The average rates of change of a function f(x) and g(x) are their slopes
The average rate of change of the function f(x) is always less than the average rate of change of the function g(x)
How to determine the average rate of change?The average rate of change of a function f(x) over the interval [a,b] is calculated as:
[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]
The average rates of change of the functions over the intervals are:
A. 0 ≤ x ≤ 3
[tex]m_1 = \frac{f(3) - f(0)}{3 - 0} = \frac{5 * 3 - 5 *0}{3 - 0} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(3) - g(0)}{3 - 0} = \frac{25 * 3 - 25 *0}{3 - 0} = 25[/tex] --- g(x)
B. 0 ≤ x ≤ 2
[tex]m_1 = \frac{f(2) - f(0)}{2 - 0} = \frac{5 * 2 - 5 *0}{2 - 0} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(2) - g(0)}{2 - 0} = \frac{25 * 2 - 25 *0}{2 - 0} = 25[/tex] --- g(x)
C. 3 ≤ x ≤ 6
[tex]m_1 = \frac{f(6) - f(3)}{6 - 3} = \frac{5 * 6 - 5 *3}{6 - 3} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(6) - g(3)}{6 - 3} = \frac{25 * 6 - 25 *3}{6 - 3} = 25[/tex] --- g(x)
D. 1 ≤ x ≤ 2
[tex]m_1 = \frac{f(2) - f(1)}{2 - 1} = \frac{5 * 2 - 5 *1}{2 - 1} = 5[/tex] ---- f(x)
[tex]m_2 = \frac{g(2) - g(1)}{2 - 1} = \frac{25 * 2 - 25 *1}{2 - 1} = 25[/tex] --- g(x)
From the above computation, we can see that:
The average rate of change of the function f(x) = 5x is always less than the average rate of change of the function g(x) = 25x
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André paid a $65 annual fee to register with a car rental company. The company charges $8.50 for each hour a car is rented. What is the rate of change of the function that represents André's cost for renting a car over the course of a year?
A. $8.50 per hour
B. $65 per year
C. $73.50 per hour
D. $73.50 per year
Answer:
I dont know if this is the right answer, but my best guess is that it is A.
Step-by-step explanation:
The rate of change of the function that represents André's cost for renting a car over the course of a year $8.50 per hour.
What is the rate of change?
The rate of change is the cost by which the cost of renting the car increases by. The cost of renting the car increases by $8.50 per hour.
The annual fee can be described as the fixed cost of renting the car per year.
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The ratio of red candy to green candy in a bag is 3 to 4
If there were 36 pieces of green candy in the bag, how many pieces of candy in the bag were red?
Answer:
27
Step-by-step explanation:
we know that 4 multiplied with something is 36
=> 4x = 36
=> x = 36/4
=> x = 9
so we have to multiply 3 with 9
=> 3*9 = 27
Each side of the regular hexagon below has the same measure. A hexagon with side lengths of 2. 5 feet. If a model of the hexagon is made by using a scale factor of 6, which applies to the model? Select two options. The model represents a reduction. Each side of the model is 15 feet long. The model is proportional to the original hexagon. One side of the model can be 8. 5 feet. The scale factor is divided by 2. 5 to get the dimensions of the model.
The correct option for a regular hexagon is b) Each side of the model is
15 feet long. and c) The model is proportional to the original hexagon.
What is a regular hexagon?A regular hexagon is defined as a closed shape consisting of six equal
sides and six equal angles. The sum of the measure of angles of a
regular hexagon is 120 degrees.
It is given that a hexagon with side lengths of 2. 5 feet.
The scale factor is 6.
Since scale factor = new length/original length,
new length = scale factor × original length
= 6 × 2.5 feet
= 15 feet.
Also, each side of the hexagon increases by a constant factor of 6, the model is proportional to the original hexagon.
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Find the value of x.
A. 53°
B. 72°
C. 39°
D. 48°
Answer: 53
Step-by-step explanation:
Farm workers plant 980 beans in 35 rows. How many beans do they plant in one row
Please guys help me , i need help with this math work im not doing so good un math
Answer: If you need help on both here are both answers.... Answer 1- f(x)=6.50x+48.00 because Let
x ----> the number of adult tickets
f(x) ----> amount of money collected
To find the amount collected multiply the number of adult tickets by the cost and multiply the number of student tickets by the cost, and then sum the two quantities
The linear equation that represents this problem is
f(x)=6.50x+4.00(12)
f(x)=6.50x+48.00
and for Answer 2- Is 4
factor 1/2 out of 1/2x + 9/2
Answer:
Equation would be x + 9/2.Step-by-step explanation:
Factoring out means taking out a Number, or an unknown quantity.
So, Factor out 1/2:
New equation with old step by step:
Step 1:
Remove 1/2 from 1/2x + 9/2Step 2:
Equation should be: x + 9/2.New equation:
x + 9/2Which equation represents the data in the table?
Answer:
c
Step-by-step explanation:
It all adds up. Ex; 2*2=4 4-3=1
and continues through the rest of the table
please no guessing (WILL GIVE BRAINILIST)
STATISTICS
Answer:
#2 mean is 90.3846154 and range is 40
#3 mean 91.9230769 and range is 20
(you might have mixed the second and third graph up)
Step-by-step explanation:
You decide to put $2,000 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 4% per year and is compounded monthly,
how long does it take until you have $3.000 without depositing any additional funds?
Answer:
12.5 years = 216 months
Step-by-step explanation:
4% of 2000= $80
1000/80=12.5
It will take 12.5 years to make $1000 on its own without adding additonal funds.
Given the function g(x)=√x+4, which of the following values cannot be the domain of g?
A. X=1
B. X=2
C. X=12
D. X=-5
Answer:
D. x = -5
Step-by-step explanation:
The square root function is only defined for non-negative arguments. For the function ...
[tex]g(x)=\sqrt{x+4}[/tex]
this means we must have ...
x +4 ≥ 0
x ≥ -4 . . . . . . subtract 4 from both sides
All of the numbers on your answer choice list are more than -4 except -5.
x = -5 is not in the domain of g(x)
What is the most common amount of hours students spent studying? (2 points)
A line plot with the title, time students spent studying, and the line is measured in hours. The horizontal line goes from one third to three. In between, there are seven tick marks labeled as two thirds, one, one and one third, one and two thirds, two, two and one third, two and two thirds. The tick mark one third has two xs, the tick mark two thirds has one x, the tick mark one has four xs, the tick mark one and one third has three xs, the tick mark one and two thirds has three xs, the tick mark two has five xs, the tick mark two and one third has three xs, the tick mark two and two thirds has two xs, and the tick mark three has two xs.
a
1 hour
b
one and one third hours
c
2 hours
d
3 hours
help pls first correct answer gets brainleist
n²= 7²+3²
=49+9
=58
n= V58
=7.62m
Write an addition equation or a subtraction equation (your choice!) to describe the diagram.
Answer:
-9 - 2 = -11
Step-by-step explanation:
If QR=x+29 and PS=x–16, what is the value of x?
Answer:
61
Step-by-step explanation:
PS is a midsegment of the triangle, so is half the length of the parallel base segment.
2PS = QR
2(x -16) = x +29 . . . . . substitute given expressions
2x -32 = x +29 . . . . . eliminate parentheses
x = 61 . . . . . . . . . . . . add 32-x
HELP PLEASE. Check picture. I have tried but cannot seem to get it.
Answer:
[tex]884^{-7}[/tex]
Step-by-step explanation:
Start by simplifying the denominator of the fraction. When multiplying exponents of the same base, you can add the exponents. This is also known as the product rule.
[tex]a^x\cdot a^y=a^{x+y}[/tex]
["a" is the base, and "x" and "y" are the exponents]
Using this we find...
[tex]884^{58}\cdot884^{46}=884^{58+46}=884^{104}[/tex]
When dividing exponents of the same base, you can subtract the exponents. This is also knows as the quotient rule.
[tex]a^x\div a^y=a^{x-y}[/tex]
Using this we find...
[tex]\frac{884^{97}}{884^{104}}=884^{97-104}=884^{-7}[/tex]
Answer:
[tex]884^{-7[/tex]
Step-by-step explanation:
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Before we begin solving, let's review a few rules of exponents.
If an exponent is multiplying with another exponent and their bases are the same, you can simply add the exponents.If an exponent is dividing with another exponent and their bases are the same, you can simply subtract the exponents.≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
⇒ [tex]\dfrac{884^{97} }{884^{58} \times 884^{46} }[/tex]⇒ [tex]\dfrac{884^{97} }{884^{58 + 46}}[/tex] [#1]⇒ [tex]\dfrac{884^{97} }{884^{104}}[/tex]⇒ [tex]884^{97 - 104[/tex] [#2]⇒ [tex]\boxed{884^{-7}}[/tex]≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Dan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Dan trained his Monday clients for a total of 10 hours and his Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
*Please help me by today if able*
Is 3822 divisible by three or nine
Answer:
The number 3,822 is divisible by 3 and is not divisible by 9, because the sum of the digits is 3 + 8 + 2 + 2, which equals 15, and 15 is divisible by 3 but not by 9.
Find M angle B.
Round to the nearest degree.
Answer: 41
Step-by-step explanation:
Find x 20 and 15 geometric mean
Answer: 17.320508075689
Step-by-step explanation:
Maya bought 20 ounces of nuts at the store. How much is this in pounds? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
1.25 pounds
Step-by-step explanation:
20 divided by 16 because 16 ounces are in a pound
Can someone help me with math I need help I will attempt to give y’all help too!
Answer:
48%
Step-by-step explanation:
there are 250 cars in total 50+70 is 120 (the red or blue cars)
so there are 120 "yes" out of 250 total of 120 divided by 250 equal 0.48 or 48%
Solve each inequality.
X+5 < 6
Pls help
Answer:
x<1
Step-by-step explanation:
You would just subtract 5 from both sides of the equation. The sign does not flip because you are not multiplying or dividing any negative number across the sign. So simply x+5 (-5) < 6 (-5). On the left side the 5 would cancel out. on the other side 6-5 is equal to 1.
Answer: x<1
Answer: x < 1
Step-by-step explanation: x + 5 < 6
Subtract 5 from both sides,
x < 1
I am so confused. Help.
[tex]\large\sf\underline{ANSWER:}[/tex]
√3
x is the length of the third side
x²+1² = 2² { Pythagorean Theorem}
x²+1 = 4 {Simplify}
x²=3 {Subtract 1 from each side}
x=√3 {Take the square root of each side}
The Length of the third side is √3
#[tex]\large\sf\underline{CarryOnLearning}[/tex]
Help me, please! It's all in the question...!
Answer:
the answer is the first one
Step-by-step explanation:
because
Answer
c hope it helps
help! please! now!.............
Answer:
The answer is 133.5
Step-by-step explanation:
See the image above
What is -4x^2-6x-4 in vertex form?
[tex]y = - 4 ({x + \frac{3}{4} })^{2} - \frac{7}{4} \\ [/tex]
Joe drove 567 miles in 9 hours.
At the same rate, how many miles would he drive in 5 hours
Answer:
answer down below
Step-by-step explanation:
it would be 315
Answer:
13 hours
Step-by-step explanation:
567/9=63
she drives 63mph
it will take her 13 hours to drive
The Hire Purchase priceola microwave
a deposit of $600 and equal monthly
installmentsof$4s. Howmany installmen,
Answer:
150
Step-by-step explanation:
$600/$4 =150
=150 installments
I just need 13⅗% as a decimal please thanks
the answer to 13 3/5% as a decimal
0.136