Which table represents the graph of a logarithmic function in the form y=log3x when b>1?
Answers
Answer:
The satisfied table of the given function[tex]y = log_{b} (x)[/tex]
x 1/8 1/4 1/2 1 2
y -3 -2 -1 0 1
Step-by-step explanation:
Explanation :-
Given logarithmic function [tex]y = log_{b} (x)[/tex] if b >1
Given first table
i)
put x = [tex]\frac{1}{8}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{8} )[/tex]
[tex]y = log_{2} (2^{-3} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3[/tex]
y = -3
ii)
put x = [tex]\frac{1}{4}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{4} )[/tex]
[tex]y = log_{2} (2^{-2} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2[/tex]
y = -2
iii)
put x = [tex]\frac{1}{2}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{2} )[/tex]
[tex]y = log_{2} (2^{-1} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1[/tex]
y = -1
iv)
put x = 1 given b > 1 so we can choose b = 2
[tex]y = log_{2} (1 )[/tex] = 0
y = 0
v)
put x = [tex]2[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (2 )[/tex]
y = 1
Final answer:-
The satisfied table of the given function
x 1/8 1/4 1/2 1 2
y -3 -2 -1 0 1
The first option is correct because that table of values represents the graph of a logarithmic function in the form [tex]y=\log_b x,b>1[/tex].
Given:
The lograrithmic function form is [tex]y=\log_b x,b>1[/tex].
To find:
The table of values that represents the graph of a logarithmic function in the form [tex]y=\log_b x,b>1[/tex].
Explanation:
It is given that [tex]b>1[/tex]. Let [tex]b=2[/tex], then
[tex]y=\log_2 x[/tex] ...(i)
Substitute [tex]x=\dfrac{1}{8}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{8}[/tex]
[tex]y=\log_2 \dfrac{1}{2^3}[/tex]
[tex]y=\log_2 2^{-3}[/tex]
[tex]y=-3[/tex]
Substitute [tex]x=\dfrac{1}{4}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{4}[/tex]
[tex]y=\log_2 \dfrac{1}{2^2}[/tex]
[tex]y=\log_2 2^{-2}[/tex]
[tex]y=-2[/tex]
Substitute [tex]x=\dfrac{1}{2}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{2}[/tex]
[tex]y=\log_2 2^{-1}[/tex]
[tex]y=-1[/tex]
Substitute [tex]x=1[/tex] in (i), we get
[tex]y=\log_2 1[/tex]
[tex]y=0[/tex]
Substitute [tex]x=2[/tex] in (i), we get
[tex]y=\log_2 2[/tex]
[tex]y=1[/tex]
The table of values is:
[tex]x[/tex] [tex]y[/tex]
[tex]\dfrac{1}{8}[/tex] [tex]-3[/tex]
[tex]\dfrac{1}{4}[/tex] [tex]-2[/tex]
[tex]\dfrac{1}{2}[/tex] [tex]-1[/tex]
[tex]1[/tex] [tex]0[/tex]
[tex]2[/tex] [tex]1[/tex]
Therefore, the first option is correct.
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Related Questions
what is the quotient (2x^2+12x+18) divided by (x+3)
CHOICES:
a. 2x+6
b. 2x-6
c. 2x+4
d. 2x-4, r=1
Answers
Answer:
A. 2x+6 is the correct answer
PLEASE HELP QUICKLY!!!!!!!
Penelope and Georgia are each saving money to take a vacation. Penelope started with $710 and saved $25 each week. Georgia opened her account with $570 and saved $45 each week. In how many weeks will they have the same amount of money? Group of answer choices 7 weeks 8 weeks 13 weeks 14 weeks
Answers
Answer:
8 weeks
Step-by-step explanation:
– 4 vc2, when v = –7 and c = –2
Answers
Answer:
[tex] \boxed{112} [/tex]
Step-by-step explanation:
[tex]Evaluate - 4v {c}^{2} \: where \: v= - 7 \: and \: c= - 2 : \\ = > - 4v {c}^{2} \\ = > - 4( - 7) {( - 2)}^{2} \\ \\ {( - 2)}^{2} = 4: \\ = > - 4( - 7)4 \\ \\ - 4( - 7) = 28: \\ = > 28 \times 4 = 112[/tex]
model -5 + (-6) on the number line
Answers
Answer:
-5+(-6 )= -11 so you would pinpoint -11 on the number line
Step-by-step explanation:
some teachers travelled to school by car the table shows the number of teachers in the cars a)what was the modal number of teachers in the cars b) what was the median number of teachers in the cars c) what was the mean number of teachers in the cars
Answers
Answer:
WE need the numbers
Step-by-step explanation:
a
Answer:
a)3
b)3
c)?
Step-by-step explanation:
Solve x - 3 < -1. Graph the solution.
Answers
Answer: x < 2
Explanation: To solve for x in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.
Since 3 is being subtracted from x, we add 3
to both sides of the inequality to get x < 2.
Before we graph, write your answer in set notation.
We can write this as {x: x < 2}.
It's important to understand what this means.
This means that any number less than 2 is a solution to this inequality.
I have graphed the inequality for you below.
Start with an open dot on +2.
We use an open dot because +2 is not included as a solution.
Then draw an arrow going to the left.
Here is a pattern made from sticks:
a) How many sticks would be in pattern number 6?
Answer: 32
b) How many sticks would be in pattern n?
Answer: ____
Answers
Example:
6x5= 30
30+2=32
Recursive formula of an arithmetic sequence is given by the expression,
[tex]T_n=a+(n-1)d[/tex]
Where, [tex]T_n=[/tex] nth term
[tex]a=[/tex] First term of the sequence
[tex]n=[/tex] Number of term
[tex]d=[/tex] Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
[tex]T_n=a+(n-1)d[/tex]
[tex]T_n=7+(n-1)5[/tex]
[tex]T_n=5n+2[/tex]
If [tex]n=6,[/tex]
[tex]T_n=7+(6-1)5[/tex]
[tex]T_n=7+25[/tex]
[tex]T_n=32[/tex]
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Solve this using the substitution method please!! Y=425x+1139/Y=495x
Answers
Identify the 9th term of the given geometric sequence. [/tex]1/3, −1/9, 1/27, −1/81, ....
HELP ASAP PLEASE!!!
Answers
Step-by-step explanation:
Before we find the ninth term, we need to find the common ratio. The common ratio in a geometric sequence is the number that every number after the first one is multiplied by. For example, in the sequence {2, 4, 8, 16, 32, ...}, the common ratio is 2.
Now, for our example, the numbers in the sequence alternate between negative and positive numbers. What does that tell us about the common ratio? Well, the common ratio has to be negative because the negative sign keeps alternating.
So we know the common ratio is negative. But what about the rest of the number? Well, we can see that the ratio has a 1 in the numerator because the numerator is the same throughout the sequence (aside from the alternating negative sign).
Now that we've narrowed down the possibilities to -1/x, let's figure out the denominator of the common ratio. The denominator changes from 3 to 9 to 27 to 81. Do you see a pattern there? Each denominator is 3 times the value of the previous denominator. The denominator of the common ratio, then, must be 3.
Ok. We have our common ratio, -1/3, but the question we still need to find the 9th term in the sequence. Well, we can write out the pattern until we get to the term we want. But what if you were trying to find the one hundredth or the one thousandth term? That would take a very long time to write out. Instead, we can take the first number in the sequence (1/3) and multiply it by the our common factor to the power of the remaining terms. As a formula, this looks like: [tex]a_{1} *f^{n-1} = a_{n}[/tex], where a is your first term, f is your common factor and n is the number of the term you are trying to find.
So, finally, we can solve the problem.
1/3 * (-1/3)⁸ = a₉
1/3 * 1/6561 = 1/19683
So the value of the ninth term of the given geometric sequence is 1/19683.
I hope you learned something and it wasn't too difficult to understand.
Answer:
^^ what he said xD
Step-by-step explanation:
It was snowing again and I smiled as I stared at the white flakes fluttering by my window. It was (capitalized the C)Christmas, and my day had been one of the best all year. First I (had removed) awakened in the morning to the sound of my brother (added the n to runing)running madly around the house, yelling that it was Christmas. Jumping out of bed, (capitalized the i that was there)I skipped happily down the stairs, with my brother at my heels, and made my way to the Christmas tree in the living room. My parents(apostrophe removed from between the t and s) groggily walked down the stairs to watch us open (up removed) our presents. My Mom sat down on the couch and dad plopped himself on the floor, grumbling something about coffee. I started opening my presents because, after all, its ladies first. Ripping open the wrapping paper, I stared down at my brand(removed dash)new pink boom box. It was beautiful!(question mark changed to exclamation) (capitalized e)Even more, it came with little, stick-on jewels to decorate the boom box. Mom and Dad finally got their coffee and we all took turns watching each other open presents. I got(get turned to got) many more presents that were absolutely amazing. (changed every one into one word)Everyone spends the rest of the day admiring their gifts and playing with their new toys. "I will remember this Christmas forever,"(added endnote) I thought. (capitalized s)Sighing contentedly, I finally turned away from the snow (removed the e from what was danceing)dancing outside the window and rejoined my family.
Please help! Correct answer only!
In a raffle, one ticket will win a $900 prize, and the remaining tickets will win nothing. There are 500 in the raffle. If you have a ticket, what is the expected payoff?
Answers
Answer:
" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80
Step-by-step explanation:
Take the probability of winning into consideration;
[tex]Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars[/tex]
Solution ; " Expected Payoff " ⇒ $ 1.80
As a member of the Game Shop rewards program, you get a 12% discount on purchases. All sales are subject to an 8% sales tax. Write functions to model the discount and the sales tax, then identify the rule for the composition function that calculates the final price you pay Games Shop.
Answers
Answer:
the answer is 1.041
Step-by-step explanation:
you will do.... 12*8/100
The function to model the amount after the discount is x - 0.12x
The function to model the amount after the sales tax is x + 0.08x.
The rule for the composition function calculates the final price you pay Games Shop is x - 0.04x.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
12% = discount on purchases.
8% = sales tax.
Now,
If the item cost $x
The function to model the amount after discount.
f(x) = x - (12/100)x = x - 0.12x
The function to model the amount after the sales tax.
g(x) = x + (8/100)x = x + 0.08x
Now,
The rule for the composition function calculates the final price you pay Games Shop.
= x + 0.08x - 0.12x
= x - 0.04x
Thus,
The function to model the amount after the discount is x - 0.12x
The function to model the amount after the sales tax is x + 0.08x.
The rule for the composition function calculates the final price you pay Games Shop is x - 0.04x.
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X^2-11=53 in the simplest form
Answers
Answer:
x=±8
Step-by-step explanation:
You add 11 on both sides
x^2=53+11
x^2 = 64 so
x=8 or x=-8
Mrs. Jackson made a line plot of the times it took students to complete a project.
She made a line plot to display the data.
Line plot named as ALTDCTime Spent Completing ProjectALTDC shows a number line from 0 to 5. The number line is divided into 10 equal parts. 1 dot on 1, 2 dots on one and half, 4 dots on 2, 3 dots on two and half, 2 dots on three and half, 1 dot on 4 and 1 dot on four and half is given.
Part A
What is the outlier in the data set?
A. 1
B. 2
C. 3
D. There is no outlier.
Part B
Which explains your reasoning in Part A?
A.
There is no value that is very different from the other values.
B.
This is the most common value in the data set.
C.
This value is very different from the other values.
D.
There are no data values above this number.
Answers
Answer: D
Step-by-step explanation: D
Simplify
4a x 6a
8a?
Answers
Answer:
[tex]=24a^2[/tex]
Step-by-step explanation:
[tex]4a\cdot \:6a=24a^2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:6=24\\=24aa\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\aa=\:a^{1+1}\\=24a^{1+1}\\=24a^2[/tex]
Answer:
Simply multiply across.
since they both have the same base(a),add the powers ie.(1+1)=2.
Hence 4a×6a=24a²
Zara ate 75 almonds this week, or 150% as many as she ate last week. How many almonds did Zara eat last week?
Answers
Zara ate 50 almonds last week which is 150% as many as she ate last week.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that Zara ate 75 almonds this week, or 150% as many as she ate last week.
Let's assume that she eat x almonds last week
As per the given question, we can write the percentage would be as
⇒ 150% of x = 75
⇒ (150/100) x = 75
Apply the cross-multiplication operation,
⇒ 150x = 7500
Divided by 150 into both sides of the above equation,
⇒ x = 7500/150
⇒ x = 50
Therefore, she eat 50 almonds last week.
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Select all the numbers that are in the range of the function f(x)=3-0.5x if the domain is {1,3,4}
Answers
Answer:
1
Step-by-step explanation:
Answer:
1,1.5,2.5
Step-by-step explanation:
f(x) = 3 - .5x
The domain is 1,3,4 so theses are the only inputs
f(1) = 3 - .5 = 2.5
f(3) = 3 - .5(3) = 3- 1.5 = 1.5
f(4) = 3 - .5(4) = 3-2 =1
The only outputs are 1,1.5,2.5
plzz answer this question i will mark brainliest
Answers
Answer:
Step-by-step explanation:
line 1.
y=3
line 2.
x=-1.2
line 3.
x=3
line 4.
y=-2.6
length=3-(-1.2)=3+1.2=4.2
width=3-(-3)=3+3=6
area=4.2×6=25.2
Can someone please please help me
Answers
Please help!!!
a boat measures 40m long and 10m wide.
a scale model of the boat measures 50cm long.
what is the scale factor of the model?
Answers
Answer:
1 : 80
Step-by-step explanation:
So you want to check Length of model : Length of real boat
50 cm : 40 m
But since the units don't match, make 40 m into 4000 cm
50 cm : 4000 cm
Divide both sides by 50 and you get
1 : 80
I WILL MARK YOU BRAINLIEST!!!! HELP PLZZ
Answers
Answer:
exponential growth
Step-by-step explanation:
f(x) = 2 * 2^x
This is in the form
y = a * b^x where a is the initial value and b is the growth rate or decay rate
b > 1 so it is growth
This is the exponential form
y = mx+b is the linear form
-7 written as a fraction is _____
Answers
Explanation: -7/1 is an improper fraction, meaning it’ll just equal to seven. Whenever there’s a one as a denominator, remember, in this case, it’s just -7.
One circle has a diameter of 10 inches. A second circle has a diameter that is twice the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?
Answers
Answer:
[tex]78.54:314.16[/tex]
Step-by-step explanation:
First circle area with diameter 10 inches =
[tex]\pi r^2[/tex]
[tex]\pi \times 5^2[/tex]
[tex]=78.53981[/tex]
Second circle area with diameter 20 inches =
[tex]\pi r^2[/tex]
[tex]\pi \times 10^2[/tex]
[tex]=314.159265[/tex]
[tex]78.53981:314.159265[/tex]
Answer:
78.5 : 314.2
Step-by-step explanation:
Diameter of the first Circle = 10 inches
Diameter of the second Circle = 2(10) [TWICE] = 20 inches
So,
Area of the first circle:
Radius = 5 inches
Area = πr²
A = (3.14)(5)²
A = 78.5 inches²
Area of the second circle:
Radius = 10 inches
Area = πr²
Area = (3.14)(10)²
Area = 314. 2 inches
Now the ratio of the area of smaller circle to the larger circle is
78.5 : 314.2
How many square inches are in 60 ft.
Answers
Find the slope of the line that passes through (2, 12) and (5, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
The right answer is -2/3
please see the attached picture for full solution
Hope it helps
Answer:
[tex]slope = - \frac{2}{3} [/tex]
Step-by-step explanation:
[tex](2 \: \: \: ,\: \: \: 12) = > (x1 \: \: \: , \: \: x2) \\ (5 \: \: \: ,\: \: \: 10) = > (y1 \: \: \: , \: \: \: y2)[/tex]
[tex]slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{12 - 10}{2 - 5} \\ = \frac{2}{ - 3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Una fábrica mando a hacer recipientes que están formando por un cilindro y un cono unidos por la base, el volumen es de 41.86cm3, si el radio es de 2cm ¿cual es el largo del recipiente?
Answers
Answer: Suponiendo que la altura del cono y la del cilindro son iguales.
[tex]\pi r^2\times h+\frac{1}{3} \pi r^2\times h=41.86\\\pi (2)^2\times h+\frac{1}{3} \pi (2)^2\times h=41.86\\\\Solving\;for\;h\\h=2.49833[/tex]
How old am I if 2 times my age increased by 244 is 400?
Answers
Answer:
78
Step-by-step explanation:
400-244=156
156/2=78
Answer:
78 years old
Step-by-step explanation:
400 − 2 x = 244
400 − 244 = 2 x
156 = 2 x
so the answer would be 78 years old...
Hope that was helpful.Thank you!!!
Megan has three candles of the same length to provide light. Candle A burns for exactly 72 minutes. Candle Burns twice as fast as Candle A. Candle C burns 3 times as fast as candle B. What is the greatest total number of minutes of light all three candles can provide?
Answers
Answer:
Candle B: 36 minutes
Candle C: 12 minutes
Step-by-step explanation:
Since Candle A burns for 72, and Candle B burns twice as fast, we can divide the 72 by 2 in order to get the time it burns. We will then see that Candle B burns for 36 minutes.
Candle C burns 3 times as fast as candle B so we can divide the 36 minutes it takes for candle B to burn by 3 to get how long it takes Candle C to burn. We then see that it takes 12 minutes for candle C to burn.
Hope this helps!
What is the 5th term of the linear sequence below?
−
-5,-2,1,4,7,
Answers
Answer:
The sequence has '+3' each time, so the next will be 10
Step-by-step explanation:
it is 10 cuz it goes from -5 adding 3
how many 1/2’s are in 5 and 3/4’s
Answers
Answer:
11 and a 1/2
Step-by-step explanation:
I'm not sure if this is correct but here is my reasoning....
per every 1 there are two 1/2's so multiply 5x2 to get 10.
next, 1/2 is equivelent to 2/4 so subtract 3/4-2/4 (adding another 1/2 to our previous answer of 10 to get 11) and you have 1/4 left.
lastly, since 1/4 is half of 1/2, add 1/2 to 11 to get the final answer of 11 and a 1/2.
there are 11 and a half 1/2's in 5 and 3/4.
multiply the polynomials (4x^2+3x+7(8x-5)
A. 32x^3-44^2-71x-35
B. 32x^3-4x^2-41x+35
C. 32x^3+4x^2+41x-35
D. 32x^3+4x^2+41x+35
Answers
Answer:
32x^3 + 4x^2 + 41x - 35
Step-by-step explanation:
Multiply each of the terms in bracket 1 with those in bracket 2.
4x^2 x 8x = 32x^3
4x^2 x -5 = -20x^2
3x x 8x = 24x^2
3x x -5 = - 15x
7 x 8x = 56x
7 x -5 = -35
Now, put them together and simplify:
32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35
After simplifying:
32x^3 + 4x^2 + 41x - 35
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