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
A cone has a height of 7ft and a radius of 4ft which equation can find the volume of the cone v=1.3 (7.2)
Answers
Answer:
The volume of a cone is:
V=(hπr^2)/3, where h=height and r=radius
V=(7π4^2)/3
V=112π/3 ft^3
V≈117.29 ft^3 (to nearest hundredth of a cubic foot)
Step-by-step explanation:
What does this problem equal?
(h-k)(3) =
Answers
Answer:
3h−3k
Step-by-step explanation:
hope this helped
Expand and simplify . 4a(2+3b)-5b(4a-10). PLEASE HELP. BEST ANSWER RECEIVES A BRIANLIEST
Answers
Answer:
12a+62b
Step-by-step explanation:
4a(2+3b)-5b(4a-10)
opening brackets
=8a+12b-20a+50b
=8a-20a+12b+50b
=-12a+62b
expand_and_simplify
(
4
⋅
a
⋅
(
2
+
3
⋅
b
)
-
5
⋅
b
⋅
(
4
⋅
a
-
10
)
.
)
=−5⋅b⋅(4⋅−10).+8⋅+12⋅⋅
=
-
5
⋅
b
⋅
(
4
⋅
a
-
10
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.
+
8
⋅
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⋅
b
A pharmacy claims that the average medication costs $32, but it could differ by as much as $8. Write an absolute value inequality to determine the range of medication costs at this pharmacy.
Answers
Answer:
| 32 - c | [tex]\leq[/tex] 8
Step-by-step explanation:
c represents the cost of the medication
This absolute value inequality makes sure that the difference is less than or equal to 8, whether or not the medication is $8 more or less than the average.
Answer:[x - 32] <(with line under it) 8
Step-by-step explanation:
pls help plsplsplsplsplsplspspslpssplsplsplspslpslpslsplspsps
Answers
Answer:
Option A, Option C, Option E
Step-by-step explanation:
The area of a kite can be identified through 1 / 2 of the multiplication of each diagonal. The first diagonal is equivalent to the addition of 50 cm and 10 cm, while the second is of length 20 cm + 20 cm.
[tex]1 / 2 * ( 50 + 10 ) * ( 20 + 20 ),\\1 / 2 * ( 60 ) * ( 40 ),\\( 30 ) * ( 40 ),\\\\Area of Kite = 1200 square cm[/tex]
Consider the first option. If we take a look at the bit 2 * ( 1 / 2 * 20 * 50 ) the 2 and 1 /2 cancel each other out, leaving you with 20 * 50 = 1000 . Respectively in the expression 2 * ( 1 / 2 * 20 * 10 ) the 2 and 1 / 2 cancel each other out, leaving you with 20 * 10 = 200;
[tex]1000 + 200 = 1200 square cm,\\Option A - Correct![/tex]
The second option considers the expression 2 * ( 1 / 2 * 20 * 60 ). Again, the 2 and 1 / 2 cancel each other out, leaving you with 20 * 60;
[tex]20 * 60 = 1200 square cm,\\Option B - Correct![/tex]
Option C is a similar version of option a, besides the fact that the 1 / 2 doesn't exist. Thus, Option C is incorrect!
Option D is a similar version of option a as well, but as the 2 doesn't exist, it is incorrect!
This last option, option E is taken as 1 / 2 of the multiplication of the diagonals, and thus is correct!
[tex]1 / 2 * ( 40 * 60 ),\\1 / 2 * ( 2400 ),\\1200 square cm\\\\Correct![/tex]
I need help im lazy :)
Answers
Answer:
[tex]x=-8[/tex]
Step-by-step explanation:
→All you need to do for this equation is, divide both sides by -300. You do this to get "x," by itself:
[tex]2400=-300x[/tex]
[tex]\frac{2400}{-300} =\frac{-300x}{-300}[/tex]
[tex]-8 = x[/tex]
How do you solve the inequality 2x-3<-52x−3<−5
Answers
Answer:
Idk it really hard to do
Please help ASAP! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answers
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
how old am I?
16
17
4
Answers
Answer:
16
Step-by-step explanation:
(if u are 4, i'm gonna scream)
Answer:
16
Step-by-step explanation:
If you are 4, just no.
A white tail deer can sprint at speeds up to 30 mph American bison can run at speeds up to 3520 ft./min. which animal is faster and by how many miles per hour
Answers
Answer:
Bison, by 10 mph
Step-by-step explanation:
Convert ft/min to mi/hr.
3520 ft/min × (1 mi / 5280 ft) × (60 min / hr) = 40 mi/hr
The bison is faster than the deer by 10 mph.
What common fraction must be added to 1/6 to equal 1/2(Working please)
Answers
Why?
Because 1/6 + 2/6 = 3/6, and 3/6 = 1/2
Hope this Helps!
Answer:
1/3
Step-by-step explanation:
let the common fraction be x
we get,
1/6 + x = 1/2
x = 1/2 - 1/6
x = 6 - 2/12
x = 4/12
x = 1/3
VERIFICATION:1/6 + x = 1/2
1/6 + 1/3 = 1/2
3 + 6/18 = 1/2
9/18 = 1/2
1/2 = 1/2
Which point is in the solution set of the system of inequalities
shown in the accompanying graph?
A. (0,4)
B. (2,4)
C. (-4,1)
D. (4,-1)
Answers
Answer: Option c.
Step-by-step explanation:
The dotted line means that the points in the line do not belong to the system, while the other line has all the points on the line.
Now, the point we are looking for must be a solution for both inequalities, so it must be in the region of the graph that is double shaded. (this would be the area at the left)
You now can take each point and see where it is located in the graph, if it is inside the double shaded area, then it is the correct answer.
Now, you will see that the only point that lies inside the double shaded area is the point (-4,1), so the correct option is c.
The point (-4, 1) is in the solution set of the system of inequalities.
An inequality shows the non equal comparison between two numbers or variables.
Given the inequalities as shown in the graph, the solution set of the inequalities is the point that lies on the dark shaded portion.
The dark shaded portion is the solution of the inequality.
From the graph the point (-4, 1) lies on the dark shaded portion.
Therefore the point (-4, 1) is in the solution set of the system of inequalities.
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Kathleen bought 8.3 ounces of walnuts. The next day, she used 1.7 ounces of them in a recipe. How many ounces does she have left?
Answers
Answer:
6.6 ounces left
Step-by-step explanation:
Take the amount she had and subtract the amount she used
8.3-1.7 =6.6
Answer:
She has 6.6 ounces left.
1/3 of the members Voted know what fraction of the members did not know
Answers
Answer:
2/3 did not vote no
Step-by-step explanation:
1/3 voted no
The total is 1
1 - 1/3
3/3 -1/3
2/3 did not vote no
The following data shows prices of meal options at Bob's Burgers. Bob
wants to construct a histogram from this graph. Prices of Meal Options at
Bob's Burgers: $6, $7, $7, $8,$9,$10, $10, $11, $11, $12,$12, $13, $13, $13,
$13,$14, $14, $14, $15, $15, $15, $15, $16, $16, $17. How many meals could
belong in the interval $10.99 - $13.99? *
Answers
Answer:
Step-by-step explanation:
The number of meals that could
belong in the interval $10.99 - $13.99 is represents the frequency of that interval. The interval is also called the class width. Since there are no decimals, the meals must be greater than or equal to $11 and lesser than $14. Looking at the data, the meals that fall within the interval are
$11, $11, $12,$12, $13, $13, $13,$13
The frequency is 8
Therefore, 8 meals could
belong in the interval $10.99 - $13.99
I need help ASAP I shall give brainlyist (idk how to spell)
Answers
Explanation: The formula for the volume of a cylinder is pi (3.14 here) * r^2 * 3
Thus, we have 235.5=3.14r^2*3
Dividing both sides by 3 leaves us with 78.5=3.14r^2
Dividing both sides by 3.14 gives us 25=r^2
To solve the equation, we take the sqrt of both sides and we find that r is 5 cm.
Answer:
[tex]5cm[/tex]
Step-by-step explanation:
[tex]r=\sqrt{\frac{V}{\pi h} } \\=\sqrt{\frac{225.5}{\pi *3} } \\=5cm[/tex]
could someone please help with these three? I got a few minutes left and I'm clueless IM IN NEED OF HELP!!
Answers
Answer:
Student 1 has the correct answer
Student 2 started of OK but then divides the number of white marbles by the number of non-white marbles, which is incorrect.
Student 3 reports a probability larger than 1 which is impossible. Also the answer is not in percentages.
Translate this sentence into an equation.
The product of Victor's age 7 and is 84 .
Use the variable v to represent Victor's age.
Answers
Answer:
The product of Victor's age and 7 is 84 in equation form is 7v=84
Step-by-step explanation:
Let v be the Victor's age.
We are supposed to Translate this sentence into an equation
The product of Victor's age and 7 is 84
Victor's age = v
Product of victor's age and 7 =[tex]7 \times v[/tex]
We are given that their product is 84
So,[tex]7 \times v =84[/tex]
Hence The product of Victor's age and 7 is 84 in equation form is 7v=84
Rina is 6x+3/8 feet tall and Ryan is 5x+1/8 feet tall. How much taller is Rina than Ryan
Answers
Answer:
Rina is 1/4 feet taller than Ryan
Step-by-step explanation:
(height of Rina)-(height of Ryan)
6x+3/8-(5x+1/8)
6x+3/8-5x-1/8
x+3-1/8
x+2/8
x+1/4
What is the answer ?????????????????
Answers
Answer:
The answer is :
[tex] \cos(51) = 0.63[/tex]
[tex] \sin(63) = 0.89[/tex]
[tex] \tan(12) = 0.21[/tex]
a cuboid has length 4.2 m breadth 1.4 m and height 1.2 m . find the number of cubes each of lengh 20cm ,which canbe cut from the cuboid.
Answers
l= 4.2 m = 4.2 * 100 = 420 cm
b = 1.4 m = 1.4*100 = 140 cm
h =1.2 m =1.2 *100 =120 cm
Volume of cuboid = l*b*h = 420 * 140 * 120 = 705600 cubic cm
Volume of cube = a*a*a = 20*20*20 = 8000 cubic cm
No.of cubes = Volume of cuboid / volume of cube
= 705600 / 8000 = 882 cubes
or 420*140*120 / 20*20*20 = 42*14*12/2*2*2 = 21*7*6 = 882 cubes
a Fair coin is tossed 3 times. What is the probability of getting at least one heads and at least one tails?
Answers
Answer:
b. 75%
Step-by-step explanation:
Here are all the outcomes of three coin tosses:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
There are a total of 8 possible outcomes.
1 outcome is all heads.
1 outcome is all tails.
6 outcomes have at least one heads and 1 tails
p(at least 1 heads and at least 1 tails) = 6/8 = 3/4 = 75%
What is the per capita GDP of the United States?
Answers
Answer:
The per capita GDP will be "$62,790".
Step-by-step explanation:
Per capita GDP seems to be a calculation including its overall production of such a nation to take that GDP as well as dividing it by the number of individuals in that region. GDP per capita is particularly evident when analyzing one country or state to the next, as it indicates the remarkable success of that same country.So that the above seems to be the right answer.
David correctly factored the expression m2 -12m - 64 which expression did he write ?
1. (m - 8)(m - 8)
2. (m - 8)(m + 8)
3. (m - 16)(m + 4)
4. (m + 16)(m - 4)
Answers
Answer:
Step-by-step explanation:
Hints: look at the last term (-64) and the middle term (-12m).
Note that 64 is the product of 4 and 16, and that -4(16) = -64 or (-16)(4) = -64. the last term of thh given expression. Furthermore, if we look at the composition of the middle term (-12m), we realize that 4 - 16 = -12 must lead towards a solution.
Focus on possible Answer 3: Here -16m + 4m = -12m (which is what we'd hoped for, matching the middle term of the given expression.
Then m^2 - 12m - 64 = (x - 16)(x + 4) (Answer 3)
A biologist uses a box-shaped fish trap that measures 1/4meter by 2/3meter by 3/5meter. What is the volume of the trap in the cubic meters.
Answers
To find the volume of a box-shaped fish trap, we have to multiply the three dimensions of it:
(1/4 m)* (2/3 m)* (3/5 m)
= (1*2*3)/ (4*3*5) m^(3)
= 6/ 60 m^(3)
= 1/10 m^(3)
= 0.1 m^(3)
The volume of the box-shaped fish trap is 0.1 m^(3).
Hope this is helpful~
Which of the equations below represents a line parallel to the y-axis? A. x = -y B. x = y C. x = 4y D. x = 4
Answers
Answer:
D
Step-by-step explanation:
A line parallel to the y- axis is a vertical line with equation
x = c
where c is the value of the x- coordinates the line passes through, thus
x = 4 is the equation of a line parallel to the y- axis → D
Which is equivalent to 64 Superscript one-fourth?
Answers
Step-by-step explanation:
Info : 2^(6)=64
then
64^(1÷4) = (2^(6))^(1÷4)
=2^(6÷4)
=2^(3÷2)
=2√(2)
=2.828427124746
Answer:
2√2
Step-by-step explanation:
edge 2020
URGENT!!!!! LAST QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!!URGENT!!!!!
16. Which piece of information below will not help you prove that triangles ABC and DEF are congruent using ASA?
IF YOU REALLY LOOK YOU CAN SEE THE LETTERS BUT IN CASE HERE:
PIC BELOW ON THE LEFT TRIANGLE: A IS ON THE BOTTOM LEFT. B IS AT THE TOP, POINTY PART, C IS ON THE BOTTOM RIGHT
ON THE RIGHT TRIANGLE: D IS ON THE BOTTOM LEFT. E IS AT THE TOP, POINTY PART, F IS ON THE BOTTOM RIGHT
A) AC=DF
B) AB=DE
C) B=E
D) A=D
Answers
Answer: A) AC=DF
Step-by-step explanation:
Angle-Side-Angle (ASA) Postulate: If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.
Answer A is the only one that wouldn’t help you prove that these triangles are congruent.
NEED ANSWERS FAST AS CAN, I WILL GIVE BRAINLIEST TO THE RIGHT ANSWERS. 1.Using the following image, find the midpoint of the line by completing the problems below. 2.Given the points (−2,5)and (6,−1)the midpoint is? 3.Given the points (9,−4)and (−5,2)the midpoint is ? 4.Given the points (−2,−5)and (−6,7)the midpoint is...The graph doesn't go with 2-4
Answers
Answer:
Calculate distance first - so using the image we know that if we use pythogorean theorm we can get 2 vectors of this line, 1 completely vertical and one completely horizontal. Apply pythogorean theorm to the line and use for all other question. So 6^2+2^2=c^2
36+4=c^2
distance √40 half of it is √10
So we can use for this for it. (4-√10, 0-√10) so its (4-√10, -√10) for first one
Now that we dont have the image for the line we can apply the distance formula because we dont have clear view of points for #2. -2-6 = -8 then we need 5-1 = 4, -8^2+4^2 = c^2 so then sqrt(80) is distance. 2√5 is half. So then we subtract from (-5, 2) highest point on graph.( -5-√20, 2-√20).
Since this is heavily on writing I expect you to do the rest. Calculating the distance and pythogorean theorm on your own.
First 2 answers are
(4-√10, -√10)
( -5-√20, 2-√20)
8.
Describe how the graph of y = |x|- 4 is like the graph of y = |x| and how it is different.
