Final answer:
No, y = 0 is not the asymptote of all functions of the form f(x) = ab^x. The y = 0 line is called the x-axis and is only an asymptote for certain functions. Functions of the form f(x) = ab^x do not have y = 0 as an asymptote.
Explanation:
No, y = 0 is not the asymptote of all functions of the form f(x) = ab^x. The y = 0 line is called the x-axis and is only an asymptote for certain functions. In order for a function to have y = 0 as an asymptote, the limit of the function as x approaches infinity or negative infinity would need to be 0. For example, the function f(x) = 1/x has y = 0 as an asymptote because as x approaches infinity or negative infinity, the function approaches 0. However, functions of the form f(x) = ab^x do not have y = 0 as an asymptote because as x approaches infinity or negative infinity, the value of the function either approaches infinity or approaches 0, depending on the values of a and b.
The area of the triangle shown is represented by A= square root of s(s-10)(s-7)(s-5), where s is equal to half the perimeter. What is the height of the triangle? Round your answer to the nearest tenth.
There are two prominent, nationally circulated newspapers, The Wall Street Journal and USA Today. Among all libraries across the country, 45% subscribe to The Wall Street Journal and 40% subscribe to USA Today, while only 25% subscribe to both The Wall Street Journal and USA Today. If a library is selected at random, what is the probability that it subscribes to The Wall Street Journal but not USA Today?
Answer:
20% = 0.2
Step-by-step explanation:
Let A = Wall Street Journal = 45%
Let B = USA Today = 40%
Let C = Both = 25%
C = A∩B = 25%
The focus is to determine that a random library subscribes to A only
The probability of subscribing to A = 45%
However, there are subscribers to A that are also subsribed to B
This group is C = 25%
To find the probability of subscribing to A only;
Probability of A only = P{A} - P{A∩B} = P{A} - P{C}
P{A} only = 45% - 25% = 20%
P{A} only = 0.2
The scatterplot below shows the number of hours that some high school students spend on working and on video games.
Which statement about the scatterplot is true?
In general, the number of hours spent working does not affect the number of hours spent on video games.
In general, the amount of weekly time spent working is equal to the amount of weekly time spent on video games.
As the amount of time spent working increases, the amount of time spent on video games increases.
As the number of hours spent working increases, the amount of time spent on video games decreases.
Answer:
D
Step-by-step explanation:
As the number of hours spent working increases, the amount of time spent on video games decreases.
What is the relationship between radius and diameter of a circle
What is the differencence betwenn the volume
Here’s another for you people - 5/6k = 1/6
A cube-shaped item needs to be painted. The item’s edge length is 2 centimeters. What is the total surface area that will be painted? 16 cm² 24 cm² 32 cm² 48 cm²
Answer: A) 24
Hope This Helps ^_^
4) A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes.
a) Write a system of equations to represent the situation. Explain what your x and y will represent.
b) Solve the system of equations.
c) How much commission does she earn for selling each suit and each pair of shoes?
The sales associate earns a commission of $13 for each suit sold and $8 for each pair of shoes sold, found by solving the system of equations representing her commission earnings for two different weeks.
To represent the sales associate's commission earnings, we will use two variables: let x be the commission for each suit sold, and y be the commission for each pair of shoes sold.
(a) System of Equations:
The first week's commission can be represented by the equation 3x + y = 47. The second week's commission can be written as 7x + 2y = 107.
(b) Solving the System:
Multiply the first equation by 2 to get 6x + 2y = 94.Subtract the first modified equation from the second week's equation: (7x + 2y) - (6x + 2y) = 107 - 94.This simplifies to x = 13, meaning the commission for each suit is $13.Substitute x = 13 into the first equation: 3(13) + y = 47.Solve for y: 39 + y = 47, so y = 8.(c) The commission for each pair of shoes is $8.
Solve this quadratic word problem
How many rectangular faces does a hexagonal pyramid have ?
What are the new coordinates of L if parallelogram LMNO is translated down 20 units?
Answer:
The answer is [tex](-4,-19)[/tex]
Step-by-step explanation:
Firstly, we have to determine the coordinates of L before the translation.
If we see the graph, we can see that the coordinate "x" is -4 and the coordinate "y" is 1. So, the original coordinates of L are [tex](4,1)[/tex]
Then, we have to determine the vector of translation. We know that the parallelogram LMNO is translated down 20 units, so it means that it moved only in the negative vertical direction. Then the coordinate of the vector is [tex](0,-20)[/tex]
Finally, in order to determine the new coordinates of L, we have to add the original coordinates of L with the coordinates of the vector of translation, that is:
[tex](-4+0,1-20)\\(-4,-19)[/tex]
So, the new coordinates of L is [tex](-4,-19)[/tex]
The driving distance from the Sports Arena to Christinas house is 10 9/10 miles the distance from the Sports Arena to Luke’s house is 2 7/10 Miles how much greater is the driving distance between the sports arena in Kristen’s house then between the sports arena in Luke’s house
Draw two different figures that each have a perimeter of 20 units
Is my answer correct?
Will give brainliest!!
The dimensions of triangle A are four times the dimensions of triangle B. The area of triangle B is 15cm 2. what is the area of triangle A
1.3-2.1g when g is 1.9. Can you please help? I keep getting 2.69 but the paper shows the answer to be 5.29
Samir knows that the volume of prism is 40 cubic units . He also knows that the width can of the prism is 2 units and the height is 5 units. What is the length of the prism?
Final answer:
The length of the prism is 4 units, which is determined by dividing the volume of the prism (40 cubic units) by the product of its width (2 units) and height (5 units).
Explanation:
Samir knows that the volume of a prism is 40 cubic units, the width is 2 units, and the height is 5 units. To find the length of the prism, we can use the formula for the volume of a prism: V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Plugging in the known values, we get 40 = l × 2 × 5. To solve for l, we divide both sides of the equation by the product of the width and height (2 × 5), yielding l = 40 / (2 × 5) = 40 / 10 = 4 units. Thus, the length of the prism is 4 units.
. Greg has a school debt of $9 875. He wants to make biweekly payments and pay off the loan in 4 years. If the interest rate is 6.3% compounded biweekly, how much are his payments?
Which sentence best describes the function shown?
A) The function is odd.
B) The function is even.
C) The function is symmetric about the x-axis.
D) The function is symmetric about the origin.
Answer:
B) The function is even.
Step-by-step explanation:
The function shown in the graph is ƒ(x) = |x|. This function is symmetric about the y-axis and is therefore, even.
In simple words: If you fold the picture in half then the lines should be on top of each other and become one. If this happens, then this is an even function.
Points P(6, –8) and Q(–18, 2) are plotted on the coordinate plane.
Enter the distance, in units, between points P and Q.
2/3 - 1/6 finding the common denominator show me how to do it
A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum balance requirement is charged a service fee.
Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the number of months since the account was open.
If an initial deposit of $2,713.00 is made to the account with a monthly service fee of 5%, what will be the value of B after 13 months? Round to the nearest cent.
To find the current balance B after 13 months with an initial deposit of $2,713.00 and a 5% monthly service fee, you multiply the initial deposit by 0.95 to the power of 13, resulting in a balance of approximately $1,392.64.
Explanation:The student's question involves using a given mathematical formula to find the current balance of a savings account affected by a monthly service fee. The formula provided states that the current balance B is equal to the initial deposit I times the quantity (1 - monthly service fee f) raised to the power of the number of months n. To calculate the current balance after 13 months, given an initial deposit of $2,713.00 and a monthly service fee of 5%, you'd perform the following calculation:
Convert the percentage fee to a decimal: 5% = 0.05.Subtract the service fee from 1: 1 - 0.05 = 0.95.Raise the difference to the power of the number of months: 0.9513.Multiply the result by the initial deposit: $2,713.00 × 0.9513.Using a calculator, this gives:
B = $2,713.00 × (0.9513) ≈ $2,713.00 × 0.5133421 ≈ $1,392.64
Rounded to the nearest cent, the value of B after 13 months is $1,392.64.
There are 52 blades of grass in 2 in2 of lawn. There are 580 blades of grass in 8 in2 of the same lawn. Which equation models the y blades of grass found in x in2 of lawn?
The equation that models the relationship between the number of blades of grass (y) and the area of lawn (x) is y=88x−124. This equation represents the rate of 88 blades per square inch with an initial count of 52 blades.
To find the equation that models the relationship between the number of blades of grass (y) and the area of lawn (x), we can use the given information to form a linear equation.
Step 1: Determine the rate of change. Subtract the initial number of blades from the final number and divide by the change in area: (580 - 52) / (8 - 2) = 528 / 6 = 88 blades per square inch.
Step 2: Write the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 3: Plug in the slope (m = 88) and one point (x = 2, y = 52) to find the y-intercept:
52 = 88(2) + b
52 = 176 + b
b = -124
Step 4: Write the equation:
y = 88x - 124
You are playing a game and it is your turn to spin the spinner shown. There are four possible results: blue, green, yellow, or purple. What is the probability that you land on purple?
You have a 25% chance on landing on any of the colors
You Look at all of the possible ways you can land on which is purple, Blue, Green, and Yellow there are four colors in the spinner if you divide the number of colors (4) and divide it by 100 you will get 25 and that is your answer
round each amount to the nearest hundred to find an estimate of: 3891÷289
0.746, 0.745, 0.75 in order from largest to smallest. Please
Lauren's scores on her math tests are 93,91,98,100,95,92,and 96. What score does Lauren need to get on her next math test test so that the mean and the mediam stay the same?
Lauren needs to get a mean/median score in order to keep from changing either of those values. She needs a 95.
_____
In order, the scores are
... 91, 92, 93, 95, 96, 98, 100
The median is the middle of these, 95, and the problem statement tells us the mean is the same (which it is).
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If Lauren were to get a higher score, it would raise the mean. The median would shift to halfway between 95 and 96. The score that makes the new mean be 95.5 is 99. The mean and median would be the same (again), but they wouldn't stay the same value they are now.
Likewise, if Lauren were to get a lower score, it would reduce the mean. The median would shift to halfway between 93 and 95. The score that makes the new mean be 94 is 87. The mean and median would be the same (again), but they wouldn't be the same value they are now.
If Lauren got 87, 95, or 99 on her test, her mean and median scores would be the same. They would only stay the same if she got a 95.
Which ordered pair is a solution to the system of equations?
Anthony has added a line of best fit to the scatterplot at right. Do you agree with where he put the line? Explain your reasoning
Solve for x. x/4 = 3/8 A) 2/3 B) 3/2 C) 3/32 D) 7/8