Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₉3.3
Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 3.3}{log \\9}[/tex]
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 [tex]a^N=x[/tex] is an exponential function 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.
Some important formulas of logarithms are :
log_c (a) +log_c (b) = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
[tex]log_9{3.3}[/tex]
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
[tex]log_9{3.3}[/tex] = [tex]\frac{log \ 3.3}{log \ 9}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 3.3}{log \\9}[/tex]
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Deepa needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4.25 hours and charged her $167
for parts. The total was $655.75. Write and solve an equation which can be used to
determine 2, the cost of the labor per hour.
Answer:115
Step-by-step explanation:
(4.25x) + 167= 117.35
ction T...
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Question 4 (25 points)
Charley wants to start taking golf lessons. There is a one-time fee of $45 to sign up, then it costs $80 per month. a) Write an equation to model
this problem. b) What will be the total cost after 7 months?
a
d
C = 45m +80; The total cost will be $395 after 7 months.
C = 80m + 45; The total cost will be $605 after 7 months.
C = 45m +80; The total cost will be $125 after 7 months.
C = 80m + 45; The total cost will be $125 after 7 months.
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Find the 96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
arithmetic sequence 1, -12, -25, .. .1,−12,−25
an arithmetic sequence can be written as
a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d
nth tern of an arithmetic sequence is
aₙ= a+ (n-1)d
a= first term of an arithmetic sequence
d = common difference of an arithmetic sequence
n = number of terms in an arithmetic sequence
So in the above arithmetic sequence
a= 1
d= -13
n= 96
a₉₆= 1+ (96-1)(-13)
= 1- (95)13
= 1- 1235
= -1234
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
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2 You hang two strands of Decorative light strand one change color every 30 seconds straight to change every 45 seconds both strands just change color how many seconds will the strands change color at the same time
The two strands of Decorative light will shine at same time after every 15 seconds.
What is defined as the Highest common factor?The greatest of all their common factors is the Highest Common Factor (HCF) of more than one number. As a result, it is also known as the greatest common factor (GCF).There isn't an exact formula for determining the greatest common factor of two numbers. However, when considering prime factorization, we can write a statement that aids in evaluating the greatest common factor of more than one number.The stated condition are-
The light strand one change color every 30 seconds.
The light strand second change color every 45 seconds.
Prime factorization of both number are;
30 = 2×3×5
45 = 3×3×5
The numbers with highest power are;
HCF(30, 45) = 3×5 = 15.
Thus, the time after which both the light strands will change colour at the same time is 15 seconds.
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Name the property illustrated by the statement " (7a * 2b) + 3c = 3c + ( 7a * 2b)" Group of answer choices Associative Property of Multiplication Associative Property of Addition Commutative property of Multiplication Commutative Property of Addition
The property illustrated by the statement where the equation is given as (7a * 2b) + 3c = 3c + (7a * 2b) is the Commutative Property of Addition
How to name the property illustrated by the statement?The equation is given as
(7a * 2b) + 3c = 3c + (7a * 2b)
The Commutative Property of Addition states that
a + b = b + a
In this case
a = (7a * 2b) and b = 3c
When the Commutative Property of Addition is applied using the above variables, we have
(7a * 2b) + 3c = 3c + (7a * 2b)
Hence, the property illustrated by the statement where the equation is given as (7a * 2b) + 3c = 3c + (7a * 2b) is the Commutative Property of Addition
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Students in Mr. Kendrick's class are divided into two groups for an activity. Students in group A must always tell the truth. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if he and Janeka are in group A or B, Jonah says, "We are both in Group B. " To which group does each student belong? Explain your reasoning
In the class of Mr. Kendrick's, Jonah is in Group B and Janeka is in Group A using the concept of Logical Reasoning.
As per the question statement, we are given that in Mr. Kendrick's class, students are divided into two groups for an activity. Students in group A must always tell the truth and correct info. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if Jonah and Janeka are in group A or B, Jonah says, "We are both in Group B. "
By their statement and using the concept of Logical Reasoning, we can conclude that Jonah is in Group B and Janeka is in Group A.
As Jonah said, "We are both in Group B. " and as both the students can't be in same group so Jonah lied and hence he is in group B and Janeka is in group A.
This is a classic example of Logical Reasoning.
Logical Reasoning: Working through a set of rules that govern a scenario is a method of problem-solving known as logical reasoning.
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⚡️PLEASE HELP-URGENT⚡️
I only need help with 34.. but I. So confused and I need to go to bed
-12
----- = -4 that's the key to the operation so -4x 3
3
Determine if the sequence below is it arithmetic or geometric in determine the common difference/ratio in the simplest form 125,25,5
The sequence given by the terms 125,25,5 is a geometric sequence with common ratio 1/5.
In a geometric sequence, each term following the first is found by multiplying the preceding one by a constant, non-zero quantity known as the common ratio.
The nth term of a geometric series with first term a and common ratio r is given by [tex]a_n=ar^{n-1}[/tex] .
In the given sequence, the first term denoted by a is 125. The second term is 25 and the third term is 5.
Ratio of the second term to first term = 25/125 = 1/5
And the ratio of third term to second term is = 5/25 =1/5
Hence since the ratios are equal therefore the sequence is geometric, and the common ratio is 1/5 .
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The product of two positive integers is always
Answer: positive
Step-by-step explanation: That's just how it works. It's an algerbra rule. Hope that helped. Have a nice day.
Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.
HELP..........................
Answer: D
Step-by-step explanation:
3. ASSESS REASONABLENESS Two moving truck companies offer the same
vehicle at different rates. At Haul-n-Save, the truck can be rented for $30,
plus $0.79 per mile. At Rent It Trucks, the truck can be rented for $75,
plus $0.55 per mile.
a. Write equations for the total cost of renting a truck from each company.
b. Graph the equations on the same coordinate plane. Examine the graph
to estimate after how many miles of driving the total rental cost will be
the same from each company.
c. Check your estimate. How reasonable is your estimation?
Justify your reasoning.
Using linear functions, it is found that:
a. The equations are given by: H(x) = 30 + 0.79x, R(x) = 75 + 0.55x.
b. The costs will be the same after 187.5 miles.
c. The estimate from the graph is reasonable, as it is the value of x for which both equations are equal.
What is the definition of a linear function?A linear function is defined according to the following rule:
y = mx + b
In which:
m is the slope of the function, also called the rate of change of the function, given by the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For each function in the context of this problem, we have that:
The slope is the cost per mile.The intercept is the rent cost.Hence the equations for each company are given as follows:
H(x) = 30 + 0.79x.R(x) = 75 + 0.55x.The graph is given at the end of the answer, and from the intersection point, we have that the costs will be the same after 187.5 miles.
Numerically, this value is given as follows:
H(x) = R(x)
30 + 0.79x = 75 + 0.55x
0.24x = 45
x = 45/0.24
x = 187.5.
Hence the estimate from the graph is reasonable.
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Ryan wants to buy two video games. One costs $35.89 and the other costs $43.65. He estimates the total cost of the two games to be about $80. Is his estimate higher or lower than the actual cost? Explain.
Answer:
Actual cost = 35.89 + 43.65 = 79.54 so it is some what lower than estimated cost.
Step-by-step explanation:
PLEASE HELP ME! Find the percent of change when 40 is increased to 83. If necessary, round your answer to the nearest tenth.
51.8% increase
51.8% decrease
107.5% increase
107.5% decrease
The percent of change when 40 is increased to 83 to the nearest tenth is: C. 107.5% increase.
The types of percentage.In Mathematics, there are two main types of percentage and these include the following:
Percentage decreasePercentage increaseMathematically, percentage increase can be calculated by using this formula:
Percentage increase = [Final value - Initial value]/Initial value × 100
Substituting the given parameters into the formula, we have;
Percentage increase = [83 - 40]/40 × 100
Percentage increase = 43/40 × 100
Percentage increase = 1.075 × 100
Percentage increase = 107.5%.
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Which of the following equations have an infinite solution set?
The equation has infinite solutions is the last option:
6(x - 1) = 2*(3x - 3)
Which equation has an infinite solution set?Any equation in which we can remove the variable has infinite solutions (because it does not depend on the value of x) only if the equation is true.
Let's look at the fourth equation:
6(x - 1) = 2*(3x - 3)
If we expand both sides, we will get:
6x - 6 = 2*3x - 2*3
6x - 6 = 6x - 6
So we have the exact same thing in both sides, if we remove 6x - 6 in both sides we will get:
0 = 0
Then this equation has infinite solutions.
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Find the exact value of cos (-315)° .
Answer:
[tex]\frac{1}{\sqrt{2}}[/tex]
Step-by-step explanation:
cos(-315)° = cos 315°
The cosine function is an even function.cos 315° = cos 45°
cos(360°-x)=cos(x)This is equal to
[tex]\frac{1}{\sqrt{2}}[/tex]
Anybody know the answer to this question?
Answer:
slope 1/3
y = -2
x=1/3-2
Step-by-step explanation:
slope 1/3
y = -2
x=1/3-2
Look at the image.
Please help
Answer:
well, best i can do for you : F
Step-by-step explanation:
Calculator soup
I forgot how to do this stuff, sorry
PLEASE HELP!!!!
Translation using the rule
(x. y)-(x-5. y).
Answer:
P= (-12,0)
Q= (0,-8)
R= (-2,-16)
P'= (-17,0)
Q'= (-5,-8)
R'= (-7,-16)
Step-by-step explanation:
Assuming that each square is equal to one point, the shape is in quadrant 3, where all coordinates are negative.
Determine where each coordinate is for P, Q, and R; then move over each x coordinate by -5 (a.k.a. subtract 5).
This will give you your translation to P', Q', and R'.
Please let me know if I made any mistakes, and hope this helped!
İfadesinin en sade şekli aşağıdakilerden hangisidir?
Answer:
A
Step-by-step explanation:
if the test scores of a class of 35 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 65.6, then the mean of the combined group is
The mean of the combined group of classes is 69.35
Mean is given by by dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).
It is given that,
The mean of test scores of a class having 35 students = 73.1
And,
The mean of test scores of a class having 26 students = 65.6
We need to find,
The mean of the combined group of classes = mean of both classes
Mean of both classes = [tex]\frac{73.1 + 65.6}{2}[/tex]
= [tex]\frac{138.7}{2}[/tex]
= 69.35
Hence, 69.35 is the mean of the combined group of classes
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Solve each equation. If necessary, round to the nearest ten-thousandth. log₇3 x=3
The solution of the given equation by rounding off it to the nearest ten-thousandth is 7.8295.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: log₇3x = 3
We are given a logarithmic expression: log₇3x = 3 —- 1
We know that log₇3 = log 3 / log 7 and log (ab) = log a + log b
Using in equation 1, we have,
log₇3x = 3
log 3x / log 7 = 3
(log 3 + log x) / log 7 = 3
log 3 + log x = 3 × log 7
log 3 + log x = 2.535
log x = 2.535 - 0.4771
log x = 2.0579
x = 7.8295
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 7.8295.
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Four friends are on vacation in Hawaii.
Leilani is hiking in Oahu at 952 m in elevation.
Keanu is snorkeling at -2 m in elevation.
Kiah is scuba diving at 608 m in elevation.
Kanoa is enjoying a picnic at 4 m in elevation.
Which friend is closest to sea level?
6000 was rounded to 1 significant figure.
What is the lower bound?
1. Find the sum of the measures of all the angles in all of the triangles shown in
this diagram.
The sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.
We need to find the sum of the measures of all the angles in all of the triangles shown in this diagram.
What is the triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
The sum of all the angles of the triangle is equal to 180°.
From the figure, by counting, we get there are 20 triangles.
As we know, the sum of all the interior angles of a triangle is 180°.
So, the sum of the measures of all the angles in all of the triangles = The number of triangles × 180°
= 20 × 180°
= 3,600°
Therefore, the sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.
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10. The mass of planet Earth is about
5.98 x 1024 kilograms. How many significant
digits does this number contain?
The scientific notation has 3 significant digits.
What is a scenic notation?A significant number is the the numbers that are in in the coefficient of an expression in scientific notation, 5, 9 and 8 are the significant numbers.
Scientific notation is used in expressing large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example, the number : 1 x 10² is equivalent to 100
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Yuson must complete a certain number of hours of community service. she does 2 hours of service each day. after 8 days, yuson has completed half of her required community service.
Answer:
i don't know what the question is but the total amount of comunity service she must do is 32 hours
Step-by-step explanation:
2 x 8 = 16 16 x 2 or 16 + 16 = 32 thus she must complete 32 hours of comunity service and she has already completed 16 hours of comunity service so she has 16 hours left to complete.
hope this helped = )
Solve the equation
sec x=√2 in the interval 0≤x≤2π
[tex]\displaystyle\\Answer:\ x=\frac{\pi }{4} \ \ \ \ \ x=\frac{7\pi }{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\secx=\sqrt{2} \ \ \ \ 0\leq x\leq 2\pi \\\\\frac{1}{cosx} =\sqrt{2} \\\\cosx=\frac{1}{\sqrt{2} } \\\\cosx=\frac{(1)(\sqrt{2)} }{(\sqrt{2})(\sqrt{2)} } \\\\cosx=\frac{\sqrt{2} }{2} \\\\x=\frac{\pi }{4} \\\\x=\frac{7\pi }{4}[/tex]
Bill and Ted plan to buy a ps4 for $299.00. Games for the system cost $60 each. They plan to buy one console to share. If bill and Ted buy 1 console and 3 games, how much will they spend total?
Answer:
$459
Step-by-step explanation:
60x3=180
$299+180=$459
On a map 2cm represents 30 mi. The actual distance between two towns is 75mi. What is the distance between the towns on the map
On the map, the separation between the two towns would be 5 cm.
Detailed explanation:
First, consider 2 cm and 30 miles as a ratio, which means that wherever you measure 2 cm with a ruler on a map, 30 miles will be scaled to that location.
Then, using some logic, we can state that if 2 cm = 30 mi, then 4 cm = 60 mi (double the 2 cm will result in doubling the 30 cm), and 1 cm = 15 mi (if you divide the 2cm by 2, 30mi will also be divided by 2). Because of this, 5cm (4cm + 4cm + 1cm) on the map equals 75mi (which is 30mi + 30mi + 15mi).
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