Question:
Approximate log base b of x, log_b(x).
Of course x can't be negative, and b > 1.
Answer:
f(x) = (-1/x + 1) / (-1/b + 1)
Step-by-step explanation:
log(1) is zero for any base.
log is strictly increasing.
log_b(b) = 1
As x descends to zero, log(x) diverges to -infinity
Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.
Find a such that f(b) = 1
1 = f(b) = (-1/b + 1)/a
a = (-1/b + 1)
Substitute for a:
f(x) = (-1/x + 1) / (-1/b + 1)
f(1) = 0
f(b) = (-1/b + 1) / (-1/b + 1) = 1
Tom and his brothers caught 100 fish on a week-long fishing trip. the total weight of the fish was 239 pounds. part 1 out of 3 enter the expression that will find the weight of one fish. assume that the weight of each fish is the same. the expression that gives the weight of one fish is ÷ .
Answer:
Expression that gives weight of 1 fish: [tex]\frac{239}{100}[/tex].
The weight of 1 fish is 2.39 pounds.
Step-by-step explanation:
We have been given that Tom and his brothers caught 100 fish on a week-long fishing trip. The total weight of the fish was 239 pounds.
Assuming that the weight of each fish is the same, we can find weight of 1 fish by dividing the total weight of fish by total number of caught fish.
[tex]\text{The weight of 1 fish}=\frac{239}{100}[/tex]
Therefore, the expression that gives the weight of 1 fish is [tex]\frac{239}{100}[/tex].
Upon dividing 239 by 100 we will get,
[tex]\text{The weight of 1 fish}=2.39[/tex]
Therefore, the weight of 1 fish is 2.39 pounds.
plsplsplsplsplsplspls help!!!!!!!!
Answer:
1. My estamite, close to -1
2. 1.5
3. Remote interior angles
4. 84
5. 60 degrees
Step-by-step explanation:
The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.
How does the average rate of change between Years 1 and 5 compare to the average rate of change between Years 11 and 15?
The average rate of change is about 13
as fast in Years 1 to 5.
The average rate of change is about 3 times as fast in Years 1 to 5.
The average rate of change is about 12
as fast in Years 1 to 5.
The average rate of change is 2 times as fast in Years 1 to 5.
Answer: (B) 3 times as fast
Step-by-step explanation:
rate of change is the "slope" between the given interval.
f(x) = 125(.9)ˣ
f(1) = 125(.9)¹
= 112.5
f(5) = 125(.9)⁵
= 73.8
[tex]\dfrac{f(5) - f(1)}{5 - 1} = \dfrac{73.8-112.5}{5-1} = -\dfrac{38.7}{4} = -9.675[/tex]
********************
f(11) = 125(.9)¹¹
= 39.2
f(15) = 125(.9)¹⁵
= 25.7
[tex]\dfrac{f(15) - f(11)}{15 - 11} = \dfrac{39.2-25.7}{15-11} = -\dfrac{13.5}{4} = -3.375[/tex]
********************
The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.
PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER
What is the equation of the line represented by the table of values below?
A. Y = 3x - 2
B. Y = -3x + 2
C. Y = 3x + 2
D. Y = -3x - 2
Answer:
Step-by-step explanation:
I NEED HELP NOW WHAT IS THE ANSWER PLZ HELP 40 POINTS
Answer:
B 8 n^18
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length of a square
64 n^36 = s^2
Take the square root of each side
sqrt(64 n^36 )= sqrt(s^2)
Sqrt(ab) = sqrt(a) sqrt(b)
sqrt(64) sqrt(n^36) = s
8 n^18 =s
Simplify: (7+2a)·3–20 =
Final answer:
The expression (7+2a)·3−20 simplifies to 1 + 6a. You distribute the 3 to the terms inside the parentheses and then subtract 20 from 21 to combine like terms.
Explanation:
To simplify the algebraic expression (7+2a)·3−20, we start by distributing the 3 to both terms inside the parentheses.
7·3 + 2a·3 − 20 = 21 + 6a − 20
Next, we eliminate terms wherever possible by combining like terms. We subtract 20 from 21, which gives us:
21 − 20 + 6a = 1 + 6a
So, the expression simplifies to:
1 + 6a
We can check if this is reasonable by substituting a value for 'a'. If 'a' is 3, for example, then:
1 + 6×3 = 1 + 18 = 19
Which is the result we would expect after simplifying the original expression with 'a' being 3.
15 Points!!!!!!!!! Mike attends basketball practice sessions every week. The coach assesses his progress at the end of each session by asking him to attempt 10 free throws. Prior to starting the sessions, Mike missed 6 out of 10 free throws. At the end of the first practice session, Mike missed 5 of his 10 free throws. At the end of the second session, he missed 4 of his 10 free throws. This constant decrease in the number of missed throws continues until Mike does not miss any of his 10 free throws at the end of a practice session. If the number of free throws Mike misses is dependent on the number of practice sessions he has attended, select the appropriate domain that describes this relationship.
A. D = [0, 10]
B. D = {0, 1, 2, 3, 4, 5, 6}
C. D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
D. D = [0, 6]
Answer:
In the case of Mike's free throws, the Domain that describes this relationship can be either B or D.
Step-by-step explanation:
In the case of a relationship that represents a 'constant' increase or decrease, we know that there will be an independent and dependent variable. The independent variable is our 'x' value and the dependent variable is our 'y' value. In this case, they tell us that the number of free throws Mike misses is dependent on the number of practices sessions he has attended. Therefor, 'x' would represent the number of practices and 'y' would represent the number of missed free throws. At the start, before practices or an 'x' value of 0, Mike, misses 6 free throws. He continues to decrease his missed throws by for each practice, until the sixth practice where he misses none. So, the 'x' values would be 0, 1, 2, 3, 4, 5, and 6. This can be shown by letter 'B', which includes all numbers, or letter 'D', which represents all numbers between, and including 0 and 6.
Answer:
I'd choose B since it includes all of the numbers.
Step-by-step explanation:
What is the slope of the line through (-7,-2)(−7,−2) and (-6,7)(−6,7)? Choose 1 answer: Choose 1 answer: (Choice A) A -\dfrac19− 9 1 (Choice B) B -9−9 (Choice C) C 99 (Choice D) D \dfrac19 9 1
[tex]\bf (\stackrel{x_1}{-7}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{7-(-2)}{-6-(-7)}\implies \cfrac{7+2}{-6+7}\implies \cfrac{9}{1}\implies 9[/tex]
PLEASE SOMEONE HELP NOW 30 points!!!!!!!!!!!
The answer to this question is -6.
To solve this problem, we need to understand certain properties about exponents. To begin, let's remember that when we raise a number, the base, in this case y, to a certain power that is then raised to another power, we multiply these two exponents together when evaluating. Another important concept that is vital to understanding this problem is that negative exponents are positive exponents in the denominator of fractions. For example, y^-4 = 1/y^4.
Using this knowledge, we know that b * 4 must equal 24 (because raising a power to another power implies multiplication). Therefore, we know that the magnitude of the variable b must be six. However, we must also recognize that y^24 is in the denominator of the answer, which means that one of the exponents of the variable y must be negative. Since the exponent 4 is not negative, the exponent of b, or 6, must be.
Therefore, your answer is -6.
If you do not understand my explanation, feel free to ask me any clarifying questions.
Hope this helps!
Answer:
-6
Step-by-step explanation:
(y^b)^4 = 1/ (y^24)
We know (a^b)^c = a^(b*c)
and 1/ y^a = y ^ -a
y ^(4b) = y ^ (-24)
When we have the same bases, the exponents must be the same
4b = -24
Divide by 4
4b/4 = -24/4
b =-6
Given: f(x) = x2 + 7x + 10. From the Rational Root Theorem, we know p=10 and q=1. List all potential roots using the ratio p/q.
Answer:
There are 8 roots
1,2,5,10,-1,-2,-5,-10
Step-by-step explanation:
The rational root theorem says take all the factors of p over all the factors of q
p = 1,2,5,10
q = 1
roots ± 1,2,5,10
--------------------
1
roots ±1, ±2, ±5,±10
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
Its the graph at the bottom right.
Step-by-step explanation:
Adding f(x) and g(x) we get
-x^2 + 3x + 5 + x^2 + 2x
= 5x + 5 = (f+ g)(x)
This has a slope of 5 and a y-intercept of 5, so its bottom right graph.
(f + g)(x) is a composite function of f(x) and g(x), and it is represented by graph (c)
The functions are given as:
[tex]\mathbf{f(x) = -x^2 + 3x + 5}[/tex]
[tex]\mathbf{g(x) = x^2 + 2x}[/tex]
To calculate (f + g)(x), we make use of the following formula
[tex]\mathbf{(f + g)(x) = f(x) + g(x)}[/tex]
So, we have:
[tex]\mathbf{(f + g)(x) = -x^2 + 3x + 5 + x^2 + 2x}[/tex]
Collect like terms
[tex]\mathbf{(f + g)(x) = x^2-x^2 + 3x+ 2x + 5 }[/tex]
Evaluate the like terms
[tex]\mathbf{(f + g)(x) = 5x + 5}[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where m represents the slope, and c represents the y-intercept
So, by comparison:
[tex]\mathbf{m = 5}[/tex]
[tex]\mathbf{c = 5}[/tex]
The graph that has a slope of 5, and a y-intercept of 5 is graph (c)
Hence, graph (c) represents (f + g)(x)
Read more about composite functions at:
https://brainly.com/question/20379727
What is the radical expression that is equivalent to the expression
(35)^1/4?
Enter your answer as a radical.
For example, if your answer is
3√14,
enter it like this: cuberoot(14)
Hello from MrBillDoesMath!
Answer:
fourthroot(35)
Discussion:
The question is a bit unclear as to the desired answer.... but here goes!
(35)^1/4 is the fourth root of 35, that is, symbolically, fourthroot(35).
Note the fourth root of a number is the same as the square root of the square root of the number.
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
Simplify -4m + 5n - 2 - 3m + 3n + 7.
A) -7m + 8n - 9
B) -7m + 8n + 5
C) -7m2 + 8n2 - 9
D) -m + 8n - 9
-4m + 5n - 2 - 3m + 3n + 7 combine like terms
= (-4m - 3m) + (5n + 3n) + (-2 + 7)
= -7m + 8n + 5 → B)I have $4.85 in my pocket what fraction in simplest form represents the amount of money I have in my pocket
Answer:97/20
Step-by-step explanation:
There are 8 brooms and 6 mops in a janitors closest. What is the ratio of the number of mops to the number of brooms
Answer:
The ratio of mops to brooms is 3:4
Step-by-step explanation:
To find this, we first need to simply plug in the numbers.
Mops:Brooms
6:8
Now we can simplify by noticing that both are divisible by 2
3:4
Answer:
IT SAID 3/7 FOR ME!
HDJKSHFNDSKLFDSFDS
Step-by-step explanation:
What is the equation of the line that contains the point (3,-1) and has the same slope as the the line y=1/3x+5
Answer:
y = 1/3x - 2
Step-by-step explanation:
Line y = 1/3x + 5 has slope 1/3, so the line we are looking for also has slope 1/3.
y = 1/3x + b
We know a point, so we plug in the values of x and y, and we solve for b.
y = 1/3x + b
-1 = (1/3)(3) + b
-1 = 1 + b
b = -2
Now that we know b, the equation is:
y = 1/3x - 2
What is the quotient (3x2 + 4x − 15) ÷ (x + 3)?
Answer: (3x-5)
Step-by-step explanation:
first we set it up x+3[tex]\sqrt{3x^2 +4x-15}[/tex]
we want to get rid of 3x^2 first so, x*3x= 3x^2
then we subtract x+3[tex]\sqrt{3x^2 +4x-15}[/tex]
distribute :3x*3=9x - (3x^2 +9x)
0 -5x
now we want to get rid of -5x, we use -5
-5(x+3)=-5x-15 x+3[tex]\sqrt{-5x-15}[/tex]
-(-5x-15)
0, so reminder of 0
Suppose that Spain has a workforce of 22.85 million people, and that the average salary for each person is €24,200 annually. Spain has imports of €290.85 billion and exports of €200.13 billion. If the Spanish government levies a 7% tariff on exports, an 18% tariff on imports, and a 21% income tax, how will the revenue gained from tariffs and the revenue gained from income tax compare?
D. The government will earn €49.7616 billion more from income tax than from tariffs.
Step-by-step explanation: According to E2020
Answer:
The answer is D: The government will earn €49.7616 billion more from income tax than from tariffs.
Step-by-step explanation:
Rearrange the formula V = 1 3 πr2h for h. A) h = 3V πr2 B) h = V 3πr2 C) h = 3πr2 V D) h = πr2 3V
Answer:
A) h = 3V/ πr^2
Step-by-step explanation:
V = 1/ 3 πr^2h
Multiply each side by 3
3V = 3*1/ 3 πr^2h
3V = πr^2h
Divide each side by πr^2 to isolate h
3V /πr^2 = πr^2/πr^2 h
3V /πr^2 = h
Please answer this question !! 98 points and brainliest!!
Answer:
x > -3
Step-by-step explanation:
5x+ 7 > 2(x-1)
Distribute the 2 on each side
5x+7 > 2x -2*1
5x+7 > 2x-2
Subtract 2x from each side
5x-2x +7 > 2x-2x-2
3x + 7>-2
Subtract 7 from each side
3x+7-7>-2-7
3x>-9
Divide by 3 on each side
3x/3 >-9/3
x > -3
Which equation represents a proportional situation?
y = – 3x + 4
y = 3x – 12
y = –2x + 23
y = 9x
Answer:
option D is correct.
y=9x represents a proportional situation
Step-by-step explanation:
If two quantities are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other i.e,
y = |k|x ; where |k| is constant proportionality.
By definition :
y =9x where k =9 is constant , represents a proportional relationship.
Answer:
The correct answer option is y = 9x.
Step-by-step explanation:
From the given equations as the possible answer options, y = 9x is the correct answer which represents a proportional situation.
Two values (variables in this case) are said to be proportional if they change in a way such that there is a constant multiple multiplied to one of the values.
Here, in the equation y = 9x, y and x are the two variable and 9 is the constant multiple.
You need about one and a half hours to set up a computer workstation. At this rate how many hours should it take you to set up seven of these workstations?
Answer: About 10.5 hours
Which scenario would make someone vulnerable to identity theft? A. including a Social Security number on an income tax form B. missing monthly payments on a car loan for three months C. opening a credit card account to purchase a household appliance D. using a public library computer to access confidential bank information
Answer:
The correct answer is option D
Step-by-step explanation:
The use of personal information though a public computer can make personal information prone to adulteration and misuse as identity theft
When a Social Security number is mentioned on an income tax form it remains private and does not get exposed. Like wise missing monthly payments for a car loan has no relevance to data stealing. In case of opening a credit card account, the information provided are secured with the availed banking service
Answer:
Randell uses a computer at a public library to view his bank account online.
Step-by-step explanation:
Using a publicly accessible computer to view sensitive information can lead to that information being divulged to others using the same computer.
solve this identifying holes, vertical asymptotes, and horizontal asymptotes for
f(x)=x²+7x+12/-x²-3x+4
[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{Vertical asymptotes:}\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\\boxed{x=-4\ and\ x=1}\\\\\text{Horizontal asymptotes:}[/tex]
[tex]\lim\limits_{x\to\pm\infty}\dfrac{x^2+7x+12}{-x^2-3x+4}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\dfrac{7}{x}+\dfrac{12}{x^2}\right)}{x^2\left(-1-\dfrac{3}{x}+\dfrac{4}{x^2}\right)}=\dfrac{1}{-1}=-1\\\\\boxed{y=-1}[/tex]
Two less than three– fourths of a number is ten. What is the number?
A. 10 2/3
B. 13 1/3
C. 15 1/3
D. 16
Answer:
Option D. 16
Step-by-step explanation:
Let
x ----> the number
we know that
The linear equation that represent this problem is equal to
[tex]\frac{3}{4}x-2=10[/tex]
Solve for x
Multiply by 4 both sides
[tex](4)*\frac{3}{4}x-2*4=10*4[/tex]
[tex]3x-8=40[/tex]
Adds 8 both sides
[tex]3x-8+8=40+8[/tex]
[tex]3x=48[/tex]
Divide by 3 both sides
[tex]3x/3=48/3[/tex]
[tex]x=16[/tex]
therefore
The number is 16
A new sports store recently opened downtown that specializes in baseball cards. Delmar has over 200 baseball cards in his collection and plans to see how much money he can get for some of his cards. After looking through Delmar's cards, the dealer tells Delmar that 15 of the cards can be sold for $23.50 each, and 27 of the cards can be sold for $32.50 each. The rest of the cards can be sold somewhere in the range of $3 to $10 each. If Delmar sells all of the cards worth $23.50 and $32.50, how much money would Delmar receive?
Answer: 15 of the cards can be sold for $23.50 each, and 27 of the cards can be sold for $32.50 each. This is all he wants to sell so the answer would be (23.5 x 15) + (27 x 32.5)
$1230
Please mark brainliest.
Step-by-step explanation:
Yuki bought a pound of confetti for \$12$12. What is the price, in dollars, per ounce of confetti? There are 1616 ounces in 11 pound.
Answer:
$0.75
Step-by-step explanation:
We have been given that Yuki bought a pound of confetti for $12.
To find the price of per ounce of confetti, we will divide the total price of 1 pound confetti by number of ounces in 1 pound.
1 pound = 16 ounces.
Let us divide 12 by 16 to find the price of confetti per ounce.
[tex]\text{Price of per ounce confetti}=\frac{12}{16}[/tex]
[tex]\text{Price of per ounce confetti}=\frac{3}{4}[/tex]
[tex]\text{Price of per ounce confetti}=0.75[/tex]
Therefore, the price of per ounce confetti is $0.75.
please help on this one?
Answer:
D
Step-by-step explanation:
The factorization of these is ...
A: F(x) = (x -3)(x +3)² . . . . 3 real roots, one with multiplicity 2.
B: F(x) = (x -3)³ . . . . 3 real roots, one with multiplicity 3.
C: F(x) = (x +3)³ . . . . 3 real roots, one with multiplicity 3.
D: F(x) = (x +3)(x² +9) . . . . 1 real root, 2 complex roots.
_____
Note
A graphing calculator is helpful in factoring these. The quadratic factor of option D was found using synthetic division, after the real root was found using the graphing calculator.
Which is a coordinate rule for the translation of f(x) to g(x)?
(x, y) → (x – 4, y)
(x, y) → (x, y – 4)
(x, y) → (x, y + 4)
(x, y) → (x + 4, y)
The coordinate rule for a translation tells how to move each point in f(x) to create g(x). Different rules correspond to different shifts: left, down, up, or right by 4 units.
Explanation:The coordinate rule for a translation indicates how to move each point in a graph to create a new function. For example, a rule of '(x, y) → (x – 4, y)' would indicate that every point of the function f(x) would move 4 units to the left to create the new function g(x). Similarly, the coordinate rule '(x, y) → (x, y – 4)' would move every point 4 units down, '(x, y) → (x, y + 4)' would move every point 4 units up, and '(x, y) → (x + 4, y)' moves every point 4 units to the right. Depending on which direction you want to move the function f(x) in to create g(x), any of these coordinate rules could be valid.
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A coordinate rule for a transformation tells us how to move each point in the plane. The four provided rules indicate left, down, up, and right translations respectively. The specific translation from f(x) to g(x) would depend on their exact positions.
Explanation:The question is asking about the coordinate rule for the translation of one function to another, specifically f(x) to g(x) in a two-dimensional plane. A coordinate rule for a transformation tells us how to move each point in the plane.
For example, the rule (x, y) → (x – 4, y) means that we translate each point 4 units to the left. The rule (x, y) → (x, y – 4) moves each point 4 units down. (x, y) → (x, y + 4) moves each point 4 units up, and (x, y) → (x + 4, y) moves each point 4 units to the right.
The exact translation from f(x) to g(x) would depend on the specific position and movements of these functions on the coordinate grid, which is not provided in the question.
Learn more about Coordinate Transformation here:https://brainly.com/question/37212834
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MATH HELP PLEASE I WILL GIVE 82 POINTS
Angle FEG = 90 degrees based on the square marker symbol in the diagram.
Angle ABE = 90 degrees as well because BEF is 90 (supplementary to FEG) and because ABE and BEF are alternate interior angles
Angle D is 40 degrees. Why? because triangle DEG is a reflection of triangle FEG (this can be proven using SAS)
Angle EGF is 50 degrees. With any right triangle, the acute angles add to 90, so 40+50 = 90, or put another way 90-40 = 50