more quickly.
Solution:
The slope intercept form of a line is
Where m is slope and b is y-intercept.
On comparing with the slope intercept form, we get
On comparing with the slope intercept form, we get
Since, 
, it means the absolute rate of change of second function is greater than the first function.
Therefore, the second function is changing more quickly.
(1/3) of (14-1/3) = (1/3) x (43/3) = (43/9) = about <em>(4 and 7/9) gallons</em>.
Answer:
The solutions are x = 1.24 and x = -3.24
Step-by-step explanation:
Hi there!
First, let´s write the equation:
log[(x² + 2x -3)⁴] = 0
Apply the logarithm property: log(xᵃ) = a log(x)
4 log[(x² + 2x -3)⁴] = 0
Divide by 4 both sides
log(x² + 2x -3) = 0
if log(x² + 2x -3) = 0, then x² + 2x -3 = 1 because only log 1 = 0
x² + 2x -3 = 1
Subtract 1 at both sides of the equation
x² + 2x -4 = 0
Using the quadratic formula let´s solve this quadratic equation:
a = 1
b = 2
c = -4
x = [-b± √(b² - 4ac)]/2a
x = [-2 + √(4 - 4(-4)·1)]/2 = 1.24
and
x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24
The solutions are x = 1.24 and x = -3.24
Have a nice day!
Question 1 Answer:
Aunt 1 and Grandma 1 would fill gift bags.
Mom and Aunt 2 would make centerpieces.
You and Grandma 2 would blow up balloons.
Since you are pairing up to complete the tasks, these pairs each have the shortest times in their respective categories and therefore are the most logical pairing to complete tasks.
Question 2 Answer:
We use algebra and our previous pairings to determine the length of each task.
<u>Gifts Bags --> 6/7 hours</u>
x = time together
= rate of completion
Aunt 1 = 
Grandma 1 = 
<u>Centerpieces --> 7/4 hours</u>
x = time together = rate of completion
Mom = 
Aunt 2 =
<u>Balloons --> 15/16 hours</u>
x = time together = rate of completion
You = Grandma 2 = 
Shortest amount of time to complete all tasks is:
≈ 3.54 hours
Converting hours to hours and minutes --> 3 hours 32 minutes
Therefore they must arrive by 5:28pm to complete the tasks in time to leave at 9:00pm.
,so first split them into separate shapes (refer to pic) then calculate each one
I started with the triangle
8×6=48 and 48÷2=24 so the triangles area its 24
next the rectangle
12×8=96
and I did the triangle shape cut out of the square
4×3=12 12÷2=6 so its area is 6
and the squares area is 8×8=64
but u need to subtract 6 from 64 because that area is missing
then you get 64-6=58
then add all the areas
58+24+96 to get your answer of 178m
