Write the logarithmic expression as a single logarithm with coefficient , and simplify as much as possible. Assume that all variable expressions represent positive real numbers.
1/2ln(b^2+1)-1/2ln(b+1)
Answer:
hope you can understand
The equation of a curve is y = x³ + 4x. Show that the value of y increases when x increases. ² is a decreasing function.
We will see that f'(x) > 0, which means that f(x) is an increasing function.
How to prove that the function is increasing?
For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.
Here we have the cubic function:
f(x) = x³ + 4x
If we differentiate this, we get:
f'(x) = df(x)/dx = 3x² + 4.
And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.
If you want to learn more about cubic functions:
https://brainly.com/question/20896994
#SPJ1
5 ⟌94.3
108.86
18.86
188.6
18.68
Answer:
18.86
Step-by-step explanation:
5 ⟌94.3
90 ÷ 5 = 18
18
5 ⟌94.3
-90
-----------------
4.3
cant divide by 4 so add a decimal
5 × 0.8 = 4
18.8
5 ⟌4.3
- 4.0
---------------
0.3
5 × 0.06 = 0.3
18.86
5 ⟌0.3
- 0.3
--------------
0
I hope this helps!
ASAP HELP NOWWWWW
What are the solutions for the following system of equations? –3x2 + 4y = 21 4x2 + y = 10 (1, 6) and (0, 10) (–1, 6) and (1, 6) (1, 6) and (3, 12) (–1, 6) and (3, 12)
The solutions for the following system of equations will be (–1, 6) and (1, 6). Then the correct option is B.
What is the solution of the equations?The equations are given below.
–3x² + 4y = 21 ...1
4x² + y = 10 ...2
Multiply equation 1 by 4 and equation 2 by 3, then we have
–12x² + 16y = 84
12x² + 3y = 30
Add both equations, then we have
19y = 114
y = 6
From equation 2, we have
4x² + 6 = 10
4x² = 4
x² = 1
x = ±1
x = 1, –1
Then the correct option is B.
More about the solution of the equations link is given below.
https://brainly.com/question/545403
#SPJ1
volunteers for a fair prepared 12 1/2 liters of smoothies. At the end of the day, the volunteers had 2 5/8 remaining. How many liters of smoothies were sold?
The liters of smoothies sold is 9 7/8 liters.
What is an Equation?An equation is a statement formed when two algebraic expressions are equated by an equal sign.
The volunteer prepares 12 1/2 = 25/2 liters of smoothies
The remaining amount of smoothies is 2 5/8 = 21/8 liters of smoothies
Let the amount of smoothies sold is x liters
Then the equation formed to determine the value of x is
x = (25/2) - (21/8)
x = 79/8
x = 9 7/8 liters
Therefore, the liters of smoothies sold is 9 7/8 liters.
To know more about Equation
https://brainly.com/question/10413253
#SPJ2
What is the average collection period??
Answer:
an accounting metric used to represent the average number of days between a credit sale date and the date when the purchaser remits payment.
Solve for D: 70D + 6 - 9D= 35 + 4D - 20.
Answer:
The answer is D = 9/57
Step-by-step explanation:
Get the variable D by itself as stated to solve for D.
I got the other numbers to the other side.
70D + 6 - 9D = 35 + 4D - 20.
(70D - 9D - 4D) = (35 - 20 - 6)
57D = 9
D = 9/57
Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5+ 1.25x
X=the number of weeks that have passed
Y = the height of the plant
How tall will with plant be after 7 weeks?
After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 2.5 + 1.25x
Plug x = 7 weeks
y = 2.5 + 1.25(7)
y = 11.25 units
Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ1
Which of the following is equivalent to:
(2x³ + 2) + (5x³ + 3)
Answer:
Step-by-step explanation:
2x^3 + 5x^3 + 2 + 3 = 7x^3 + 5
What is the volume of the cylinder below?
-----
-
2112
O O
A. 408 units3 B. 2448 units3
O
C. 204772 units 3
O
D. 20471 units
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
We need to find volume of the given Cylinder, with information :
radius (r) = 12 units height (h) = 17 units[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi r²h[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot(12) {}^{2} \sdot17[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot144{}^{} \sdot17[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = 2448 \pi \: \: unit {}^{3} [/tex]
So, correct choice is B
The volume of the given cylinder is 2448π cubic units
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of the given cylinder
Radius is 12 units
Height is 17 units
Volume of cylinder= πr²h
Plug in the values of radius and height
Volume = π×12²×17
=π×144×17
=2448π cubic units
Hence, the volume of the given cylinder is 2448π cubic units
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ5
A family plan for a cell phone has a monthly base price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) (in $) of a family for x additional family members added is C(x)=
The linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
How to get the linear equation?
Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.
Then if there are x family members added, the cost will be:
$75 + $10.99*x
Then the linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Khloe goes to a store an buys an item that costs xx dollars. She has a coupon for 15% off, and then a 8% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Khloe paid at the register.
Answer:
0.93x
Step-by-step explanation:
the total amount is:
x(1-15%+8%)=0.93x
so the answer is 0.93x
Find the product 3 radical -3 and 3 radical -5
[tex]\left(\sqrt[3]{-3} \right) \left(\sqrt[3]{-5}\right)\\\\=\left( \sqrt[3]{-1}\right \sqrt[3]{3}) \left(\sqrt[3]{-1} \sqrt[3]{5} \right)\\\\=\sqrt[3]{(-1)(-1)} \cdot \sqrt[3]{(3)(5)}\\\\=\sqrt[3]{1} \cdot \sqrt[3]{15}\\\\=1\cdot \sqrt[3]{15}\\\\=\sqrt[3]{15}[/tex]
The mean price of a textbook is $82, and the range of prices are $16. What are the possible prices for the textbook?
$82, $82, $82, $82, $98
$90, $90, $74, $74, $74
$82, $82, $88, $76, $82
$82, $84, $90, $80, $74
Answer: D (82, 84, 90, 80, 74)
Finding Range:
To find range, you must subtract the smallest number to the highest number in that number pattern.
For example, the highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).
Range is basically the most easiest to find out of median, mean, and mode. You just have to find the greatest-smallest = range.
Finding Mean:
To find mean, you must add all the numbers up then divide the sum by the QUANTITIY of all the numbers.
For example, if we add 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).
Mean is basically easy to find as you just add all the numbers and divide it by how much numbers make that sum.
Conclusion:
In conclusion, the mean and range all match a possible price of the textbook, having a range of $16 and a mean of $82. Thus, D is the right answer.
The correct option is D (82, 84, 90, 74)
What is range?Range is subtract the smallest number to the highest number in that number pattern.
What is mean?Mean is addition of all the numbers up then divide the sum by the quantities of all the numbers.
The highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).
Addition of 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).
Therefore, the possible prices for the textbook is the possible prices for the textbook is (82, 84, 90, 74).
Learn more about the mean of price here:
https://brainly.com/question/32623119
#SPJ2
In the diagrams, the pre-image is shown with a dashed line and the image is shown with a solid line. Which
transformation represents a dilation?
5
543-11-
4 5 X
Save and Exit
Next
Submit
Mark this and return
Answer:d
Step-by-step explanation:
Which of the following are not trigonometry identities? Check all that apply
Answer:A
Step-by-step explanation:
Good luck on the exam!
You roll two number cubes.
Let event A = You roll an even number on the first cube.
Let event B= You roll a 6 on the second cube.
Are the events independent or dependent? Why?
O A. Dependent, because 6 is an even number.
о B. Dependent, because both cubes have six sides.
O C. Independent, because they have no outcomes in common.
D. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
Answer:
Step-by-step explanation:
If you roll an even number it doesn't just get rid of the number off the cube, it still exists
Events A and B are independent.
These events have no outcomes in common,
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Events A and B are independent because the outcome of one event does not affect the probability of the other event.
The fact that 6 is an even number is not relevant to the independence of the events.
Event A is the event of rolling an even number on the first cube, which has three even and three odd numbers.
Event B is the event of rolling a 6 on the second cube, which has one 6 and five non-6 numbers.
These events have no outcomes in common, and the outcome of the first roll does not affect the outcome of the second roll.
Therefore,
Events A and B are independent.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ5
Question 15(Multiple Choice Worth 1 points)
(01.05 MC)
Which expression is rational?
04.121221222...
by
√36
O√21
O1.192744502...
Answer:
Second option
Step-by-step explanation:
Given the following question:
We are given four choices and we need to determine which choice is a rational number. In order for any integer to be a rational number you have to be able to write it as a fraction.
In this case, options one and four are immediately excluded since they are repeating decimals. They cannot be written as a fraction which leaves us with the second option or the third option.
[tex]\sqrt{36}[/tex]
[tex]\sqrt{36} =6\times6[/tex]
[tex]=6=\frac{6}{1}[/tex]
[tex]=\frac{6}{1}[/tex]
Your answer is the second option or "sqrt36."
Hope this helps.
PLEASE HELP TIMER!!!!!!!!!!!!!
Answer:
Answer: -3/2
Step-by-step explanation:
#KEEPSAFE
#GOODLUCK
#STUDYWELL
The price of a 7-minute phone call is $1.75. What is the price of a 13 minute phone call?
Answer:$3.25
Explanation:
Since the 7 min phone call is at 1.75, that means that one minute of phone call time is 0.25. 13 minutes would be 0.25*13=3.25
hope this helps
Polygon ABCD is plotted on a coordinate plane and then rotated 90° clockwise about point C to form polygon A′B′C′D′. Match each vertex of polygon A′B′C′D′ to its coordinates.
Graph of rigid functions on a coordinate plane. A quadrilateral vertices are plotted at A (4, 6), B (5, 3), C (4, 2), and D (1, 2) in quadrant 1. Interior are of quadrilateral is shaded.
The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)
How to match the vertices of the polygon?The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.
The vertices of polygon ABCD are given as:
A = (4, 6)
B = (5, 3)
C = (4, 2)
D = (1, 2)
The rule of rotation about point C is:
(x,y) = (a + b - y, x + b - a)
Where:
(a, b) = (4, 2) --- the point of rotation.
So, we have:
(x,y) = (4 + 2 - y, x + 4 - 2)
(x,y) = (6 - y, x + 2)
The above means that:
A' = (6 - 6, 4 + 2) = (0,6)
B' = (6 - 3, 5 + 2) = (3,7)
C' = (6 - 2, 4 + 2) = (4,6)
D' = (6 - 2, 1 + 2) = (4,3)
Hence, the image of the rotation and their vertices (i.e. coordinates) are:
A' = (0,6)
B' = (3,7)
C' = (4,6)
D' = (4,3)
Read more about rotation at:
https://brainly.com/question/4289712
#SPJ1
question 14, thank you
The parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
Path of the parametric equations
The given parametric equation can be expressed as follows;
x = 3 + cosθ
y = 2sinθ
From the given options, a plot of the various equation can be used to determine the paths of the equation.
For; x = 3 + cos(2θ) and y = 2sin(2θ), its parametric plots is same as original equation since the equation [3 + cos(2θ) and y = 2sin(2θ)] changed at equal rate of the angles.
Thus, the parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).
Learn more about parametric equation here: https://brainly.com/question/51019
#SPJ1
Which expression is equivalent to…
Answer:
the 3rd one ez clapppppppp
Howard and Jane are surveying their neighbors about the community garden. Their questions, written on the survey, are below: Howard: Did you visit the garden this month? Jane: How many times do you visit the garden in a month? Who wrote a statistical question and why?
Answer:
Step-by-step explanation:
Note
Answer: Jane's question
Howard merely asked if a visit had taken place. There isn't a number anywhere or one that can be implied.
Jane asked for a number. It requires that the responder gives a number with no embellishment. The question asks for the number of times something has occurred and there is a time frame for the answer. That usually is the characteristic of a statistical survey.
If Bank A charges a monthly service
fee of $2.50 and a per-check fee of
$0.15, while Bank B charges a
monthly service fee of $4 and a per-
check fee of $0.05, which bank will
charge a customer more in fees if
she writes 18 checks per month, and
by how much?
The bank which will charge a customer more in fees if she writes 18 checks per month, and by how much is Bank A by $0.30
How to write and solve equation?let
x = number of checksBank A = 2.50 + 0.15x
= 2.50 + 0.15(18)
= 2.50 + 2.7
= $5.20
Bank B = 4 + 0.05x
= 4 + 0.05(18)
= 4 + 0.9
= $4.9
Difference in charges = $5.20 - $4.90
= $0.30
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
identify the matrix transformation of angle TUV, which has coordinates T(0,1), U(1,2), and V(2,0) for 90 degree rotation clockwise. Then identify the correct vertices of the image
3. Find sin A and cos B exactly.
B
a
C
6
4
A
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{6^2 - 4^2}=a\implies \sqrt{36-16}=a\implies \sqrt{20}=a\implies 2\sqrt{5}=a \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies sin(A)=\cfrac{\sqrt{5}}{3} \\\\\\ cos(B )=\cfrac{\stackrel{adjacent}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies cos(B)=\cfrac{\sqrt{5}}{3}[/tex]
Find all solutions.
x +4x=0
Answer: x = 0
Step-by-step explanation:
Given:
x + 4x = 0
Combine like terms:
5x = 0
Divide both sides of the equation by 5:
x = 0
We can also check our work by graphing. See attached, intercepts of the x-axis are solutions.
A solid sphere is cut into 12 equal wedges. The volume of each wedge is
V=³. Solve the formula for r.
The complete question is
"A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. Solve the formula for r."
A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. The value of r is (9V/π)^1/3.
What is the volume of the sphere?It is given that;
The Volume of a sphere = V = 4/3πr³
Dividing into 12
4/3 x 1/12 πr³ = 1/9πr³
V = 1/9πr³
Cross multiply
9V = πr³
Divide both sides by π
9V/ π = πr³/ π
9V/ π = r³
Take the cube root of both sides
r = (9V/π)^1/3
Thus, The value of r is (9V/π)^1/3.
Learn more about sphere;
https://brainly.com/question/23917548
#SPJ1
6. A department store uses a
market research survey to
determine the types of products
various consumer groups are
buying.
Choose all that apply.
The characteristics that best
describe surveys are:
Answer choices:
Work with a wide variety of
formats
Involve studying subjects in their
environment, which is not
controlled in any way
May collect either facts or
opinions