value of x in given logarithmic equation is = 2000
What is logarithmic function ?In, mathematics a logarithmic function is inverse of exponential function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function
x is the expression
Mathematically, if [tex]a^x = N[/tex] is and exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to given statement,
log x - log 2 =3
using formula, log a - log b = log a/b
=> log x/2 = 3
=> x / 2 = 10³
=> x = 2 . 10³ = 2000
Thus solution for this equation is x =2000.
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WILL GIVE BRAINLEST!!!
Which shows the best use of the associative and commutative properties to make simplifying [tex]\frac{1}{6} -8+3- \frac{5}{6} +9[/tex] easier?
A. (1/6 - 5/6) + [3+9+ (-8)]
B. (3 +1/6) + [9+(-8)+(-5/6)]
C. [1/6 + (-8)] + [3+(-5/6) +9]
D. [3 +9 + 1/6] + [ - 5/6 + (-8)]
Answer:
a
Step-by-step explanation:
There are 62 people at the commuter area waiting to catch carpool vans. Each van can fit 9 people. How many vanes will be needed to transport everyone so that no one is left behind?
Answer:
7 vans
Step-by-step explanation:
62 ÷ 9 = 6.86.8 is not a whole number, so when you round it to the nearest whole number you get 7.[Also, 9 × 7 = 63, which is close to 62]∴ 7 vans will be needed.
Answer:
7 vans
Step-by-step explanation:
Each van can take 62 people so you share the 62 among the vans, and each van is 9,therefore 62÷9=6.888889 and people cannot be in decimals so you round the figure to a whole number which is equal to 9.
simplify 6/22 = ?/? please help
Answer:
3/11
Step-by-step explanation:
divide each side by 2
Answer:
3/11
Step-by-step explanation:
Let's simplify the value,
→ 6/22
→(6 ÷ 2)/(22 ÷ 2)
→ 3/11
Thus, the value is 3/11.
In an arithmetic series, s40 = 1900 and u40 = 106. find the value of the first term and the common difference.
The first term and common difference of the arithmetic series are -11 and 3.
How to solve an arithmetic series?In the arithmetic series, S₄₀ = 1900 and U₄₀ = 106
Hence,
Sₙ = n / 2 (2a + (n - 1)d)
S₄₀ = 20(2a + 39d)
S₄₀ = 40a + 780d
1900 = 40a + 780d
Uₙ = a + (n - 1)d
U₄₀ = a + 39d
106 = a + 39d
Combine the equation
a + 39d = 106
40a + 780d = 1900
20a + 780d = 2120
40a + 780d = 1900
20a = - 220
a = -220 / 20
a = -11
Hence,
106 = a + 39d
106 = -11 + 39d
106 + 11 = 39d
117 = 39d
divide both sides by 39d
d = 117 / 39
d = 3
Therefore, the first term and common difference of the arithmetic series are -11 and 3.
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You have solved equations containing square roots by squaring each side. You were using the property that if a=b then a²=b² . Show that the following statements are not true for all real numbers.
a. If a²=b² then a=b .
If a² = b² , then a = b is not true for all real numbers.
We know that ' if a = b, then a² = b²'.
We need to prove that the converse of this statement is not always true.
i.e., we need to show that if a² = b² , then a = b is not true for all real numbers.
To show that a statement is wrong we just need to find a counter example for the statement.
For this, let a = -5 and b = 5.
Clearly, a ≠ b
But -5² = 25 and 5² = 25
That is, a² = b² but a ≠ b.
Hence we proved that 'If a² = b² , then a = b is not true for all real numbers'.
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The expression 0.036m³/₄ is used in the study of fluids. Which best represents the value of the expression for m=46 x 10⁴ ?
(A) 636
(B) 1460
(C) 1660
(D) 16,600
The value of the expression 0.036m³/₄ is determined by algebraically substituting the value of m=46 x 10⁴ and solving the radical expression.
In the given radical expression, 0.036 is a constant and m is a variable with a power of ¾.
We will solve for the variable term first which will be written as a radical and multiply it with the constant.
Substituting m=46x10⁴ in the expression 0.036m³/₄.
0.036m³/₄=0.036(46x10⁴)³/₄
Now rewrite the expression as a radical,
0.036(46x10⁴)³/₄= 0.036∜(46*104)3
Multiply the exponents within radicand term,
= 0.036∜(463*1012)
Now simplify the expression,
= 0.036∜(463*(103)4
= 0.036*103 *∜463
= 0.036*103 *∜97,336
= 36 ∜97,336
= 36*17.66≈636
Hence, the correct answer is option A.
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Mariam took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.90 plus $1.25 per mile. The total fare was $6.65, not including the tip. Write and solve an equation which can be used to determine m, the number of miles in the taxi ride.
Equation:
Answer: m =
Answer:
are there options?
Step-by-step explanation:
89 + 38 x 2 = ?
Giving crown
Answer: 254
Step-by-step explanation:
89 + 38 x 2
89 + 38 = 127
127 x 2 = 254
Two of Ms. Cole's Earth science classes have 23 students each. Box plots for recent test scores for these two classes are
displayed.
Third Period
←++ ++ ++
45 50 55 60 65 70 75 80 85 90 95 100
Which statement about the scores is true?
▬
Fifth Period
1
+++
++
45 50 55 60 65 70 75 80 85 90 95 100
The option B , which says that the mean of the two data sets are equal is the correct statement.
To answer the question we need to understand the meaning of a boxplot
A boxplot is a standardized way of showing the distribution of data based on a five number summary minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
According to the problem showed in question ,
As we can see from the two box plots that the mean for both the box plots is less than 80 but greater than 75.
Hence we can say that the mean of the two given data sets are equal
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wwwwwhat is a/-3-6=-1
Evaluate each logarithm.
log₁₂ 144
The logarithmic equation log₁₂ 144 = 2
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if is an exponential function is [tex]a^N=x[/tex] then, this can be converted to logarithmic function as [tex]log_ax=N[/tex]
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
According to statement,
log₁₂ 144
this can be written as ,
log₁₂ (12²)
= 2 log₁₂ (12)
= 2 . 1 (as, log a with base a = 1 )
= 2
Thus , log₁₂ 144 = 2
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What is the equation of the line that passes through the point (2,-1)and has a slope of 1
Answer:
y = x - 3.
Step-by-step explanation:
We use the point-slope form of the straight line:
y - y1 = m(x - x1) where m = slope and (x1, y1) is a point on the line.
So, for this line we have:
y - (-1) = 1(x - 2)
y + 1 = x - 2
y = x - 2 - 1
y = x - 3.
How much can 4 go into 150
Answer:
37.5
Step-by-step explanation:
37.5
4 | 150.0
- 12 ↓
---------------
30.0
- 28 ↓
-----------------
20
- 20
--------------------
0
I hope this helps!
What is the solution of each system of equations? Solve using matrices.
b. [4x-6y=9 -10x+15y = 8]
The system of equations which is as represented in the task content above when solved by elimination, substitution or matrices has no solution.
This goes to say that the above given system of equations ultimately has no solution using matrices
What is the solution of the system of equations given in the task content?It follows from the task content that the solution pair of the system of equation as given in the task content is to be determined.
Given system of equation;
4x-6y=9
-10x+15y = 8
By multiplying the first equation by 5 and the second equation by -2; we have;
20x - 30y = 45
20x - 30y = -16
Hence, it is evident that the system of equations above has equal slope but different intercept equations.
Consequently, subtract equation 2 from 1 so that we have;
0 = 61....an equality which doesn't hold true.
Ultimately, the system of equations has no solution.
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A 1200 gram sample of radioactive matter will completely decay (be undetectable) in 10 hours. There exists a set of ordered pairs (t. m), where t is the amount of time in hours that the substance has been decaying, and m is the mass in grams that has decayed.
If t≥ 0, what is the range of m?
Using it's concept, the range of the function is given as follows:
0 ≤ m ≤ 1200.
What is the range of a function?The range of a function is the set that contains all possible output values for the function.
For this problem, we have to consider these two bullet points next, considering the mass is the output value of the function.
The smallest possible mass for the substance is of 0 grams, as after the substance decays to 0 grams, it will not assume a negative value, it will just disappear.The greatest possible mass for the substance is the initial mass of 1200 grams, as the substance does not adquire mass with time, it just loses it.Considering these masses, the range of the function is given as follows:
0 ≤ m ≤ 1200.
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PLS HELP I NEED RN AND ALSO THANKS!!
A Picture of the work is attached
The side AC is 8.5 cm.
What is AC?We know that a triangle is a polygon that has three sides. There are so many kinds of triangle such as;
Right angle triangleScalene triangle Isosceles triangle Equilateral triangleIn this case what we have is a right angled triangle ABC. Having seen this, we now have to find the side that has been marked AC in the triangle shown.
In this case, we are required to obtain the side that has been marked as AC and we have to use the given side AB and the angle that is given as angle BAC.
Now;
AB = 11 cm
Angle BAC = 39 degrees
AC = unknown
Thus we now have to make use of the trigonometric ratios;
Cos θ = opposite/ adjacent
opposite = AC
Adjacent = 11 cm
AC= 11 cm cos 39 degrees
AC = 8.5 cm
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Please help me please please
Simplifying the problem, 4 - 9 + 5 - 1 - 6 + 11 would give the result of 4.
How to simplify equation?In order to simplify the problem given of 4 - 9 + 5 - 1 - 6 + 11, you can put the numbers into brackets and then carry out math operation:
= (4 - 9) + (5 - 1) - (6 + 11)
Solving the numbers in the brackets gives:
= -5 + 5 - 1 - 6 + 11
= 4
In conclusion, the simplified form would be 4.
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Is 4 x 10³ or 2 x 10⁸ larger in value? Explain why.
Need some help with this..
Answer:
Step-by-step explanation:cevaplandıında banada haber verin rez kardeşlerim
Jordan's t-shirt business sells long sleeve shirts for $15 and short sleeve shirts for $10. he needs to make at least $300 to buy a new heat press machine. so far, fewer than 28 people have purchased shirts. which system of inequalities fits this scenario?
The system of inequalities fits in this scenario are x + y & lt; = 2815x + 10Y & lt;= 300.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a & gt; b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered. In the given questions the inequalities are x + y & lt;= 2815x + 10y & lt;= 300
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HELP PLEASEEEEEEEEEE
Answer:
11:50 AM
Step-by-step explanation:
We should first find the sum of the times it would take her to clean each room, along with the break time.
Kitchen = 80 minutes
Lounge = 40 minutes
Bedroom = 90 minutes
Bathroom = 35 minutes
Break = 45 minutes
[tex]\text{Total time (in minutes) } = 80 + 40 + 90 + 35 + 45 = 290.[/tex]
We should then divide this amount of minutes by 60 to find how many hours it took her.
[tex]\text{Total time (in hours) } = \frac{290}{60} = 4\frac56[/tex]
This means it took her 4 hours and 50 minutes to finish cleaning.
Therefore, if she started working at 7 AM and worked for 4 hours and 50 minutes, she was done by 11:50 AM.
she had to choose between two families to babysit for. the first family offers her 40 plus $5 per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make
The offer that will make her more money and how much more will she make is
The first offer$15 dollars moreThis is further explained below.
Which offer will make her more money and how much more will she make?Generally, the equation for the total made is mathematically given as
T= flat rate +(hours worked*hourly pay)
Therefore, for the first family
T= 40 + (6+5)
T=$51
For the 2nd family
T'= 20 + (6+10)
T'=$36
In conclusion, the offer that will make her more money and how much more will she make is
T'=51-36
T'=$15
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CQ
Simone wants to babysit this weekend to make some extra money she changes a flat fee then changes per hour or part thereof that she babysits Saturday afternoon she will babysit for 6 hours she had to choose between two families to babysit for. the first family offers her 40 plus $5 per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make
Solve. Check for extraneous solutions. 2(x-1)⁴/₁+4=36
No extraneous solution to the equation
The equation is
2[tex](x - 1)^{4/1}[/tex] + 4 = 36
We have to find the extraneous solution of the equation and for this first, we need to find the value of x.
2[tex](x - 1)^{4}[/tex] + 4 = 36
2[tex](x - 1)^{4}[/tex] = 32
[tex](x - 1)^{4}[/tex] = 16
x - 1= 2
x = 3
Now we will put the value of x in the equation.
2[tex](3 - 1)^{4}[/tex] + 4 = 36
2 [tex]2^{4}[/tex] + 4 = 36
2 × 16 + 4 = 36
32 + 4 = 36
36 = 36
Therefore we get that there is no extraneous solution to the equation, x = 3 is the solution of the equation.
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Measure of each numbered angel m<1=38
The measures of the angles are <1 = 38, <2 = 142, <3 = 38 and <4 = 142
How to use the diagram to find the angle measures that satisfy each case?The diagram that completes the question is added as an attachment
From the diagram, we have
<1 + <2 = 180 degrees --- supplementary angles
Given that
<1 = 38 degrees
We have
38 + <2 = 180
Evaluate
<2 = 142
Also, we have
<3 = <1
<4 = <2
This means that
<3 = 38
<4 = 142
Hence, the measures of the angles are <1 = 38, <2 = 142, <3 = 38 and <4 = 142
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Write 0.33 as a percentage.
Answer:
33%
Step-by-step explanation:
moving the decimal two places to the right
Can someone to help me answer this
I am pretty sure it is the top right graph
how do you know when a table is a function? explain
Answer:
You know a table is a function when each element inside the domain matches with only one element within the range.
Answer: You know a table is a function when each element inside the domain matches with only one element within the range.
Step-by-step explanation: hope this helps
HELP ME ASAP PLSSS
Y = x*-0.25
Hope this helps.
The change in position from the shaded figure to the unshaded figure is best described as a __________.
a.
reflection
c.
translation
b.
transversal
d.
rotation
Please select the best answer from the choices provided
A
B
C
D
The change in position from the shaded figure to the unshaded figure is best described as a translation.
What is a translation transformation?A translation transformation is such that the entire shape is copied and then this copy is moved to another part of the graph.
In a translation, the size of the shape does not change. Other things that don't change include the orientation of the shape. It remains the exact same, but in a new location.
The shape, size and orientation of the shaded figure is the same as the unshaded figure so this is a translation.
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-160=6x-8(5x+3) what is my answer
The answer to the expression -160=6x-8(5x+3) is x = 4.
What is an expression?An expression is written in the form of variables and constants combined with arithmetic operations. There are many types of expressions in mathematics they are algebraic expressions, logarithmic expressions, trigonometric expressions, and many more.
The given expression - 160 = 6x - 8(5x+3) can be writen as,
6x - 8(5x+3) = -160.
First, we will distribute what is inside the brackets.
∴ 6x - 40x - 24 = -160.
-34x = -160 + 24.
-34x = -136.
34x = 136.
x = 136/34.
x = 4.
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