The result of the given logarithmic expression log₉27-log₉9 is log₉ 3.
What is termed as logarithms?A logarithmic term is one that embodies a number in logarithmic form. It can also be referred to as a log term.
A quantity is also the product of two or more quantities. As a result, a term could be the product of two or even more quantities, at least one of which can be in logarithmic form. In such cases, the terms are referred to as log terms.
A quantity is also the quotient of two quantities. So, if a term is also a quotient of quantities, and at least one of the quantities can be expressed in log form, the terms are mathematically referred to as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as per the given question;
= log₉27-log₉9
So, applying the Quotient Rule in the given expression;
= log₉ (27/9)
= log₉ 3
Thus, the given expression simplified in the logarithmic expression as log₉ 3.
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Please help is this true or false
Answer:
True
Step-by-step explanation:
I need help…………………..
Answer:
I believe its 3.5, 6
Step-by-step explanation:
the right arrow points to the last box and after 4 it goes to 5 then 6
the left arrow points at the 3 quarters between 4 and 2 so it's technically 3.5
hope it helps!
Problem Solving
Use the table for Exercises
13-16 that shows the average
weights of popular dog breeds.
13. Complete the table.
14. Which weight(s) have a prime
factorization of exactly three
factors?
Breed
Cocker Spaniel
German Shepherd
Labrador Retriever
Beagle
Golden Retriever
Siberian Husky
Weight (lb)
20
81
67
25
70
50
Prime Factorization
Prime numbers are those numbers that are divisible only by the number itself and by 1. Such numbers are 2, 3, 5, and 7 etc.
Factorization is when we write a given mathematical term in product of its various factors. Suppose we are provided with a mathematical expression of:
x^2 + 3x + 2
We will undergo its Factorization and write the expression in its possible factors:
( x + 1 ) ( x + 2)
By multiplying these factors, we will get the actual expression x^2 + 3x + 2.
Prime Factorization is a method of identifying which prime numbers multiply together to give the original value/expression.
Suppose we have a number 60, then the prime factors of it will be:
60
6 x 10
2 x 3 2 x 5
In the problem statement above, we are provided with some popular dog breeds, and we are expected to find the prime factors of each of the given weights of the breed.
The weights that have a prime factorization of exactly three number are as follows:
Prime factors of 20 (Cocker Spaniel)
= 2 x 2 x 5
Prime factors of 50 (Siberian Husky)
= 2 x 5 x 5
Prime factors of 70 (Golden Retriever)
= 2 x 5 x 7
Weights that have the same number in their prime factorization are:
Prime factors of 81 (German Shepherd)
= 3 x 3 x 3 x 3
Prime factors of 25 (Beagle)
= 5 x 5
So, the prime factorization of the weights of the dog breeds are being found. While Labrador Retriever 67 is a prime number itself.
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Need an answer!! Please and thank you.
Answer: 110 degrees
Step-by-step explanation:
We know that all the angles of a triangle add to 180 degrees. Notice how there are already 60 and 50 degrees on the triangle. In order to find the last angle, we subtract 110 (60+5) from 180 to get 70.
Now, we know that the angle of a straight line is 180.
So, in order to find <BCD, take 70 and subtract it from 180.
Doing this, we find that m<BCD is 110 degrees
Find the highest common factor (HCF) of 90
3. An example of an irrational number is _____.
A. -17 square root
B. square root of 16
C, -9 square root
D. square root for 1
Please help me please help me
Answer:
the third option I think it says (-1,4)
Step-by-step explanation:
So the directions are basically asking to turn in the paper 3 times ending up in the 1st quadrant. Because 90*3 equals 270 degrees. There would be only one point in the negative and there are 2 options. So, we would immediately know that the first option or the last option is wrong. I don't really know how to explain this without drawing so if you could try turning your paper 3 times then you'll see what I mean. Comment if you need any more help. Or if you have any questions. My explanation is pretty bad I apologize.
Wayne charges a flat photography fee of $100 to take pictures. He also charges $35 per hour. If Wayne made $240 to take pictures at an event, how many hours did he spend taking pictures at the event?
Answer:
100 + 35x = 240
240 - 100 = 140 = 35x
140/35 = 4
Step-by-step explanation:
4 hours, not a bad pay o.o
Answer:
4 Hours
Step-by-step explanation:
Let y=money
Let x= Hours
y=mx+b
240=35x+100
minus 100
140=35x
divide 35
4=x
three times the smaller of three consecutive even integers is four less than twice the larger
The required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.
Given:
The statement is three times the smaller of three consecutive even integers is four less than twice the larger
According to given question we have
Let the even integers be x and x + 2 .
Here, x is the smaller integer
(x + 2) the bigger integer.
By the equation is
3x =2(x + 2)-4
compare the like terms we get
x=4-4
x=0
The smaller integer=0
The bigger integer= 0+2=2
Therefore, the required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.
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Simplify each expression. Use only positive exponents. (3 x⁻⁴ y³)²
The simplified value of the expression using only positive exponents is 9y⁶/x⁸
How to simplify the expression using only positive exponents?The expression is given as
(3 x⁻⁴ y³)²
Apply the law of indices to expand the bracket
So, we have
(3 x⁻⁴ y³)² = 3² * x⁻⁴*² y³*²
Evaluate the products of exponents
So, we have
(3 x⁻⁴ y³)² = 3² * x⁻⁸ y⁶
Evaluate the exponents
So, we have
(3 x⁻⁴ y³)² = 9 * x⁻⁸ y⁶
Apply the law of indices to rewrite negative exponent
So, we have
(3 x⁻⁴ y³)² = 9y⁶/x⁸
Hence, the simplified value of the expression using only positive exponents is 9y⁶/x⁸
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What is the difference between 5 and 19?
Answer:
14
Step-by-step explanation:
19 - 5 = 14
Answer:
the difference would be 14
Tyrone makes a scale drawing of his backyard. The scale from the backyard to the
drawing is 2 ft to 1 in. The width of the patio on the drawing is 8 in. What is the
width of Tyrone's actual patio? Show your work.
Answer:The width of the patio on the drawing is 8 in.
Step-by-step explanation:
Write each equation in logarithmic form.
1/10=10⁻¹
The logarithmic form of the equation is [tex]log_{10}\frac{1}{10}=-1[/tex] .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log x The logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e. The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation [tex]\frac{1}{10} =10^{-1}}[/tex] .
Taking log on both sides , we get
[tex]log(\frac{1}{10}) =log(10^{-1})[/tex] ..(1)
Applying the property of logarithm which is given by [tex]loga^b=bloga[/tex] in equation (1) ,we get
[tex]log(\frac{1}{10}) =-log(10)[/tex]
On rearranging the above equation , we get
[tex]\frac{log(\frac{1}{10})}{log10} =-1[/tex] ..(2)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\
[tex]\frac{log(\frac{1}{10})}{log10}[/tex] can be written as [tex]log_{10}\frac{1}{10}[/tex] using property
Putting in equation (2) , we get
[tex]log_{10}\frac{1}{10}=-1[/tex]
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2+z×−1/3=3 please help
2 + z * −1/3 = 3
if that is how it is grouped, your answer is -3
Simplify the following.
a)
3x y x 2x®
Answer:
Hi i think your question implies that
Step-by-step explanation:
3xy × 2x
=6x²y
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A batting average is the ratio of hits to at bats batting averages are expressed as a decimal rounded to the nearest thousandth show two differnt ways if finding how much grater derek jeters batting average than jorge posadas batting average express as a percent
Derek Jeter average was 4.9%greater than Jorge Posada 4.9% expressed as a percent.
To express decimal as percent we need to multiply the decimal with 100 .
The average or mean is defined as the sum divided by the frequency.
Here we have four averages given in decimal
Derek Jeter average in percentage =0.334*100=33.4%
Alex Rodriguez average in percentage=0.286*100=28.6%
Jorge posada average in percentage =0.285*100=28.5%
Hideki Matsui average in percentage=0.274*100=27.4%
From the above percentages Derek Jeter average was 4.9%greater than Jorge Posada =33.4-28.5=4.9%
Or we can say it as Derek peter percentage was 14.68% greater than Jorge Posada on a scale of 100 percentage.
Hence Derek peter percentage was 14.68% greater than Jorge Posada on a scale of 100 percentage and Derek Jeter average was 4.9% greater than Jorge Posada 4.9%.
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Describe in words where cube root of 63 would be plotted on a number line. between 3 and 4, but closer to 3 between 3 and 4, but closer to 4 between 2 and 3, but closer to 2 between 2 and 3, but closer to 3
In words the place that the cube root of 63 would appear on the number line would be: between 3 and 4, but closer to 4
How to find the cube rootThe cube root of 63 would be gotten from a calculator when we use this formula
[tex]^3\sqrt{63}[/tex]
The solution that we would have from the calculator would be 3.97. The value 3.97 is known to be greater than 3 by a lot but just a little less than 4 on the number line.
3.97 can be approximated to be 4. Hence we can say that In words the place that the cube root of 63 would appear on the number line would be: between 3 and 4, but closer to 4
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△LMN with vertices L(4, 8), M(4, 3), and N(8, 8) is rotated 270° clockwise about the origin.
What are the coordinates of L′?
The image of the triangle at point L is L' = (-8, 4)
How to determine the image of the triangle when rotated?The vertices of the triangle are given as:
L(4, 8), M(4, 3), and N(8, 8)
The transformation rule is given as
270 degrees rotation
The rule of 270 degrees rotation is
(x,y) = (-y , x)
When the above rule is applied to the vertices of the triangle, we have:
L' = (-8, 4)
Hence, the image of the triangle at point L is L' = (-8, 4)
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The density of a certain material is such that it weighs 430 kilograms per cubic foot
of volume. Express this density in grams per cup. Round your answer to the nearest
whole number.
Density ( in grams per cup )= 3593
Density( in kilograms per cubic foot )=430
1 kilogram per cubic foot = 8.36 grams per cup
Density ( in grams per cup )= 3593
The density of a material indicates the density of that material in a specific area. The density of a material is defined as its mass per unit volume. Density is a measurement of how closely matter is packed together. It is a distinct physical property of a specific object. Archimedes, a Greek scientist, discovered the density principle. If you know the formula and understand the units, calculating density is simple. Density is represented by the symbol, which can also be represented by the letter D.
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(c) Using your knowledge and abilities show Andrew how to evaluate the expression correctly. State the
correct value.
The correct value of the expression is 9 and to evaluate correctly the multiplication of 2 and 0 that 2(0) must be written 0.
What is an expression?An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.
The constraint of expression is represented as = or <, >.
Given the expression,
x² - 2(x - 3) when x = 3
⇒ x² - 2(x - 3)
⇒ 3² - 2(3 - 3)
⇒ 3² - 2(0)
⇒ 9 - 0
⇒ 9.
Hence "The correct value of the expression is 9".
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The given question is an incomplete complete question shown below in the image ;
Solve the equation using multiplication or division.
-7y=28
Oy=-4
Oy = 4
O y = 14
O y = 35
Answer:
y=-4
Step-by-step explanation:
-7y=28
DIVIDE BY -7
28/-7=-4
Answer=-4
What is the image point of (-1,8)after a translation right 1 unit and up 2 units?
Answer:
so your first number in your plotted points is the x value and the next is the y value as shown here (x,y) so if it needs to go up 2 and right 1 what we do is increase the -1 to a 0 because you are moving right on the graph which makes it become a positive. now if you were to move up 2 that is your y coordinate because y controls up and down movement while x controls left and right movement so you would increase the 8 to 10 so you'll find no coordinates would end up being (0,10)
APR include:
the principle and the term on the loan
finance and interest charges on the loan
finance charges on the loan
the principle and the interest on the loan
Interest on the loan
APR include: Interest on the loan
What does APR mean?
The APR which means annual percentage rate, is the interest rate on the loan, it is expressed in annual terms which is normally compounded monthly, by monthly compounding I mean the interest is computed on monthly basis.
APR has does not have anything to do with the principle and term of the loan since the principle is the loan amount and the term is the number of periods that the borrower is allowed to make repayments until the loan is fully repaid
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k/3 +16 as an expression in words
Sometimes in math we describe an expression with a phrase
"2 more than 5"
can be written as the expression
2 + 5.
Similarly, when we describe an expression in words that includes a variable, we're describing an algebraic expression
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)
There are two ways to write the given expression in words
1.The sum of the quotient of the number k by the number 3 and the number 16.
the sum (+)
quotient k/3 = k : 3
2.The sum of the third part of the number k and the number 16.
third part = k/3
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x
10
8
What is the value of x?
X =
your ans
Step-by-step explanation:
the value of x is 6
The value of x will be 6 for the given triangle.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that in the right-angle triangle, the hypotenuse is 10, the base is 8 and the perpendicular is x.
The value of x will be calculated as:-
x² = 10² - 8²
x² = 100 - 64
x² = 64
x = √36
x = 6
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Calculate.
5*10^9/2*10^4
A sack of bread flour weighs 50. lbs. and costs $9.75.
What is the cost per pound of flour?
What is the cost per ounce of flour?
The cost per pound of flour and cost per ounce of flour is $0.195 per pound and 0.0121875 per ounces.
The cost per pound of flour and cost per ounce of flourWeight of a sack of bread flour = 50 lbsCost of a sack of bread flour = $9.75The cost per pound of flour = Cost of a sack of bread flour / Weight of a sack of bread flour
= $9.75 / 50 lbs
= $0.195 per pound
Convert pound(lbs) to ounce:1 pound = 16 ounces
50 pounds = 50 × 16
= 800 ounces
The cost per ounce of flour = Cost of a sack of bread flour / Weight of a sack of bread flour
= $9.75 / 800
= 0.0121875 per ounces
What is unit cost?This is the cost to acquire a unit of a good or service for a specific quantity that is purchased.
Therefore, the cost per pound of flour and cost per ounce of flour is $0.195 per pound and 0.0121875 per ounces.
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These two triangles are similar .Find side lengths a and b .Note The two figures are not drawn to scale
There are two teams of customer service representatives at a call center for a software company. The call center manager wants to give a prize to the team who most consistently has customer service calls with the least total call times. The two graphs show the distributions of the total call times of the two different teams. Team A 0 3 4 5 1 2 Total Call Times (minutes) Team B 0 I 2 3 4 5 Total Call Times (minutes) Which of the following provides a correct argument in support of the team that should be awarded the prize?
The correct argument in support of the team that should be awarded the prize is; Team A because their distribution of total call times is skewed to the right, which shows the majority of total call times are less than the mean.
How to interpret Skewed Graphs?
A skewed distribution is a distribution which is non-symmetric and also it has no mirror-imaging.
One common characteristic of skewed distributions, is that one tail of the distribution will be quite longer or drawn out relative to the other tail.
A distribution is said to be skewed right when one of the tail is on the right side.
A distribution is said to be skewed left when one of the tail is on the left side.
Now, we want to find the correct argument in support of the team that should be awarded the prize.
Looking at the two graphs of team A and B, we see that team A has a distribution that is skewed to the right which means majority of total call times are less than the mean.
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The length of the rectangle is 4 more than the measurement of its width. The area of the rectangle is 12 m2. Find its dimensions.
(Hint: Area of a rectangle =length x width)
Pls help
The length of the rectangle is 6 meters and the width is 2 meters.
What is perimeter?Perimeter is the sum of the lengths of all the sides of a given 2D plane figure.
A rectangle area has a length that is 4 more than its width.
Assuming the width of the rectangle to be x meter,
∴ The length of the rectangle is (x+4) meters.
Also given that the rectangle area is 12 sq meters.
We know, that the area of a rectangle is a product of its length and width.
∴ [ x × (x+4) ] = 12.
x² + 4x = 12.
x² + 4x - 12 = 0.
x² + 6x - 2x - 12 = 0.
x(x+6) -2( x+6) = 0.
(x+6)(x-2) = 0.
x + 6 = 0 Or x - 2 = 0.
x = -6 or x = 2.
We know distance can not be negative so, x = -6 is inadmissible.
So, the width of the rectangle is 2 meters and length is (x+4) = (2+4) = 6 meters.
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