Hey there :)
Let us change the sentence into mathematics:
Area of rectangle = 35 m²
Length of rectangle is 3 m more than twice the width = 3 + 3w
Width = w
We know the area formula of a rectangle
Area = length × width
Dimensions of the rectangle are:
35 = w ( 3 + 2w )
35 = 3w + 2w²
Take all values to one side and equate to 0
2w² + 3w - 35 = 0
Factor:
( 2w - 7 ) ( w + 5 ) = 0
w =
or w = - 5 ( Reject because lengths can never be negative )
Therefore the dimensions are:
Width = 3.5 mLength = 3 + 2 ( 3.5 ) = 10 m
Answer: 0.5467
Step-by-step explanation:
We assume that the test scores for adults are normally distributed with
Mean :
Standard deviation :
Sample size : = 50
Let x be the random variable that represents the IQ test scores for adults.
Z-score :
For x =85
For x =115
By using standard normal distribution table , the probability the mean of the sample is between 95 and 105 :-
Hence, the probability that a randomly selected adult has an IQ between 85 and 115 =0.5467
Answer:
A. Here the y-intercept is (0,4) and means at time 0 hours the fish is displaced 4 feet.
B. For every hour, the fish is displaced 60 more feet.
C. The domain is [0, 12].
Step-by-step explanation:
Part A:
The y-intercept is where the function intersects the y-axis. It is the point (0,b) and is always the starting value in real world situations since time begins at x=0. Here the y-intercept is (0,4) and means at time 0 hours the fish is displaced 4 feet.
Part B:
The average rate of change is the slope of the function found using the formula . Use the points (0,4) and (1,64).
For every hour, the fish is displaced 60 more feet.
Part C:
The domain is the set or group of x values in the function. Time starts at 0 and goes until the fish traveled 724 feet. What time is this at?
The function has the equation y = 60 +4. Find the time by substituting y=724.
724=60x+4
720 = 60x
12=x.
The domain is [0, 12].
Answer:
The answer to your question is (f°g)(x) = -5856x⁶ - 25529x⁴ -52710x² - 36220
Step-by-step explanation:
Data
f(x) = -12x³ + 19x² - 5
g(x) = 7x² + 15
find (f°g)(x)
Process
1.- Substitute g(x) in all the x of f(x)
(f°g)(x) = -12(7x² + 15)³ + 19(7x² + 15)² - 5
-Expand
(f°g)(x) = -12[4913x⁶ + 2205x⁴ + 4725x² + 3375] + 19(49x⁴ + 210x² + 225) - 5
-Simplify
(f°g)(x) = -58956x⁶ - 26460x⁴ - 56700x² - 40500 + 931x⁴ + 3990x² + 4275 -
5
-Result
(f°g)(x) = -5856x⁶ - 25529x⁴ -52710x² - 36220