Answer: [tex]x=0\text{ and }x=e^4[/tex]
Step-by-step explanation:
The vertical asymptote is at the zero of the argument and at points where the argument approaches to ∞ .Given function: [tex]f(x) = \ln(4 - \ln(x))[/tex]
Since, [tex]\ln 0=\infty[/tex]
Here, if
[tex]f(x)\to \infty\\\Rightarrow\ 4-\ln x=0\Rightarrow\ln x=4\Rightarrow\ x=e^4\\\text{OR}\ln x=\infty\Rightarrow\ x=0[/tex]
Hence, the vertical asymptotes of f(x) are:
[tex]x=0\text{ and }x=e^4[/tex].
Using it's concept, it is found that the vertical asymptotes of the function are: [tex]\mathbf{x = 0, x = e^4}[/tex]
A vertical asymptote of a function f(x) are the values of x for which the function is outside it's domain.
For the ln function, that is, [tex]\ln{g(x)}[/tex], they are the values of x for which:
[tex]g(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = \ln{(4 - \ln{(x)})}[/tex]
For the inner function, x = 0 is a vertical asymptote, as [tex]\ln{0}[/tex] is outside the domain.
For the outer function:
[tex]4 - \ln{(x)} = 0[/tex]
[tex]\ln{(x)} = 4[/tex]
[tex]e^{\ln{(x)}} = e^4[/tex]
[tex]x = e^4[/tex]
A similar problem is given at https://brainly.com/question/23535769
i will give you 45 for this what is 12*12/12-3/4
Answer:
11.25
Step-by-step explanation:
12*12/12-3/4
PEMDAS says multiply and divide first
from left to right
144/12 - 3/4
12 -3/4
12 - .75
Then add and subtract
11.25
Answer:
[tex]\frac{45}{4}[/tex]
Step-by-step explanation:
Apply PEDMAS
P - parenthesis
E - exponents
D - division
M - multiplication
A - addition and S - subtraction
Division is first.
12 × [tex]\frac{12}{12}[/tex] - [tex]\frac{3}{4}[/tex]
12 × 1 - [tex]\frac{3}{4}[/tex]
Followed by multiplication.
12 - [tex]\frac{3}{4}[/tex]
Subtract the numbers next.
[tex]\frac{12}{1} -\frac{3}{4}[/tex]
Make the denominators same by LCM.
[tex]\frac{48}{4} -\frac{3}{4}[/tex]
[tex]\frac{45}{4}[/tex]
A farmer grows vegetables on seven acres, fruit on six acres, and flowers on two acres. Out in his fields, he finds a ladybug. To the nearest tenth of a percent, what is the theoretical probability that the ladybug was not found within the acres of flowers? 13.3% 15.4% 84.6% 86.7%
Answer:
86.7
Step-by-step explanation:
Answer:
86.7%
Step-by-step explanation:
Correct on Edge2020
50 Pts!!! Answer ASAP.
Answer:
0.8
Step-by-step explanation:
because the template should be axr^n-1
where r is the common ratio
r=0.8
Answer:
0.8
Step-by-step explanation:
1 less than a doubled number is equivalent to 5 more than 3 lots of the number
Answer:
the number is -6 (assuming "3 lots of" means 3 times)
Step-by-step explanation:
Let the number be x
1 less than a doubled number
2x-1
5 more than 3 lots of (times???) the number
3x+5
Solve for x
2x-1 = 3x + 5
-x = 5+1
x = -6
How to do this question plz plz plz plz plz plz plz plz
Answer:
6.4 cmStep-by-step explanation:
Volume of cartoon = 5 cm × 8 cm × 15 cm
= 600 cm³
Volume of milk = 5 cm × 8 cm × 12 cm
= 480 cm³
Space = 600 cm³ - 480 cm³ = 120 cm³
Let depth be ' h '
15 × 5 × h = 480
Multiply the numbers
75h = 480
Divide both sides of the equation by 75
75 h / 75 = 480 / 75
Calculate
h = 6.4 cm
therefore, The depth of the milk is 6.4 cm
Hope this helps...
Best regards!!
For what value of x does 5^x-2 not equal zero?
a. all except 2
b. all except 0
c. all except -4
d. all except -2
e. all real numbers
Answer:
E: all real numbers
Step-by-step explanation:
the length of a rectangular plot of land exceeds the width by 7 m if the area pf the plot is 198 m square what is the length
Answer:
28.142m
Step-by-step explanation:
area of rectangle=width x lenght
so; (rotating the formula with what is given)
area of rectangle/width=lenght
197/7=lenght
28.142m =lenght
Answer:
Length is 18 m and width is 11 m
Step-by-step explanation:
So based on the information given length is seven cm more than your width, and since we don’t know the values of these, we can plot this information into a formula that looks like this: (x+7)(x)=198, which is basically how you take the area of the plot of land.
If you multiply your values, you will get a quadratic equation that looks like this x²+7x-198. If you follow the quadratic formula to solve this equation, the positive result you will get for x is 11, this is your width. And since length exceeds by 7, you just add 7 to 11 to find the length, which ends up being 18.
to verify, you can simply multiply these two values
Find the area of the triangle. Round the answer to the nearest tenth. Triangle is SSA. a= 3.7 b= 3.7 β= 70° ----- A.4.4 square units B.5.2 square units C.6.8 square units D.8.8 square units
Answer:
A. 4.40 square units
Step-by-step explanation:
The triangle is isosceles with base angles of 70°. The a.pex angle will be ...
180° -2(70°) = 40°
The area of a triangle can be computed from two sides and the angle between them as ...
A = (1/2)ab·sin(γ)
A = (1/2)(3.7)(3.7)sin(40°) ≈ 4.40 . . . square units
lf a bus travels 6 km in 10 minutes, what distance does it travel in 1second
Answer:
0.01 kmStep-by-step explanation:
[tex]6\: km\: in \:10\: minutes\\First\:lets\:convert\:10\:min\:to\:seconds\\\\1\:minute \:\:\:\:=60\:seconds\\\\10\:minutes = x \:seconds\\\\x = 60\times 10\\x = 600seconds\\\\6km\: = 600\:seconds\\x\:km = 1 \:second\\\\Cross\:Multiply\\600x =6\\\frac{600x}{600} =\frac{6}{600} \\\\x = 1/100\\\\ =0.01km[/tex]
Please answer this in two minutes
Answer:
20/29
Step-by-step explanation:
SOH CAH TOA
so its opposite/hyp...
20/29
is the answer
To mix mortar to lay bricks,you need 2.5Kg of cement,4kg of sand and 3 liters of water.Sand is sold in 10kg bags.How much cement and water will I need to add to make mortar?
Answer:
6.25 kg cement, 7.5 L water
Step-by-step explanation:
2.5 kg cement / 4 kg sand = x kg cement / 10 kg sand
x = 6.25
3 L water / 4 kg sand = y L water / 10 kg sand
y = 7.5
adi used algebra tiles to represent the product (-2x-2)(2x-1) which is true regarding axis use of algebra tiles
Answer:
She did not represent the two original factors correctly on the headers.
Step-by-step explanation:
Adi Algebra titles method is based on the field of values. In the given question the representation of of the product is not correct. The two negative titles must be in the top header so the correct sign in incorporated with the variables.
Answer:
A. She used the algebra tiles correctly.
Step-by-step explanation:
She represents each step of the equation with algebra tiles correctly, even if it could be simplified more.
John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answer:
[tex]Probability = 51\%[/tex]
Step-by-step explanation:
Given
Radius of inner circle = 5ft
Radius of outer circle = 7ft
Required
Determine the probability that the thumbtack will be placed on the inner circle
We start by calculating the area of both circles;
Inner Circle
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14 * 5^2[/tex]
[tex]Area = 3.14 * 25[/tex]
[tex]Area = 78.5[/tex]
Outer Circle
[tex]Area = \pi R^2[/tex]
[tex]Area = 3.14 * 7^2[/tex]
[tex]Area = 3.14 * 49[/tex]
[tex]Area = 153.86[/tex]
At this point, the probability can be calculated;
The probability = Area of Inner Circle / Area of Outer Circle
[tex]Probability = \frac{78.5}{153.86}[/tex]
[tex]Probability = 0.51020408163[/tex]
Convert to percentage
[tex]Probability = 0.51020408163 * 100\%[/tex]
[tex]Probability = 51.020408163\%[/tex]
Approximate
[tex]Probability = 51\%[/tex]
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs. Is it likely that his team's scores is different from the national distribution
Answer:
Yes, it is likely due to the significant difference in their average scores.Step-by-step explanation:
The average number of runs scored by a Little League team in a game is 5.7. If he chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs, their average score of the five games is expressed as shown;
Average score of 5 games = (5+9+4+11+8)/5
Average score of 5 games = 37/5
Average score of 5 games = 7.4
Comparing the average score in 5 games to the the average number of runs scored nationally, it can be seen that their difference is 7.4 - 5.7 which is 1.7. Since the difference is quite significant, then it is most likely that his team's scores is different from the national distribution.
Triangle ABC is rotated about the origin by 270° to form the triangle A′B′C′, then translated upward 10 units to form triangle A″B″C″. Which of the following statements is true for ΔABC and ΔA″B″C″? A)There isn't enough information to identify whether ΔABC and ΔA″B″C″ are congruent or similar. B)ΔABC and ΔA″B″C″ are neither similar nor congruent. C)ΔABC and ΔA″B″C″ are similar triangles. D)ΔABC and ΔA″B″C″ are congruent triangles.
Answer:
The correct answer is option:
D) ΔABC and ΔA″B″C″ are congruent triangles.
Step-by-step explanation:
Given
ΔABC is first rotated about the origin by 270° to form the triangle A′B′C′.[tex]\triangle A'B'C'[/tex] is then translated upwards 10 units to form [tex]\triangle A''B''C''[/tex]To find: The true statement among the given options.
Solution:
Let the triangle be situated in 1st quadrant.
It is rotated about the origin by [tex]270^\circ[/tex].
Now, it moves towards quadrant 2 if it is rotated clockwise. It is termed as
[tex]\triangle A'B'C'[/tex].
It is given that now it is translated 10 units upwards. i.e. 10 units added to x coordinate of each vertex to form [tex]\triangle A''B''C''[/tex].
Now, we can see that there is no change in the dimensions of the triangle. We are just changing the location of the triangle.
So, all its angles will be equal to each other and all the sides will be equal to each other.
i.e.
[tex]\angle A = \angle A''\\\angle B = \angle B''\\\angle C = \angle C''\\Side\ AB = Side\ A''B''\\Side\ BC = Side\ B''C''\\Side\ AC = Side\ A''C''[/tex]
Hence, the correct option is:
D)ΔABC and ΔA″B″C″ are congruent triangles.
Answer:A-B
Step-by-step explanation:
18.2 divided by 18 what’s the answer??
Answer:1.0111111111
Step-by-step explanation:
18.2 - 18 = .2-18 =1.0111111
Can anyone help me with this question? Which reason justifies the conclusion that ∆PST ≅ ∆RST?
Answer:
A) SAS postulate
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation:
you know that ST is equal and you also know two equal angles and one other equal side
A piece of land ABCD is in the shape of a trapezium
as shown in the diagram. AB = 40 m, BC = 39 m,
AD = 30 m, and <ABC = <BAD = 90°. Find
(a) the length of the side CD,
(b) angle BCD,
(c) the area of the land.
Answer:
a) CD = 41 m
b) 77.32°
c) 1380 square metres
Step-by-step explanation:
We can divide the trapezium as shown in the diagram below.
a) To find CD, we use Pythagoras Rule:
[tex]CD^2 = 9^2 + 40^2[/tex]
[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]
b) To find <BCD, we use trigonometric function SOHCAHTOA:
sin(BCD) = opp / hyp
sin(BCD) = 40 / 41
sin(BCD) = 0.9756
=> <BCD = 77.32°
c) The area of a trapezium is given as:
A = 1/2 (a + b) * h
where h = height = 40 m
a = top length = 30 m
b = bottom length = 39 m
A = 1/2 * (30 + 39) * 40
A = 1/2 * 69 * 40
A = 1380 square metres
The volume of a cylinder is approximately 72 feet cubed. Which is the best approximation of the volume of a cone with the same base and height as the cylinder? 24 feet cubed 216 feet cubed 24 pi feet cubed 216 pi feet cubed
Hey there! I'm happy to help!
To find the volume of a cylinder, you multiply the base by the height and then divide by three. The volume of a cone is the same as the volume of a cylinder with the same dimensions divided by three.
So, since a cone's volume is 1/3 of that of a cylinder, we just divide 72 by 3!
72/3=24
Therefore, the volume of the cone is 24 feet cubed.
Have a wonderful day! :D
Answer: its 24.
Step-by-step explanation:
y−4=7(x−6) find the x and y intercepts
need HELP ON THIS A S AP !!!!!
Answer:
803.84yd²
Step-by-step explanation:
Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]
We are given the radius of 8 yards.
Using 3.14 for pi:
[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]
The correct answer should be 803.84yd².
Brainilest Appreciated.
Answer:
803.84 yd^2
Step-by-step explanation:
4*3.14*8^2
12.56*64
803.84
brainliest pls
hope i helped
-ZYLYNN
changing fraction to percentage
Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~`
You added no fraction so i thought you wanted the definition
Convert Fractions to Percents. Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.
Hope this helped you. Brainliest wouldbe nice!
What is the value of 'x' : [tex]4x + 3 = 16[/tex]
Answer:
x = 3.25
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
...and is the order of operation.
First, subtract 3 from both sides of the equation:
4x + 3 = 16
4x + 3 (-3) = 16 (-3)
4x = 16 -3
4x = 13
Next, dvide 4 from both sides:
(4x)/4 = (13)/4
x = 13/4
x = 3.25
x = 3.25 is your answer.
~
Answer:
x = 3.25
Step-by-step explanation:
4x + 3 = 16
4x + 3 - 3 = 16 - 3
4x = 13
4x/4 = 13/4
x = 3.25
f: x 5 – 3x. (a) Find f(–1). (b) Find f –1(x).
Answer:
[tex]f(-1) = 8[/tex]
[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5 - 3x[/tex]
Required
[tex]f(-1)[/tex] and [tex]f^{-1}(x)[/tex]
Solving for f(-1)
Substitute -1 for x in [tex]f(x) = 5 - 3x[/tex]
[tex]f(-1) = 5 - 3(-1)[/tex]
[tex]f(-1) = 5 + 3[/tex]
[tex]f(-1) = 8[/tex]
Solving for [tex]f^{-1}(x)[/tex]
Let y = f(x)
[tex]y = 5 - 3x[/tex]
Interchange the position of x and y
[tex]x = 5 - 3y[/tex]
Make y the subject of formula (add 3y to both sides)
[tex]3y + x = 5 - 3y + 3y[/tex]
[tex]3y + x = 5[/tex]
Subtract x from both sides
[tex]3y + x - x = 5 - x[/tex]
[tex]3y = 5 - x[/tex]
Divide through by 3
[tex]\frac{3y}{3} = \frac{5}{3} - \frac{x}{3}[/tex]
[tex]y = \frac{5}{3} - \frac{x}{3}[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]
Twoooooooooooooooooooooooooooo
Answer:
n = 60.22
Step-by-step explanation:
Hello
To find Sn, we need to draw out equations for each a₇ and a₁₉
In an arithmetic progression,
Sn = a + (n-1)d
Where Sn = sum of the A.P
a = first term
d = common difference
a₇ = 32
32 = a + (7-1)d
32 = a + 6d ........equation (i)
a₁₉ = 140
140 = a + (19-1)d
140 = a + 18d .........equation (ii)
Solve equation (i) and (ii) simultaneously
From equation (i)
32 = a + 6d
Make a the subject of formula
a = 32 - 6d .....equation (iii)
Put equation (iii) into equation (ii)
140 = (32 - 6d) + 18d
140 = 32 - 6d + 18d
Collect like terms
140 - 32 = 12d
12d = 108
d = 108 / 12
d = 9
Put d = 9 in equation (i)
32 = a + 6(9)
32 = a + 54
a = 32 - 54
a = -22
When Sn = 511
Sn = a + (n - 1)d
Substitute and solve for n
511 = -22 + (n-1) × 9
511 = -22 + 9n - 9
511 = -31 + 9n
511 + 31 = 9n
542 = 9n
n = 542 / 9
n = 60.22
i will mark brainlist
Answer:
[tex]\boxed{x = 30}[/tex]
Step-by-step explanation:
x + 2x + 3x = 180 (Interior angles of a triangle add up to 180 degrees)
=> 6x = 180
Dividing both sides by 6
=> x = 180 / 6
=> x = 30
Answer:
x= 30
Step-by-step explanation:
3x + 2x + x = 180
6x= 180
x = 180/6
:• x = 30
which ratio forms a proportion 12/15
Answer:
[tex]\frac{20}{25}[/tex]
Step-by-step explanation:
See Attachment for Complete Question
Given
[tex]Ratio = \frac{12}{15}[/tex]
Required
Determine its equivalent proportion
[tex]Ratio = \frac{12}{15}[/tex]
Factorize the given expression
[tex]Ratio = \frac{3 * 4}{3 * 5}[/tex]
Divide the numerator and denominator by 3
[tex]Ratio = \frac{4}{5}[/tex]
We apply the same steps to the given options as follows:
1.
[tex]Ratio = \frac{21}{28}[/tex]
Factorize
[tex]Ratio = \frac{7 * 3}{7 * 4}[/tex]
Divide the numerator and denominator by 7
[tex]Ratio = \frac{3}{4}[/tex]
This is not an equivalent proportion of [tex]\frac{12}{15}[/tex]
2.
[tex]Ratio = \frac{20}{25}[/tex]
Factorize
[tex]Ratio = \frac{5 * 4}{5 * 5}[/tex]
Divide the numerator and denominator by 5
[tex]Ratio = \frac{4}{5}[/tex]
This is equivalent to [tex]\frac{12}{15}[/tex] because they both simplify to [tex]\frac{4}{5}[/tex]
There's no need to check the last option;
Hence, the option that answers the question is [tex]\frac{20}{25}[/tex]
What is the image of E for a 120° counterclockwise rotation about the center of the regular hexagon?
Answer:
N
Step-by-step explanation:
Since this hexagon has six sides, and to end up back at E again we’d need to rotate 360°, this means for every side we cross it’s a 60° turn.
Therefore, [tex]60 \cdot 2 = 120[/tex]° would be two sides.
Since we are moving counter-clockwise, the image for E would be to the left of it.
Two sides/points to the left of E is N, so the image of E for a 120° counterclockwise rotation around the center of this shape would be N.
Hope this helped!
The biomass B(t) of a fishery is the total mass of the members of the fish population at time t. It is the product of the number of individuals N(t) in the population and the average mass M(t) of a fish at time t. In the case of guppies, breeding occurs continually. Suppose that at time t = 5 weeks the population is 824 guppies and is growing at a rate of 50 guppies per week, while the average mass is 1.3 g and is increasing at a rate of 0.14 g/week. At what rate is the biomass increasing when t = 5? (Round your answer to one decimal place.) B'(5) = g/week
Answer:
The rate at which the biomass is increasing when t = 5 is 180.36 g/week
Step-by-step explanation:
Given that :
t = 5 weeks
Population N(t) = 824 guppies
Growth Rate [tex]\dfrac{dN(t)}{dt}= 50 \ guppies /week[/tex]
average mass M(t) = 1.3 g
increase rate of biomass [tex]\dfrac{dM (t)}{t}[/tex]= 0.14 g/week
Therefore; the rate at which the biomass is increasing when t = 5 is:
[tex]\dfrac{dB(t)}{dt}= M(t) * \dfrac{dN(t)}{dt}+ N(t)* \dfrac{dM (t)}{t}[/tex]
[tex]\dfrac{dB(t)}{dt}=1.3 * 50+ 824* 0.14[/tex]
[tex]\dfrac{dB(t)}{dt}=65+115.36[/tex]
[tex]\mathbf{\dfrac{dB(t)}{dt}=180.36 \ g/week}[/tex]
The rate at which the biomass is increasing when t = 5 is 180.36 g/week
The rate at which the biomass is increasing when t = 5 is 180.36 g/week
Calculation of the rate:Since time = 5 weeks, Population N(t) = 824 guppies, and growth rate = 50 guppies / week, average mass = 1.3g, and the increase rate of biomass is 0.14g/week
So,
[tex]= 1.3\times 50 + 824 \times 0.14[/tex]
= 65 + 115.36
= 180.35 g/weel
Learn more about mass here: https://brainly.com/question/3943429
What is the solution set of x for the given equation? x^2/3-x^1/3+4=6 A. -2, -1 B. 2, -1 C. -8, -1 D. 8, -1 E. 2, 8
Answer: The answer is D.
Step-by-step explanation: Ok, we start by simplifing the equation to 3√x^2 - 3√x=2. Now, by plugging the possible options in, we can find the answer. You find that -1 is a possible answer for x, so that eliminates E. Since there is no cube root for 2, we elimate A and B. By plugging in C and D, you find that C=6, not C=2. So D must be the answer.