Write expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
Answers
Solution
Note: Laws Of Logarithm To Use
[tex]\begin{gathered} (1).\text{ }log_a(M)-log_a(N)=log_a(\frac{M}{N}) \\ \\ (2).\text{ }log_a(b^n)=nlog_a(b) \end{gathered}[/tex]From the question, we have
[tex]\begin{gathered} log_3(18)-log_3(2) \\ \\ log_3(\frac{18}{2}) \\ \\ log_3(9)\text{ } \\ \\ The\text{ above expression is single logarithm} \end{gathered}[/tex]To evaluate, we have
[tex]\begin{gathered} log_3(9)=log_3(3^2) \\ \\ log_3(9)=2log_3(3) \\ \\ log_3(9)=2(1) \\ \\ log_3(9)=2 \end{gathered}[/tex]The answer is
[tex]2[/tex]Related Questions
23,000,000 in scientific notation.
Answers
Answer:
2.3 x 10⁷
Explanation:
A number is said to be in scientific notation when it is written in the form:
[tex]\begin{gathered} A\times10^n \\ \text{where:} \\ \text{A is between 1 and 10} \\ n\text{ is an integer} \end{gathered}[/tex]Given the number: 23,000,000
The number has 8 digits before the decimal point.
Therefore, in standard notation we have:
[tex]23,000,000=2.3\times10^7[/tex]Solve the following and give the interval notation of the solution and show the solution on a number line. 6x-12(3-x) is less than or equal to 9(x-4)+9x
Answers
The Solution:
The given inequality is
[tex]6x-12(3-x)\leq9(x-4)+9x[/tex]Clearing the brackets, we get
[tex]6x-36+12x\leq9x-36+9x[/tex]Collecting the like terms, we get
[tex]\begin{gathered} 6x+12x-9x-9x\leq-36+36 \\ \end{gathered}[/tex][tex]\begin{gathered} 18x-18x\leq0 \\ 0\leq0 \end{gathered}[/tex]So, the solution is true for all real values of x.
The interval notation of the solution is
[tex](-\infty,\infty)[/tex]How do I simplify my answer of 42i^2+32i+6 when the original problem was (2-6i)(3-7i)
Answers
Given problem is
[tex](2-6i)(3-7i)[/tex]Now,
[tex]\begin{gathered} (2-6i)(3-7i)=42i^2-14i-18i+6 \\ =42i^2-32i+6 \end{gathered}[/tex]We know that
[tex]i^2=-1[/tex]Using this face,
[tex]\begin{gathered} 42i^2-32i+6=-42-32i+6 \\ =-32i-36 \end{gathered}[/tex]Hence, the simplified form is
[tex]-32i-36[/tex]Identify the algebraic expression for the following word phrase: 5 less than twice a number y.
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Answer:
5-2y because 5 less is 5- and 2 twice a number is y number is y and twice mean 2
Look at the photograph and if you need anything let me know
Answers
Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.
Therefore, the answer is the first option.
O GRAPHS AND FUNCTIONSGraphing a piecewise-defined function: Problem type 1
Answers
Answer:
Explanation:
To get the plot of h(x), we just plot the given values of y at the given values of x.
For example, we are told that between x = -3.5 and -2.5, h(x) = -3. Therefore, the plot gives
The hollow circle tells us that the value x = -3.5 itself is not included. The solid circle tells us that x = -.2.5 is included. All this comes from the fact that the interval given is -3.5 < x ≤ -2.5.
Using the same method for other entries on the graph, we get our desired plot.
b. (-4,-1) Y= 4/3 x + 6What’s the equation of the line in standard form
Answers
When two lines are perpendicular, the slopes of the lines m1 and m2 are related such that
m1m2 = -1
from the given equation comparing with tyhe general form of the equation of a line (y = mx + c)
m1 = 4/3
The slope of the perpendicular line is -3/4
The equation of the line
y- -1 = -3/4(x - -4)
y + 1 = -3/4(x + 4)
y + 1 = -3x/4 - 3
Subtract 1 from both sides
y + 1 - 1 = -3x/4 - 3 - 1
y = -3x/4 - 3 - 1
y = -3x/4 - 4
This is the standard form of the equation
The polynomial expression x(3x^2+25)(10x^2+4x+6), where x is in inches, can be used to mod the number of cubic inches of cement that will be needed for a new porch. The cement contractor used 2 for the value of x.
Answers
Since x is given in cubic inches, let's split the expression like this:
[tex]\begin{gathered} h=height=x \\ w=width=(3x^2+25) \\ l=length=(10x^2+4x+6) \end{gathered}[/tex]For x = 2:
[tex]\begin{gathered} h=2in \\ w=3(2)^2+25=37in \\ l=10(2)^2+4(2)+6=54in \end{gathered}[/tex]pets : | bird | cat | dog | snake |frequency: | 3 | 5 | 11 | 1 |which of the following statments does NOT reflect the distribution of the data?a. one-fourth of the pets are catsb. snakes represent 10% of the pets on the farmc. the number of biirds and snakes on the farm make up 20% d. more than half of the pets on the farm are dogs
Answers
SOLUTION:
Case: Interpreting from tables
The total number of pets is 20
Checking the options
Option A.
One-fourth of the pets are cats
[tex]\frac{1}{4}\times20=5\text{ }pets[/tex]This is TRUE from the table
Option B
Snakes represent 10% of the pets on the farm
[tex]\begin{gathered} 10\%\times20 \\ \frac{10}{100}\times20=2\text{ }pets \end{gathered}[/tex]This is FALSE from tables as there is only 1 snake
Option C
The number of biirds and snakes on the farm make up 20%
[tex]\begin{gathered} 20\%\times20 \\ \frac{20}{100}\times20=4\text{ }pets \end{gathered}[/tex]This is TRUE from the table
Option D
More than half of the pets on the farm are dogs
[tex]\frac{1}{2}\times20=10\text{ }pets[/tex]This is TRUE from the table
1. Sally uses 312 cups of flour for each batch of cookies.
How many cups does she need to make 4 batches of cookies?
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The table below shows the relationship between the number of hours a student studied and theirgrade on a certain test.
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It is necessary to adjust the given points of the graph to a line. The general form of the equation of a line is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept of the line.
To calculate the slope m, use the following formula:
[tex]undefined[/tex]Penelope graphed the function below using the domain { 0,1,2,3,4 } .X + y = 4 Which graph did Penelope make ?
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Given data:
The given equation x+y=4.
Substitute 0 for x in the given equation.
0+y=4
y=4.
Substitute 0 for y in the given equation.
x+0=4
x=4
So, the graph of the equation must pass from (0,4) and (4,0).
Thus, the option (a) is correct.
PLEASE HELP I REALLY NEED AN ANSWER ALSO ONLY ANSWER IF YOUR GOING TO GIVE A STEP BY STEP SOLUTION
Answers
The answer of the given expression is 80.
Exponents
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
For example:-
[tex]5^4[/tex] can be written as 5*5*5*5.
Here 4 is the exponent or power and 5 is the base.
There are some laws of exponents which we use while calculating the answer to such expressions.
Given expression:-
[tex]\frac{12^7*30^5}{25^2*8^5*27^4}[/tex]
We have to simplify the given solution using the laws of exponents.
First we will divide them in their prime factors.
We know that,
[tex](x^a)^b=x^{ab}[/tex]
We can write,
[tex]12^7 = (2^2)^7*3^7=2^{14}*3^7[/tex]
[tex]30^5=2^5*3^5*5^5[/tex]
[tex]25^2=(5^2)^2=5^4[/tex]
[tex]8^5=(2^3)^5=2^{15}[/tex]
[tex]27^4=(3^3)^4=3^{12}[/tex]
Hence, we can write the given expression as follows,
[tex]\frac{2^{14}*3^7*2^5*3^5*5^5}{5^4*2^{15}*3^{12}}[/tex]
Also, we know that,
[tex]x^a*x^b=x^{a+b}\\x^a/x^b=x^{a-b}[/tex]
We can write,
[tex]{2^{(14+5-15)}*3^{(7+5-12)}*5^{(5-4)}}[/tex]
[tex]2^4*3^0*5^1[/tex] = 16*1*5 = 80
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A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 32o. From a point 2,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 35o. How tall (in feet) is the mountain? Round to two decimal places.
___________
Answers
To calculate the angle of elevation, just measure the angle formed by the line of sight and the level plain. The elevation of the peak is 10406.58 feet at its highest point.
This is further explained below.
What is the height of the mountain?Where
<A=30
AB=2000
<A B C=180-33
<A B C=147
<B C A=180-<A-<A B C
< B C A=180-30-147
<BCA=3
To begin, the side length BC may be calculated by using the following formula:
[tex]\frac{B C}{\sin A}=\frac{A B}{\sin C}[/tex]
So, we have:
B C=sin A *(A B/sin C)
B C=sin (30) *2000/sin (3)
B C=19107.3
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2. A grocery store is tracking how many people buy barbeque chips and jalapeno chips. The table shows how the number of barbeque chips and jalapeno chips are related. Ax + By = C y = mx + b Barbeque Jalapeno Write the standard form and slope intercept form equations for the scenario given. Chips (x) Chips (y) 200 100 160 140 120 180 80 220 Hint: use your calculator (STAT: Edit)
Answers
step 1
Find the slope m
we need two points
so
(200,100) and (80,220)
m=(220-100)/(80-200)
m=120/-20
m=-6
step 2
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-6
(x1,y1)=(200,100)
substitute
y-100=-6(x-200)
Convert to slope intercept form
y-100=-6x+1200
y=-6x+1300step 3
Find the equation in standard form
Ax+By=C
where
A is a positive integer
B and C are integers
so
y=-6x+1300
6x+y=1300Write an equation in slope-intercept form for the line through (-1, 1) and (0,3).
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The slope intercept form of a line can be written as:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
We have two points of the line: (-1,1) and (0,3).
Knowing that for x=0, the value of y=3 tells us that the y-intercept b is b=3:
[tex]\begin{gathered} y=mx+b \\ 3=m\cdot0+b \\ 3=b \end{gathered}[/tex]Using the other point and replacing the values of x and y in the equation we can calculate the value of the slope m:
[tex]\begin{gathered} y=mx+3 \\ 1=m\cdot(-1)+3 \\ 1-3=-m \\ -2=-m \\ m=2 \end{gathered}[/tex]Then, with m=2 and b=3, the equation becomes:
[tex]y=2x+3[/tex]Answer: y=2x+3
3A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed.Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents ofMississippl would purchase the new product. Identify a problem with the study.The conclusion is based on a small sample.
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The main problem of the research conducted is the number of participants who polled for the new product. If we want to conduct a study that represents a state, the number of participants must be close as possible to the total population of the state. Of course, 24 participants is very small sample size when we compare it to the population of the state, which means we cannot easily conclude that 50% of the residents would like to purchase the new product based on just 24 participants.
Answer: a. The conclusion is based on a small sample
You are researching the speed of sound waves in dry air
at 86°F. The linear function d = 0.217t represents the distances d (in miles) sound waves
travel in t seconds.
A. Represent the situation using a table and a graph.
B. Which of the three representations would you use to find how long it takes sound waves to travel 0.1 mile in dry air at 86°F? Explain.
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By observing the pace at which this compressed region moves through the medium, we may determine the sound speed.The speed of sound is roughly 343 meters per second or 767 miles per hour in dry air at 20 degrees Celsius.
Calculate speed of sound wave?
The formula for the airborne sound speedThe equation for the speed of sound in air as a function of absolute temperature is given by the simplification of v=RTM:v=√γRTM=√γRTM(273K273K)=√(273K)γRM√T273K≈331m 2) Time required for 1620m to be traveled at that speed: t = d / v 0.217m / 0.1 m/s) = 2.17m/ s from the beginning of the sound wave.Since you were watching the lightning, you might have wanted to know the time.Then, using the speed of light, you can determine how long it was between the lights being generated o.217 meters distant from you and Light travels at a speed of3*108 m/s, hence t = 0.217m / (3*108 m/s) = 0.000669 s.
The answer is o.000669 s, as determined in step 2, even though this time is entirely negligible.
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1) K thinks of a number, then doubles the number ,and then multiplies the result by 3 . If her final number is 65 more than her original number, then what was her original number?
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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The original number is 13.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x = 4 is an equation.
We have,
Let the number be K.
K thinks of a number, then doubles the number, and then multiplies the result by 3.
This can be written as:
(2 x k) = 2k ____(1)
3 x (2k) = 6k ____(2)
If her final number is 65 more than her original number can be written as:
6k = 65 + k _____(3)
From (3) we get,
6k = 65 + k
Subtract k on both sides.
6k - k = 65 + k - k
5k = 65
Divide both sides by 5.
5k / 5 = 65 / 5
k = 13
Thus,
The original number is 13.
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Find 164.4% of 289 round to the nearest tenths
Answers
Answer:
475.1
Step-by-step explanation:
Percent means per hundred so 164.4 % means [tex]\frac{164.4}{100}[/tex] When you divide by 100 you move the decimal 2 places to the left
1.644 x 289 = 475.116 This rounded to the nearest tenths is
475.1
Find an equation of the line. Write the equation using function notation.Through (4, - 7); perpendicular to 6y=x- 12The equation of the line is f(x)=..
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To determine the equation of the line you need to determine its slope first.
You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:
[tex]m=-\frac{1}{n}[/tex]To determine the slope of the given line, you have to write it in slope-intercept form:
[tex]y=mx+b[/tex]Where
m represents the slope
b represents the y-intercept
Given the line:
[tex]6y=x-12[/tex]-Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=-\frac{x}{6}=-\frac{12}{6} \\ y=-\frac{1}{6}x-2 \end{gathered}[/tex]The slope of this line is the coefficient of the x-term, n=-1/6
Its opposite reciprocal is:
[tex]\begin{gathered} m=-\frac{1}{n} \\ m=-(-\frac{1}{\frac{1}{6}}) \\ m=-(-1\cdot6) \\ m=-(-6) \\ m=6 \end{gathered}[/tex]The slope of the line you have to determine is m=6
Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m represents the slope of the line
(x₁,y₁) represent the coordinates of one point of the line
Replace the formula with m=6 and (x₁,y₁)=(4,-7)
[tex]\begin{gathered} y-(-7)=6(x-4) \\ y+7=6(x-4) \end{gathered}[/tex]The next step is to write the equation in slope-intercept form:
-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+7=6\cdot x-6\cdot4 \\ y+7=6x-24 \end{gathered}[/tex]-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:
[tex]\begin{gathered} y+7-7=6x-24-7 \\ y=6x-31 \end{gathered}[/tex]Finally, write the equation of the line using function notation:
[tex]f(x)=6x-31[/tex]write each decimal in word form 302.78 and 15.023
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Answer and Explanation:
302.78 can be written as THREE HUNDRED AND TWO AND SEVENTY EIGHT HUNDREDTHS or THREE HUNDRED AND TWO POINT SEVEN EIGHT.
15.023 can be written in word as FIFTEEN AND TWENTY THREE THOUSANDTHS or FIFTEEN POINT ZERO TWO THREE.
Pls help with my hw pls
Answers
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose isA. 12B. 8C. 4D. 6
Answers
Okay, here we have this:
She can eat the following options:
Sandwich with ham with or without cheese. Two choices.
Sandwich with bologna with or without cheese. Other two choices
This mean that she can eat:
Sandwich with ham with cheese with water or juice. Two options.
Sandwich with ham without cheese with water or juice. Two options.
Sandwich with bologna with cheese with water or juice. Two options.
Sandwich with bologna without cheese with water or juice. Two options.
Finally we obtain a total of: 2+2+2+2=8 options of lunches.
Thw
0.27x4.42erterttwerutiyrteyruiti
Answers
Answer:
if need to solve
Step-by-step explanation:
1.1934
if it help let me know this
It takes 14 electricians 18 days to wire a new housing subdivision. How many days would it take 24 electricians to do the same job?
Answers
Answer: 31 electricians
Step-by-step explanation:
We could set up a ratio for this problem. It takes 14 electricians 18 days to wire a new housing subdivision, so it would take 24 electricians x days to do the same job. 14/18 = 24/x. We can then cross multiply to find x.
X = 30.8 or approximately 31.
Find an angle θ with 0∘<θ<360∘that has the same:
Sine as 80∘ : θ = ______ degrees
Cosine as 80∘ : θ = _____ degrees
Answers
Answer:
sin80° = sin100°
cos80° = cos280°
Step-by-step explanation:
In general, sin(a)° = sin (180-a)° and cos(a)° = cos(360-a)°
Find x, for which 7x+8=4x-10
Answers
We are given the equation 7x+8=4x-10 and we want to find the value of x, such that the equality holds. To do so, we will start with the equation and the solve it for x. That is, we will apply mathematical operations on both sides of the equation, so we end up "ilosating" the x on one side of the equality sign. We start by
[tex]7x+8=4x\text{ - 10}[/tex]First, we subtract 4x on both sides, so we get
[tex]\text{ -10=(7x-4x)+8=3x+8}[/tex]Now, we subtract 8 on both sides, so we get
[tex]3x=\text{ -10-8=-18}[/tex]Finally, we divide both sides by 3, so we get
[tex]x=\frac{\text{ -18}}{3}=\text{ -6}[/tex]so x=-6.
Convert the fraction to a decimal. Round the quotient to hundredths when necessary70 over 45
Answers
Given:
[tex]\frac{70}{45}[/tex]Required:
We need to convert the given fraction to a decimal.
Explanation:
Divide the number 70 by 45.
[tex]\frac{70}{45}=1.555...[/tex]Round off to the nearest hundredth.
[tex]\frac{70}{45}=1.56[/tex]Final answer:
[tex]\frac{70}{45}=1.56[/tex]Given:
[tex]\frac{70}{45}[/tex]Required:
We need to convert the given fraction to a decimal.
Explanation:
Divide the number 70 by 45.
[tex]\frac{70}{45}=1.555...[/tex]Round off to the nearest hundredth.
[tex]\frac{70}{45}=1.56[/tex]Final answer:
[tex]\frac{70}{45}=1.56[/tex]if RS=2x+6 ST=x+4 and RT= 40 Find RS
Answers
RS + ST = RT
Substituting with data,
2x + 6 + x + 4 = 40
(2x + x) + (6 + 4) = 40
