Therefore, since the slope of f(x) is defined and g(x) has an undefined slope, the correct option is: d) The function f(x) has a larger slope.
To determine the slopes of the functions f(x) and g(x), we need to calculate the rate of change or the slope of each function.
The slope of a function represents how much the output (y-value) changes for a given change in the input (x-value).
For function f(x), the rate of change can be calculated as follows:
[tex]\[ \text{Slope of } f(x) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{200 \text{ pages}}{40 \text{ minutes}} = 5 \text{ pages/minute} \][/tex]
Now, let's calculate the slope for function g(x) using the given data points:
[tex]\[ \text{Slope of } g(x) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{28 - (-8)}{4 - 4} = \frac{36}{0} \][/tex]
As the denominator is zero, the slope for g(x) is undefined.
What's the sum of all the integers between √3 and √89 ?
Laying used 3/8 cup of flour and 1/3 cup of sugar in a recipe which number below is a common denominator for 3/8 and 1/3
What is the maximum height of a projectile, such as a rocket, called?
A little help would be nice :) I will award 5 stars and 15 points.
2− 0.5n=3n+16
Help
5, -10, 15, -20,... sequence
You put $500 in your bank account. With an interest rate of 5%, how long will it take the account to reach $600?
A robot can complete 8 tasks in 5/6 or an hour.each tasks takes the same amount .how long does it take the robot to complete one task
A chef has 15 3/4 lb of beans. She packs them in freezer bags that weigh 2 1/4 lb each. How many freezer bags of beans does the chef pack?
students collected 600 cans for the canned food drive that was 80% of their goal how many more cans do they need to collect to reach their goal
Answer: 150
Step-by-step explanation:
Let x be the total number of cans that was students' goal.
Given : Students collected 600 cans for the canned food drive that was 80% of their goal .
We can write 80% as 0.80
Then, we have
[tex]0.80x=600\\\\\Rightarrow\ x=\dfrac{600}{0.80}=750[/tex]
Thus, The students' goal of collecting cans for the canned food drive = 750 cans
Now, the number of food cans required to collect to reach the goal= 750-600=150
What percent of 100 is 40
find the experimental probability of rolling a 4
Final answer:
The experimental probability of rolling a 4 is calculated by dividing the number of times a 4 is rolled by the total number of rolls. It may not match the theoretical probability exactly in the short term but should converge to approximately 0.1667 as the number of trials increases.
Explanation:
To find the experimental probability of rolling a 4 with a fair six-sided die, we must consider the frequency of the event (rolling a 4) occurring among a number of trials. Since each side of the die has an equal chance of landing face up, each side has a probability of 1/6.
If a die is rolled many times, and the results are recorded, the experimental probability can be calculated as the number of times a 4 occurs divided by the total number of trials. For example, if a die is rolled 120 times and the number 4 comes up 20 times, the experimental probability for rolling a 4 would be 20/120, which simplifies to 1/6. However, since this is experimental probability, the outcome may not always exactly match the theoretical probability due to variations in the short term. Nevertheless, as the number of trials increases, we expect the experimental probability to get closer to the theoretical probability of 1/6 or approximately 0.1667 when rounded to four decimal places.
What is 121,580 Rounded to the nearest thousand?
How does the graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉?
-The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted down 7 units.
-The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted left 7 units.
-The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.
-The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted right 7 units.
The graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉ as the graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.
Modulus function / Absolute function [x]What is modulus function?A modulus function is a function that determines a number or variable's absolute value. No matter what input was provided to this function, the outcome is always positive.
Solution of function f(x) = [x]Consider different values for x.
Say,
x = -1; f(-1) = [-1] = 1
x = 1; f(1) = [1] = 1
For any value of the x, the value of the function will be positive only.
The graph is attached in the image.
Solution of function f(x) = [x] + 7Consider different values for x.
Say,
x = 0; f(0) = [0] + 7 = 0 + 7; f(0) = 7
x = -1; f(-1) = [-1] + 7 = 1 + 7; f(-1) = 8
x = 1; f(1) = [1] = 1 + 7; f(1) = 8
For any value of the x, the value of the function will be positive only, but it would be 7 units shifted up on the y axis.
The graph is attached in the image.
To know more about how to determine modulus of complex numbers?, here
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Kiera wants to increase her savings account to a balance of $1,350. Her current balance is $174 and she adds $84 a month to her savings. How many months will it take for her to reach her goal of $1,350
16 months
14 months
18 months
12 months
Solve the inequality below and then graph the solution set.
1
_ w + 3 < -6
4
Plot the line for the equation on the graph. y−2=−2(x+4)
The plot of the given line is required.
The graph is shown below with two points [tex](0,-6)[/tex] and [tex](-3,0)[/tex].
The line is
[tex]y-2=-2(x+4)\\\Rightarrow y=-2x-8+2\\\Rightarrow y=-2x-6[/tex]
Let us find two points on the line
[tex]x=0[/tex]
[tex]y=-2\times0-6=-6[/tex]
[tex](0,-6)[/tex]
[tex]y=0[/tex]
[tex]0=-2x-6\\\Rightarrow x=\dfrac{6}{-2}=-3[/tex]
[tex](-3,0)[/tex]
Join the two points on the graph and the line will be constructed.
Learn more:
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A handyman charges fixed or r to visit a customer house in addition the handyman charges an hourly rate of H for each hour worked write a formula to represent T the total amount this handyman would charge for a job that requires N hours of work
Answer:
T = HN + r
Step-by-step explanation:
A handyman charges $H for each hour worked.
If the handyman works for N hours then the expression for the charges will be = $HN
Handyman charges a fixed amount = $r
Then the total amount charged T will be represented by
T = HN + r
Therefore, formula to calculate the total charges by handyman will be
T = HN + r
can some one help me a little hard for me
How many seconds equal 3.6 hours?
how many hours is it from 12am-5am
how to express 1/243 using a negative exponent other than -1
The function f(x) is graphed on the coordinate plane.
What is f(−4) ?
Enter your answer in the box.
f(−4) =
For this case, what you should do is observe in the graph the value of the function when x = -4.
The value of the function is observed when looking at the vertical axis.
Remember that in a function of the form y = f (x) we have:
x: independent variable
y: dependent variable.
Therefore, for x = -4 we have:
f (-4) = 4
Answer:
The value of the function evaluated at x = -4 is given by:
f (-4) = 4
The greatest common factor of 56 f^3g^2 and 70 fg^3 is 7 fg^3 .
true or false
Answer: False
Step-by-step explanation:
You can see 7*3*2*f*g is not the same as 7fg3, so the statement is false.
PLEASE ANSWER!!!!! After five years of earning interest at an annual rate of 3%, an investment has earned $950 in interest. To the nearest whole dollar, determine the amount of the initial investment. Show all work for full credit.
What is 3/8 equivalent to
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\textbf{What is }\rm{\bf \dfrac{3}{8}}\large\textbf{ equivalent to?}[/tex]
[tex]\huge\textbf{Now, let's solve for the given question:}[/tex]
[tex]\mathbf{\dfrac{3}{8}}[/tex]
[tex]\mathbf{= \dfrac{3\times2}{8\times2}}[/tex]
[tex]\mathbf{\approx \dfrac{3 + 3}{8 + 8}}[/tex]
[tex]\mathbf{= \dfrac{6}{16}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{6}{16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Michael earns a base salary of $100.00 every week with an additional 9% commission on everything he sells. If Michael sold $4950.00 worth of items last week, what was his total pay?
Which graph represents the solution set of the system of inequalities?
−2x+y≤4
{
y>x+2
Answer:
Graph 2
Step-by-step explanation:
Given system of inequalities,
−2x + y ≤ 4,
y > x + 2
∵ Related equation of −2x + y ≤ 4 is,
-2x + y = 4 ⇒ y = 4 + 2x ----(1)
While, the related equation of y > x + 2 is,
y = x + 2
From equation (1),
4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2
Again by equation (1),
y = 4 + 2(-2) = 4 - 4 = 0
Hence, the intersection point of the related equation is (-2,0),
∴ Graph 1 and graph 3 can not be the graph of the given system.
Now, −2(0) + (0) ≤ 4 ( true )
That is, −2x+y ≤ 4 would contain the origin,
Also, 0 > 0 + 2 ( False )
That is, y > x + 2 does not contain the origin.
Therefore, by the above explanation it is clear that,
Grap 2 represents the solution set of the system of inequalities.
Dean needs 6060 inches of wood to build a rectangular picture frame. The length ll of the frame is twice its width ww. Three of these equations give the correct value for ww. Which equation does NOT?
Please help me!
x + 6 ≤ 8