The logarithmic expression log₃ 16 changed by the base rule is 2.52.
What is represent as logarithmic expression?The inverse about an exponential function is a logarithmic or log function. To find an exponent, we could use a log function.
To analyze earthquake magnitudes or compare the magnitudes of 2 distinct earthquakes, we must be able to transform among logarithmic and exponential forms.
Let's use this data to create our log. The logarithmic function is as follows:
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, for the stated conditions;
= log₃ 16
Using the Base Rule of log functions, the above expression can be written as,
= ㏒ₓ16/㏒ₓ3
If the base is taken as 10. Then the expression will become.
= ㏒₁₀16 /㏒₁₀3
= 1.204/0.477
= 2.52
Therefore, the value of the given log expression log₃ 16 is obtained as 2.52.
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Find the inverse of each function. Is the inverse a function?
y=-x²+5
The inverse of the function y=2x³+10 is y = [tex]\sqrt[-2]{x-5}[/tex] .
What exactly is an inverse variation?An inverse variation relationship is one in which one variable increases while the other decreases.When two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.
So,
Then,
-y² = x-5y = [tex]\sqrt[-2]{x-5}[/tex]Therefore, the inverse of the function y=2x³+10 is y = [tex]\sqrt[-2]{x-5}[/tex] .
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What is the slope of a line perpendicular to the line whose equation is 6x+y=8
The slope intercept form of a line is y=mx+c, where m is slope.slope of a line perpendicular to 6x+y=8 is 1/6
What is slope intercept form?The slope intercept form of a line is y=mx+c, where m is slope.
The equation of a line is 6x+y=8.
We need to convert to slope intercept form
y=8-6x
y=-6x+8
where m=-6 is slope of a line.
Two lines are said to be perpendicular when m1m2=-1
m1 is slope of given line and m2 is slope of other line which we have to find.
-6.m2=-1
m2=1/6.
Therefore slope of a line perpendicular to 6x+y=8 is 1/6.
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Pedro went to the store and spent $36.85. He paid with a $50 bill. How much money will he get back as
change? Show All Your Work for full credit
Answer: 13.15
Step-by-step explanation:
50
-
36.85
Answer:
Step-by-step explanation:
13.50
-8(b + 3)
I need help with this math question it has to be in distributive property.
Answer: -8b - 24
Step-by-step explanation:
For distributive property, you multiply the number outside of the parenthesis (8) by the numbers/variables inside the parenthesis (b and 3)
-8 × b = -8b
-8 × 3 = -24
Use the Change of Base Formula to evaluate each expression.
log₃54
The value of the expression log₃54 is 3.6.
Given that the expression is log₃54.
We are required to find the value of the expression by using the change of base formula.
The change of base formula is the formula that will give us the answer of a log with a different base by using only log calculations with a base of 10.
The expression is log₃54.
log₃54= log (54)/log (3)
(We know that [tex]log_{a}b[/tex]=log b/ log a)
Now we have to use the values of logarithms in the above expression to find its value.
=1.73/0.48
=3.6
Hence the value of the expression log₃54 is 3.6.
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2x + kx = m solve for x
Answer:
x=m/2+k , k≠-2
Step-by-step explanation:
2x+kx=m
Factor out x from the expression:
(2+k)x=m
Assume 2+k≠0 and divide both sides of the equation by 2+k:
x=m/2k , 2+k≠0
Rewrite the restriction:
x=m/2+k≠-2
Solution:
x=m/2+k , k≠-2
The value of x in the given expression is x = m / (k+2)
What is an expression?An expression is a mathematical statement containing variables, numerical, and they are related by at least one mathematical operation.
Given an expression, 2x + kx = m
We are asked to rearrange the values and find the value of x.
Therefore,
2x + kx = m
Since, two terms have same variable, therefore, taking x common from both,
x(2+k) = m
x(k+2) = m
Now, transpose (k+2) to right side, we get,
x = m / (k+2)
Hence, we get the value of x as, x = m / (k+2)
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Simplify m9m−3 pls answer asap
After simplification of m9m - 3 the answer is 3(3[tex]m^{2}[/tex] - 1).
Given that :
= m9m - 3
a. Reordering terms:
= 9mm - 3
b.Exponents combining:
= 9mm -3
= 9[tex]m^{2}[/tex] - 3
c.Common value factor:
= 9[tex]m^{2}[/tex] - 3
Take 3 has common
= 3(3[tex]m^{2}[/tex] - 1)
Therefore after simplification of m9m - 3 the answer is 3(3[tex]m^{2}[/tex] - 1).
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PLSS HELP :((
will mark brianlist if its the correct answer ty
Answer is B
because i did it out i dont feel like explaning lol
legend has it that the great mathematician carl friedrich gauss (1777–1855) at a very young age was told by his teacher to find the sum of the first 100 counting numbers. while his classmates toiled at the problem, carl simply wrote down a single number and handed the correct answer in to his teacher. the young carl explained that he observed that there were 50 pairs of numbers that each added up to 101. so the sum of all the numbers must be 50•101
The sum of numbers from 1 to 100 is 50 × 101.
Carl Friedrich Gauss is a renowned mathematician. He has contributed many theories to the fields of mathematics and physics.
The sum of the first hundred numbers is calculated by making pairs of two numbers. The sum of these pairs is 101.
And there is a total of 50 pairs.
So, the sum of all these numbers is,
101 ×50
= 5050
Therefore, the sum of numbers from 1 to 100 is 5050.
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Solve. Check for extraneous solutions. (x+3)¹/₂-1=x
-2 is the extraneous solution of the equation.
The equation is:
[tex](x + 3)^{1/2}[/tex] - 1 = x
To find the extraneous solution of the expression first we need to find the value of x.
[tex](x + 3)^{1/2}[/tex] = x + 1
Squaring both sides we have,
[tex](x+ 3)^{}[/tex] = [tex](x + 1)^{2}[/tex]
x + 3 = [tex]x^{2}[/tex] + 2x + 1
[tex]x^{2}[/tex] + x - 2 = 0
[tex]x^{2}[/tex] + 2x - x - 2 = 0
x ( x + 2 ) - 1 (x + 2) = 0
(x+2) (x-1)=0
x = -2, 1
Now we have to put the value of x in the equation:
x = -2
[tex](-2 +3)^{1/2}[/tex] - 1 = -2
1-1 =-2
0≠ -2
x = 1
[tex](1 + 3)^{1/2}[/tex] - 1= 1
2 - 1 = 1
1= 1
Therefore we get x = -2 is as extraneous solution of the equation and x= 1 is the solution of the equation.
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Solve the equation p + 6 = −13 for p.
Which expression is equal to √49/100
A. 7√10/10
B. √7/10
C. 7/10
D. 7/50
Answer:
A
Step-by-step explanation:
70-271=20
Answer: it's 7/10
Step-by-step explanation:
the 49 simplifies to 7, and the 100 simplifies to 10
Maria wants to write a linear function to describe the cost of a cab ride. The cab costs $3 per ride plus an additional $0.20 per mile. a. What is the function that describes the cost of the cab ride for any number of miles? b. how much is the fare for a 15-mile trip? c. How far can she afford to travel if she only has 10$
Answer:
add then simplify
Step-by-step explanation:
Kate and Ismaila were trying to describe parts of the expression 20xy.
• Ismaila said, "20 is a factor in the product 20xy."
. Kate said, "20 is the coefficient."
Who is correct?
Both Katie and Ismailia are both correct because 20 is a coefficient and factor of the expression 20xy.
How to find factor and coefficient of an expression?A coefficient is a number multiplied by a variable.
In other word, a coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial.
A factor is a number that divides another number, leaving no remainder.
Therefore, the coefficient of the expression 20xy is 20.
The factor of the expression 20xy is also 20.
Therefore, Both Katie and Ismailia are both correct.
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Answer:
there both right
Step-by-step explanation:
✔✔✔♂️♂️♀️
Simplify each number. 10,000⁰.⁷⁵
The result of simplifying each number 10,000⁰.⁷⁵ using the properties of exponents is 1
To solve this exercise we have to resolve algebraic operations following the exponent properties.
(10,000⁰)⁷⁵
Using the zero exponent rule that indicates that: any base with an exponent of zero is equal to one, we have:
1⁷⁵
One multiplied by itself many time will be one
1
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Anita is making headbands for her softball team. She needs a total of
3
4
yard of fabric. Which types of fabric cost less than $8 per yard? Write yes or no in each blank.
Fabric Total Cost for
3
4
Yard ($)
Cotton 5.54
Flannel 2.62
Fleece 4.27
Terry Cloth 6.52
Answer: The fabrics that cost less than $8 per yard are cotton, flannel and fleece.
In order to determine the cost of a yard of each material, divide the total cost of 3/4 yards of that fabric by 3/4
cost of a yard = total cost ÷
Cost of a yard of cotton = 5.54 ÷ = 6.85
Cost of a yard of Flannel = 2.62 ÷ = 3.49
Cost per yard of Fleece = 4.27 ÷ = 5.69
Cost per yard of Terry Cloth = 6.52 ÷ = 8.69
Based on the above calculations, all but Terry cloth cost less than $8 per yard
Pleaseeeee helpppppp
Answer:
56°
Step-by-step explanation:
The angles are supplementary. They add up to 180°
So ∠AYZ + ∠AYX = 180
6x+4 + 3x - 4 = 180
9x = 180
x = 20
Measure of ∠AYX = 3x - 4 = 3 x 20 - 4 = 60 -4 = 56°
Please someone solve this its homework
a. the length of the rectangle is 11 units while the width of rectangle is 7 units
b. The rectangles dimensions written as ordered pair (l, w) are
outer rectangle (11, 7)inner rectangle (5, 3)c. the points on coordinate can be (0, 0), (0, 11), (7, 11), and (7, 0).
d. The points are on the first quadrant because I plotted the points starting from the origin and moved in anticlockwise direction
How to calculate the dimensions of a rectangleGiven data
perimeter = 36 units
perimeter of inner rectangle = 16 units
From the inner rectangle as plotted: 5 units on the graph represents 5 units of the rectangle on the x axis and 3 units on the graph represents 3 units on the rectangle on the y axis.
let the length of the outer rectangle be 5x and the width be 3x such that, the perimeter is solved as:
2(5x + 3x) = 36
16x = 36
x = 2.25
For the length
= 5x
= 5 * 2.25
= 11.25
= 11 (as a possible whole number)
For the width
= 3x
= 3 * 2.25
= 6.75
= 7 (as a possible whole number)
Hence we can say that the length is 11 units and the width is 7 units
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need help please and fast
Courtney, the buyer for a small produce store and she sells 25 bags of oranges at $12 per bag. Her cost of goods sold per bag is $7. What is Courtney’s gross profit?
a. $293
b. $300
c. $175
d. $125
Factor each expression completely. 25 x²-40 x y+16 y²
The expression 25x^2 - 40xy + 16y^2 can be factored as (5x - 4y)(5x - 4y).
Factorization is defined as the process of breaking down a number or polynomial into factors that when multiplied will give the same value.
The expression 25x^2 - 40xy + 16y^2 resembles the form
ax^2 + bxy + cy^2 which has factors (mx + ny)(ox + py).
Factoring polynomial expression like 25x^2 - 40xy + 16y^2 can be done by grouping method shown earlier.
Find the two pairs of numbers whose products are 25 and 16.
Taking 5 and 5, and 4 and 4 as the pair of numbers.
(5x - 4y)(5x - 4y)
Checking the product of this factors:
(5x -4y)(5x - 4y)
25x^2 - 20xy - 20xy + 16y^2
25x^2 - 40xy + 16y^2
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what is the slope of the line that passes through the points (6,-8) and (6,-3)
We have a vertical line, so we have an undefined slope.
How to get the slope of the line?The general linear equation in the slope-intercept form is given by:
y = m*x + k
Where we define k as the y-intercept and m as the slope.
If we know that the line passes through two points (a, b) and (c, d), then the slope is given by the formula:
m = (d - b)/(c - a)
In this case we have the points (6,-8) and (6,-3), then the slope will give:
m = (-3 + 8)/(6 - 6)
Notice that the denominator becomes zero, so we have a "slope of infinity", thing that happens for vertical lines
Basically, these lines have undefined slopes, so that is the correct answer.
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Pencils are sold in boxes of 10
Erasers are sold in boxes of 14
A teacher wants to buy the same number of pencils and erasers.
Work out the smallest number of boxes of each item she should buy.
Answer:a
Step-by-step explanation:a cult
Micah sketches the graph below to represent a scenario his teacher gave him
Which scenario could Micah's graph represent?
1.Micah's plant is 1 inch and then grows at a rate of 2 inches per week (where x is the number of weeks), for a total of
y inches.
2.Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y
inches.
3.Micah's plant grows 2 inches per week (where x is the number of weeks) and has a starting height of 1 inch, for a
total of y inches.
4.Micah's plant grows 1 inch per week (where x is the number of weeks) and has a starting height of 1 inch, for a total
of y inches.
A scenario which Micah's graph could represent is: 2. Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
How to calculate the average rate of change?Mathematically, the average rate of change (slope) of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Average rate of change = (6 - 2)/4 - 0)
Average rate of change = 4/4
Average rate of change = 1.
Therefore, Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.
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Answer: b or Micah’s plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.
Step-by-step explanation:
25 students submitted the HW this week, which was 77% of the class. How many students are in the class?
Answer:
Step-by-step explanation:
25 divide 77 = 0.32467532 x 100 = 32 (Leave off the rest, there is no such thing as a fraction of a person in this)
Simplified: (25/77)*100 = 32
To check our answer we would do 32 x 77%(.77) = 24.64 round-up and you get 25!
If you are still confused please do tell :)
Which expression below is equivalent to 10x-35?
(1) 5(2x-7)
(3) 10(x-5)
12) x(10-35)
(4) 10(x-35)
scientific notation for the following numbers (with a power of 10).... someone pleaaaase help me!!! thnx bestie
26,000
425,000
630,000
2,000,000
21,000
231,000
43,000,000
(a) The scientific notation of 26,000 is 2.6 × 10⁴ .
(b) The scientific notation of 425,000 is 4.25 × 10⁵ .
(c) The scientific notation of 630,000 is 6.3 × 10⁵ .
(d) The scientific notation of 2,000,000 is 2.0 × 10⁶ .
(e) The scientific notation of 21,000 is 2.1 × 10⁴ .
(f) The scientific notation of 231,000 is 2.31 × 10⁵
(g) The scientific notation of 43,000,000 is 4.3 × 10⁷ .
The scientific notation helps US to represent the numbers that ar terribly Brobdingnagian or terribly small during a kind of multiplication of single-digit numbers and ten raised to the facility of the individual exponent. The exponent is positive if the quantity is extremely giant and it's negative if the quantity is extremely tiny a × 10ᵇ ; 1 a < ten(a) As 26000 has three zeroes which can be represented by 10³.
scientific notation is given by 26 × 10³ which on simplification gives
2.6 × 10⁴
Hence, 2.6 × 10⁴ is that the scientific notation of the quantity.
(b) As 425000 has three zeroes which can be represented by 10³.
scientific notation is given by 425 × 10³ which on simplification gives
4.25 × 10⁵
Hence, 4.25 × 10⁵ is that the scientific notation of the quantity.
(c) As 630000 has four zeroes which can be represented by 10⁴.
scientific notation is given by 63 × 10⁴ which on simplification gives
6.3 × 10⁵
Hence, 6.3 × 10⁵ is that the scientific notation of the quantity.
(d) As 2,000,000 has six zeroes which can be represented by 10⁶.
scientific notation is given by 2 × 10⁶ which on simplification gives
2.0 × 10⁶
Hence, 2.0 × 10⁶ is that the scientific notation of the quantity.
(e) As 21000 has three zeroes which can be represented by 10³.
scientific notation is given by 21 × 10³ which on simplification gives
2.1 × 10⁴
Hence, 2.1 × 10⁴ is that the scientific notation of the quantity.
(f) As 231000 has three zeroes which can be represented by 10³.
scientific notation is given by 231 × 10³ which on simplification gives
2.31 × 10⁵
Hence, 2.31 × 10⁵ is that the scientific notation of the quantity.
(g) As 43,000,000 has six zeroes which can be represented by 10⁶.
scientific notation is given by 43 × 10⁶ which on simplification gives
4.3 × 10⁷
Hence, 4.3 × 10⁷ is that the scientific notation of the quantity.
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Question: scientific notation for the following numbers (with a power of 10).... someone pleaaaase help me!!! thnx bestie
26,000
425,000
630,000
2,000,000
21,000
231,000
43,000,000
Answer: (a) The scientific notation of 26,000 is 2.6 × 10⁴ .
(b) The scientific notation of 425,000 is 4.25 × 10⁵ .
(c) The scientific notation of 630,000 is 6.3 × 10⁵ .
(d) The scientific notation of 2,000,000 is 2.0 × 10⁶ .
(e) The scientific notation of 21,000 is 2.1 × 10⁴ .
(f) The scientific notation of 231,000 is 2.31 × 10⁵
(g) The scientific notation of 43,000,000 is 4.3 × 10⁷ .
The scientific notation helps US to represent the numbers that ar terribly Brobdingnagian or terribly small during a kind of multiplication of single-digit numbers and ten raised to the facility of the individual exponent.
The exponent is positive if the quantity is extremely giant and it's negative if the quantity is extremely tiny a × 10ᵇ ; 1 a < ten
(a) As 26000 has three zeroes which can be represented by 10³.
scientific notation is given by 26 × 10³ which on simplification gives
2.6 × 10⁴
Hence, 2.6 × 10⁴ is that the scientific notation of the quantity.
(b) As 425000 has three zeroes which can be represented by 10³.
scientific notation is given by 425 × 10³ which on simplification gives
4.25 × 10⁵
Hence, 4.25 × 10⁵ is that the scientific notation of the quantity.
(c) As 630000 has four zeroes which can be represented by 10⁴.
scientific notation is given by 63 × 10⁴ which on simplification gives
6.3 × 10⁵
Hence, 6.3 × 10⁵ is that the scientific notation of the quantity.
(d) As 2,000,000 has six zeroes which can be represented by 10⁶.
scientific notation is given by 2 × 10⁶ which on simplification gives
2.0 × 10⁶
Hence, 2.0 × 10⁶ is that the scientific notation of the quantity.
(e) As 21000 has three zeroes which can be represented by 10³.
scientific notation is given by 21 × 10³ which on simplification gives
2.1 × 10⁴
Hence, 2.1 × 10⁴ is that the scientific notation of the quantity.
(f) As 231000 has three zeroes which can be represented by 10³.
scientific notation is given by 231 × 10³ which on simplification gives
2.31 × 10⁵
Hence, 2.31 × 10⁵ is that the scientific notation of the quantity.
(g) As 43,000,000 has six zeroes which can be represented by 10⁶.
scientific notation is given by 43 × 10⁶ which on simplification gives
4.3 × 10⁷
Have an awesome night/day<3
Find the value of x.
-2x = 3x + 6
Answer:
x= -6/5
Step-by-step explanation:
-2x=3x +6
collect like terms
-6=3x+2x
-6=5x
x= -6/5
Answer: x= -6/5 make that a fraction
decimal form: x= -1.2
mixed number form: x= - 1 1/5, 1 is the whole number
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
help me please
show your solution
Answer:
Rule: Multiplying ×5 in turn
50 { third term}
1,250 {fifth term}
Step-by-step explanation:
2 × 5 = 10 {second term}
10 × 5 = 50 { third term}
50 × 5 = 250 { fourth term}
250 × 5 = 1,250 {fifth term}
The ratio of impressions to fans is a measure of:_____.
a. fan acquisition
b. community
c. engagement
d. amplification
The ratio of impressions to fans is a measure of fan acquisition.
What is social media marketing?Social media marketing is the use of social media platforms and websites to promote a product or service. Although the terms e-marketing and digital marketing are still dominant in academia, social media marketing is becoming more popular for both practitioners and researchersGiven is to find the ratio of impressions to fans.
The ratio of impressions to fans is a measure of fan acquisition. Social marketing campaigns begin with fan acquisition, which involves using any of a variety of means, from display ads to News Feed and page pop-ups, to attract people to your Web page.
Therefore, the ratio of impressions to fans is a measure of fan acquisition.
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