Any equation in the variable x that contains a logarithm is called a logarithmic equation.
What are the features logarithmic function?The graphs of all logarithmic functions will have the following characteristics: The graph of logarithmic functions passes through the points (1,0). If the base of a logarithmic function is greater than 1, then the graph increases.Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ayLogarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos)Two kinds of logarithms are often used in chemistry: common (or Briggian) logarithms and natural (or Napierian) logarithms. The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number.To learn more about logarithmic function refers to:
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The biotic factors of an ecosystem are arranged in feeding levels based on what they utilize for food or energy. Each of these feeding levels is called a
The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.
What is a trophic level?The trophic level of an organism is the position it occupies in a food web. The trophic level of an organism is the number of steps it is from the start of the chain.
Below are the list of the trophic levels:
1st Trophic Level (Producer) : Makes its own food2nd Trophic Level (Primary Consumer): Consumes producers3rd Trophic Level (Secondary Consumer): Consumes primary consumers4th Trophic Level (Tertiary Consumer): Consumes secondary consumersThe biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.
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Five chess players take part in a tournament. Every player plays once with each of his/her opponents. How many games are play?
There is a total of 10 games played.
How many games are played?
There are 5 players, If we select a given player, then that player will play one game with each of the other 4 players.
So we have 4 games at the moment.
Now we select one of the other 4 players, (we don't count the one we choose before). The one that we choose now will play one game wich each one of the remaining 3, so we add 3 more games.
Now we do the same with the remaining 3, this time we add 2 more games.
Now we do that with the remaining 2, now we add 1 more game.
Adding all the games we have:
4 + 3 + 2 + 1 = 10
There is a total of 10 games played.
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PLEASE HELP BEST ANSWER GETS BRIANLIST
Answer:
-3
Step-by-step explanation:
So just like the picture provides, the slope can be defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]. So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.
So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.
Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3
The slope is -3
A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a:
A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a negative correlation.
What is negative correlation?When two variables move in opposite sizes and directions from one another, so that when one increases, the other drops, and vice versa, this is referred to as having a negative correlation or inverse correlation.
In order for investors to profit from price increases in some assets when others decline, negative correlation is used when building diverse portfolios.
Over time, the correlation between two variables might change significantly. Bonds and stocks typically have negative correlation.
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Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make any payments
toward it. write the equation to represent the situation, and solve it using the inverse relationship between exponential
and logarithmic expressions.
type the correct response in the box. use numerals instead of words. round your answer to the nearest tenth.
Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which:
A(0) is the initial value.
r is the growth rate, as a decimal.
In this problem:
Her initial balance is of $300, hence . A(0)=300
The growth rate is of 15%, hence R =0.15
Then,
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]
It will reach $450 after t years, for which A(t) = 450, hence:
[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]
It will take about 2.9 years for Emma's balance to reach $450
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In ΔABC, BD is perpendicular to AC as shown in the figure.
Which equations are true?
Answer:
2nd, 3rd, and 6th option are correct
Step-by-step explanation:
using a²+b²=c² those are the obly that meet the criteria (im pretty sure)
In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.
What is a right angle triangle?
A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.
Given that,
ABC is a right angle triangle.
And BD is perpendicular to AC.
To show the equations which are true,
Use Pythagorean theorem,
(Hypotenuse)² = (base)² + (height)²
In triangle ABC,
AC² = AB² + BC²
In triangle ABD,
(AB)² = AD² + BD²
And in triangle BCD,
BC² = CD² + BD²
Therefore, option (2), (3) and (6) are correct.
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Determine whether the point (1,5) is a solution to the system of equations g(x)=3x+2 f(x)=|x-1|+1
Point [tex](1,5)[/tex] is a solution of the equation [tex]g(x)=3x+2[/tex] and point [tex](1,5)[/tex] is not a solution of equation [tex]f(x)=|x-1|+1[/tex]
Why point [tex](1,5)[/tex] is solution of the equation [tex]g(x)=3x+2[/tex] ?
If point [tex](1,5)[/tex] is solution of the equation then they must satisfy the equation.
So we need to check one by one
[tex](x,y)=(1,5)[/tex]
equation [tex]g(x)=3x+2[/tex]
We can write as
[tex]y=3x+2\\5=3*1+2\\5=5[/tex]
So point [tex](1,5)[/tex] is solution of this equation.
Equation [tex]f(x)=|x-1|+1[/tex]
We can write as
[tex]y=|x-1|+1\\5=|1-1|+1\\5=0+1\\5\neq 1[/tex]
So point [tex](1,5)[/tex] is not solution of equation [tex]f(x)=|x-1|+1[/tex]
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Your family is going on vacation for two nights. You don't want to spend more than $135 on a hotel room for your vacation. Write an inequality to represent how much you can spend each night on your hotel room.
Answer:
x ≤ 135/2
Step-by-step explanation:
x is the cost per night. You have to pay for 2 nights, and you do not want to spend more than $135 total. Another way to say that, is you want to spend less than or equal to $135.
x = cost per night
2 = number of nights
2x = total cost
Total cost must be less than or equal to $135.
2x ≤ 135
Divide each side by 2.
x ≤ 135/2
What is the surface area of the figure below?
Round your answer to the nearest tenth square foot?
(The answer choices are in the picture. Thank you!)
Answer:
856.5ft^2
Step-by-step explanation:
I took the test.
Someone help me please
Answer:
x=15
Step-by-step explanation:
Use the Pythagorean Theorem: a^2+b^2=c^2
1. a = 20, b = x, c = 25
2. 20^2+b^2= 25^2
3. Expand: 400+b^2= 625
4. Subtract + Simplify: b^2= 625-400
5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225
6. Last Step: Simplify: b = 15.
Here is a similar problem for you to solve, put your answer in the comments.
a= 12, b=5, c=?
Solve for c using the Pythagorean theorem.
if you shift the absolute value parent function, F(x)= IxI, right 9 units, what is the equation of the new function?
A. G(x)=IxI-9
B. G(x)=Ix+9I
C. G(x)=Ix-9I
D. G(x)=IxI+9
Darlene says that 1/4 is greater than 1/3 because 4 is great than 3. is she correct?
No she is not correct 1/3 is great that 1/4
Answer:
No, she isn't correct because if the numerator are same but if denominators is different,then the fraction with smaller denominator is greater.
what is meant by green mathematics?
give meaningful answer .
[tex]4222125.[/tex]
who can give the first answer
The green mathematics tells about the impulse response of an in homogeneous linear differential operator.
According to the statement
we have to explain the green mathematics.
In mathematics, Actually there is a Green Function which was founded by a mathematician George Green.
In this function, a Green's function is the impulse response of an in homogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.
The example of green function is the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.
Actually in this function, it gives the relationship between the line integral of two dimensional vector over a closed path by a integral.
In this there is a green theorem, which relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.
So, The green mathematics tells about the impulse response of an in homogeneous linear differential operator.
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The angle formed by the line of sight and the horizontal line can best be described as a(n)
The angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
The angle of elevation is says to be the angle made between a horizontal plane and a straight line to a given object that is elevated off the ground.
Therefore, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.
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What are the domain and range of g of x equals negative 3 times the square root of the quantity x minus 1? D: (1, ∞) and R: (0, ∞) D: [–3, ∞) and R: [0, ∞) D: (–3, ∞) and R: (–∞, 0) D: [1, ∞) and R: (–∞, 0]
The domain of the function is [1, ∞) and the range is [0, ∞)
How to determine the domain and the range?The equation of the function is given as:
g(x) = 3√x - 1
The domain is the possible values of x.
Set the radicand to greater than or equal to 0
x - 1 >= 0
Add 1 to both sides
x >= 1
This can be rewritten as:
[1, ∞)
Breakdown
g(x) = 3√x - 1
x - 1 >= 0
x >= 1
[1, ∞)
The range is the possible values of y.
Set the radicand to 0
g(x) = 3 * 0
Evaluate the product
g(x) = 0
This can be rewritten as:
[0, ∞)
Breakdown
g(x) = 3√x - 1
g(x) = 3 * 0
g(x) = 0
[0, ∞)
Hence, the domain of the function is [1, ∞) and the range is [0, ∞)
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Answer:
Correct answer is D: [1, ∞) and R: (-∞, 0]
Step-by-step explanation:
Insert the given function on desmos to observe the following explanation.
The domain (x values) begin at 1, and go on to positive infinity (the squared bracket indicates a stop/start at that certain point). The range goes into negative infinity (y values) and begins at the y value of 0, so it does not go above that point on the y axis (hence the squared bracket).
Determine if the expression −7m³ + m + 9m³ is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial
1: "represents" a polynomial
2: "does NOT represent" a polynomial
⊰___________________ ___________________________________ __⊱
Answer:
Yes, it is a polynomial
Step-by-step explanation:
This polynomial is a trinomial, since it has 3 terms (the prefix tri means three) and its degree is 3 (the degree of a polynomial is the largest exponent in that particular polynomial).
Done !! Hope this made sense to you !!
⊰________________________________________________________⊱
[tex]\small{\pmb{\tt{CALLIGRAPHY}}[/tex]
Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical form.
17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.
How do you find the length of the diagonal of a regular hexagon?Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.
For a polygon, the SUM of the internal angles is:
(n-2) * 180 (n=6 for hexagon)
(6-2)*180 = 720 Thus EACH angle is : 720/6 = 120 degrees
Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.
There are 180 degrees in any triangle:
(180-120) / 2 = 30 degrees for each of the smaller angles.
Now use the law of sines:
10/sin30 = x/(sin120)
10/(.5) × (sqrt3 )/ 2 = x
10 sqrt 3
10/sin30 × sin 120 = 17.32
17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.
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What is the domain of the following set of ordered pairs?
{(-2,-5), (-3,8), (12,6), (8, -3), (4,0), (-5, -7)}
○ a. {-5, 8, 6, -3, 0, -7}
O b. {-2, -5, -3, 8, 12, 6}
○ c. {8, −3, 4, 0, − 5, −7}
O d. {-2, -3, 12, 8, 4, −5}
Answer:
D. {-2, -3, 12, 8, 4, −5}
Step-by-step explanation:
The domain is the set of x coordinates, so the answer is {-2, -3, 12, 8, 4, −5}.
Bailey tossed a coin 10 times. The results were 7 heads and 3 tails.
What is the experimental probability of tossing tails?
answer as a fraction
A scalene triangle whose angles are all congruent possible or impossible
Answer:
impossible
Step-by-step explanation:
a scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.
because all 3 angles must be different, they cannot be congruent.
because if angles are congruent, it means that they are of equal size.
the desired definition is a paradox or oxymoron. it contradicts itself and can never be true.
Answer:
it cannot have all angles congruent: impossible.
Step-by-step explanation:
by the definition scalene, it means no angle is the same length. meaning, to have all the sides congruent (the same length) that would be impossible and it can never happen. if you would like a congruent triangle, an isosceles or equilateral is the triangle you're looking for.
can a pyramid be constructed from polygons alone
(d) Percentage of viewers given they are 18 to 34 who prefer videos on a mobile or laptop device. (Round your answer to 2 decimal places.)\
52.94% of the viewers prefer videos on a mobile or laptop device
How to determine the percentage?The given parameters are
Viewers that prefer videos on a mobile or laptop device = 18
Total number of viewers = 34
The percentage of voters in this category is then calculated as
Percentage = 18/34 * 100%
Evaluate the expression
Percentage = 52.94%
Hence, 52.94% of the viewers prefer videos on a mobile or laptop device
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Can someone help me with this question?
Step-by-step explanation:
Find lower quartile first: 1/4 (61)th term which equals to 15.25th term. Use your graph to estimate where 15.25 is and draw a line till it meets tne curve. As soon as it touch the curve, continue the line downward and you'll get LQ in kg. Secondly, find upper quartile: 3/4(61)th term which equals to 45.75th term. Proceed the same thing I mentioned above for lower quartile. Then the formula for interquartile range is upper quartile minus lower quartile and you'll get the answer in kg.
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag. ( insert picture of it)
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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Maggie has $9 less than does her brother Ron,
who has d dollars on Tuesday. If Ron gives
Maggie $6 on Wednesday, and she does not
spend any of her money, which of the following
is an expression for the amount of money, in
dollars, that Maggie has?
A) 2d + 6
B) 2d - 3
C) d + 15
D) d-3
The expression that shows the amount of money in dollars that Maggie has d - 3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let d represent the amount of money Ron has on Tuesday. Hence:
Money Maggie has = d - 9 + 6 = d - 3
The expression that shows the amount of money in dollars that Maggie has d - 3
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Factor the polynomial expression 3x2+2.
A. (3‾√x+2‾√i)(3‾√x−2‾√i)
B. (3‾√x+i)(3‾√x−i)
C. (3‾√x+2‾√)(3‾√x−2‾√)
D. (3x+2‾√i)(3x−2‾√i)
Using the Factor Theorem, the expression 3x² + 2 is factored as follows:
[tex]3x^2 + 2 = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, the expression is:
3x² + 2.
The roots are found as follows:
[tex]3x^2 + 2 = 0[/tex]
[tex]x^2 = -\frac{2}{3}[/tex]
[tex]x = \pm \sqrt{-\frac{2}{3}}[/tex]
[tex]x_1 = -i\sqrt{\frac{2}{3}}[/tex]
[tex]x_2 = i\sqrt{\frac{2}{3}}[/tex]
Hence the factored expression is:
[tex]3x^2 + 2 = \left(x + i\sqrt{\frac{2}{3}}\right)(x - 1\sqrt{\frac{2}{3}}\right) = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]
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Find the volume of the pyramid. Round to the nearest tenth if necessary.
Answer:
53.7
Step-by-step explanation:
The area of the rectangular base is 7(2.3)=16.1.
So, the total volume is (1/3)(16.1)(10), which is about 53.7
Right angle triangle
8x - 21
3x-7
6x
Finds value of x
Step-by-step explanation:
Pythagoras :
c² = a² + b²
the only problem : we don't know which one of the 3 expressions is the longest side (= c = Hypotenuse).
let's try with 8x -21
(8x - 21)² = (3x - 7)² + (6x)²
64x² - 336x + 441 = 9x² - 42x + 49 + 36x²
19x² - 294x + 392 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 19
b = -294
c = 392
x = (294 ± sqrt(86436 - 4×19×392))/(2×19) =
= (294 ± sqrt(56644))/38 =
= (294 ± 238)/38
x1 = (294 + 238)/38 = 532/38 = 14
x2 = (294 - 238)/38 = 56/38 = 28/19 = 1.473684211...
I assume, we are looking for a whole number solution.
so, x = 14 is the solution.
Which of the following best explains the value of Sine StartFraction pi Over 3 EndFraction on the unit circle below
The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.
According to the statement
we have to give the terms which explain the sin (pi/3) perfectly.
And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.
And Now we explain all terms below
So,
"Right Triangle is a triangle whose one of the angle measures 90° "
And "The hypotenuse is a longest side of the right triangle.
And"Unit Circle is a circle with radius 1."
For given question,
We have been given a unit circle.
So, We need to find the sin (pi/3)
We know, in a right triangle for any angle , θ
Sinθ = Opposite side of angle / Hypotenuse
So, for , Sin(pi/3) = Opposite side of angle / 1
Sin(pi/3) = Opposite side of angle
Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.
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Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5
The equation that runs through the location (4,-6) has the slope-intercept form, [tex]y=-\frac{3}{4}x-3[/tex] .
Formation of the equationA line's equation written in the slope-intercept form:
y=mx+b
where m= slope & b= y-intercept
The slope of two parallel lines is equal.
Currently, we know the line's equation:
[tex]y=-\frac{3}{4} x-5[/tex]
here, slope, m= [tex]-\frac{3}{4}[/tex]
A line equation is created by adding the slope's value and the point's coordinates (4, -6):
[tex]-6=-\frac{3}{4}(4)+b[/tex]
⇒ -6=-3 +b [adding 3 to both sides]
⇒-3=b
⇒b= -3
Hence the solution is [tex]y=-\frac{3}{4}x-3[/tex] .
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