For all [tex]\log_{x_{1}} M[/tex] there is a [tex]\log_{x_{2}}N[/tex] such that [tex]N = M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex]. The logarithmic expression log ₂ 8 is equivalent to the logarithmic expression log ₃ 27.
How to find equivalent logarithms
Logarithms are trascedental function, that is, a function that cannot be described algebraically.
Let suppose we know that [tex]\log _{x_{1}} M = \log_{x_{2}} N[/tex] such that x₁ ≠ x₂. We proceed to prove that for all [tex]\log_{x_{1}} M[/tex] there is a [tex]\log_{x_{2}} N[/tex] by logarithm properties below:
[tex]\log_{x_{1}} M[/tex] Given[tex]\frac{\log_{x_{2}}M}{\log_{x_{2}}x_{1}}[/tex] Base change[tex]\frac{1}{\log_{x_{2}}x_{1}} \cdot \log_{x_{2}} M[/tex] Associative property[tex]\log_{x_{2}} M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex] [tex]n\cdot \log a = \log a^{n}[/tex][tex]N = M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex] ResultFor example, let suppose that x₁ = 2, M = 8 and x₂ = 3, then the value of N is:
[tex]N = 8^{\frac{1}{\log_{3} 2} }[/tex]
N = 27
Thus, for all [tex]\log_{x_{1}} M[/tex] there is a [tex]\log_{x_{2}}N[/tex] such that [tex]N = M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex]. The logarithmic expression log ₂ 8 is equivalent to the logarithmic expression log ₃ 27.
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Rectangle A'B'C'D' was created by dilation Rectangle ABCD using D as the center of dilation.
What is the scale factor of the dilation?
Based on the scale factor, how many copies of ABCD, including the original, should fit inside A'B'C'D?
In Rectangle , 16 copies of ABCD fit inside A'B'C'D'.
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
DA = 3
D'A' = 12
Scale factor DA/D'A' = 3/12 = 1/4
The scale factor = 1/4
The scale factor = 1/4
area ratio = 1/16
16 copies of ABCD fit inside A'B'C'D'.
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14. Which of these functions is linear?
A. xy = 12
B. y = x5 - X4
C. 3x + 5y = 9
D. y - 2 = x(x + 1)
Answer:
3x + 5y = 9
Explanation:
A linear function is represented by the equation: y = mx + b
In option C:
3x + 5y = 9 is a linear equation as it has slope and y-intercept
Linear means degree is 1
#A
xy=12Not linear
#B
y=x⁵-x⁴Degree is 5 not linear
#C
3x+5y=9Linear
#D
y-2=x²+xDegree is 2 hence quadratic
Round 5.78575184279 to the nearest whole number.
Answer:
6
Step-by-step explanation:
5.7 is already immediately 6 because if a number after the whole number is 5 or more you round up.
6
Step-by-step explanation:
Which situation does NOT yield variability?
Select one:
How many days are in a leap year?
How many siblings does each person in your class have?
How many miles do you travel in your car each day?
Options A and B situation does NOT yield variability that is A. How many days are in a leap year? B. How many siblings does each person in your class have?
What is statistical data?Statistics deals with the study of variability. The statement is said to be statistical if there would be variability in that data.
A. How many days are in a leap year?
This situation does NOT yield variability because the question is answered by a single value. It does not need any collecting data that vary.
B. How many siblings does each person in your class have?
This situation does NOT yield variability because the question is answered by a single value. It does not need any collecting data that vary.
C. How many miles do you travel in your car each day?
This situation yield variability because the question is answered by collecting data.
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Which equation is equivalent to log subscript 3 baseline (x 5) = 2? 3 squared = left-bracket log subscript 3 baseline (x 5) right-bracket cubed 2 cubed = left-bracket log subscript 3 baseline (x 5) right-bracket squared 3 squared = x 5 2 cubed = x 5
The equation that is equivalent to the considered equation of log is given by: Option E: 2^3 = x+5
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get [tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]
Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
Log with base 10 is written as [tex]\log(x)[/tex] simply.
The equation given is:
[tex]\log_3(x+5) = 2[/tex]
By using the definition of log, which says [tex]a^b = c \leftrightarrow \log_a(c) = b[/tex], we get:
[tex](x+5) = 2^3[/tex] or [tex]2^3 = x+5[/tex]
Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]
(we used the fact that the question is asked in a way that expresses that there is only one equivalent equation. Plus we used the fact that as option E is a sure equivalent version, so it is correct option).
Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]
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See the picture for my question.
Which number is the best estimate of 2.3 x 3.6?
O A. 6
OB. 8
O c. 9
OD. 12
Answer:
B. 8
Step-by-step explanation:
Explanation: 2.3x3.6 is 8.28, and we round down to 8 because 8.28 is closer to 8 than 9.
Please help!! 50 points!!!!
Jim walks 3 miles per hour slower than his friend Steve runs. Steve runs 4 miles per hour slower than his friend Matt rides his bike. Jim walks 25 miles in the same time Matt rides his bike 60 miles. Steve runs 16 miles in the same time Matt rides his bike 24 miles.
Part A: Write an equation to calculate Jim's speed.
Part B: Write an equation to calculate Steve's speed.
Part C: Write two equations that can be used to calculate Matt's speed.
Answer:
Jim=S-3
Steve=M-4
U figure out the last part. I helped
Step-by-step explanation:
Answer:
See below ~
Step-by-step explanation:
Let Jim, Steve, and Matt have speeds of j, s, and m respectivelyFrom the problem :j = s - 3 [Jim]s = m - 4 [Steve]Jim takes same time to walk 25 miles at it takes Matt to ride 60 milesj = 25/t₁ and m = 60/t₁Steve runs 16 miles in the same time Matt rides his bike 24 miless = 16/t₂ and m = 24/t₂Equating Matt's Speed in both cases
60/t₁ = 24/t₂t₁/t₂ = 5/2 = 2.5t₁ = 2.5t₂Now, taking Equation 1 :
j = s - 325/t₁ = 16/t₂ - 325/(2.5t₂) = 16/t₂ - 310/t₂ = 16/t₂ - 36/t₂ = 3t₂ = 2 st₁ = 2.5(2) = 5 secondsEq.1) m = 60/5 [Matt]Now, taking Equation 2 :
s = m - 416/t₂ = 24/t₂ - 48/t₂ = 4t₂ = 2 secondsEq.2) m = 24/2 [Matt]Answer number 9 please thanks
dont mind the answer that I picked on accident and pls dont send no PDF or a image to download
Answer:
I guess that X measures 50° because X and 50 are vertically opposite angles...
!!20 points and Brainliest!!! PLEASE ONLY ANSWER IT IF YOU KNOW THE ANSWER PLEASE!!!
What should be done to x^2 - 12x to create a perfect square?
A) add 36
B)subtract 6
C)add 6
D)subtract 36
Answer:
add 36
Step-by-step explanation:
give me brainliest
Answer:
add 36
Step-by-step explanation:
solve 6x=2y+8, 4x+5y+10=47 by substitution method
the value of x= 3
and the value of y=5
Answer:
(x , y) = (3 , 5)Step-by-step explanation:
[tex]\begin{cases}6x=2y+8&\\ 4x+5y+10=47&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}12x=4y+16&\\ 12x+15y+30=141&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}12x=4y+16&\\ (4y+16)+15y=111&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}12x=4y+16&\\ 19y+16=111&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}12x=4y+16&\\ 19y=95&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}12x=4y+16&\\ y=\frac{95}{19}=5 &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}12x=20+16=36&\\ y=5 &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}x=3&\\ y=5 &\end{cases}[/tex]
What is the slope of the line 3 = 4 + 5?
Answer:
4/3 = slope
Step-by-step explanation:
What is the Pythagorean Theorem and when can you use it?
Step-by-step explanation:
The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle.
You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the third side.
I urgently need help!! Please!!
Answer: f= [tex]x^2+4x+8+(7/3x-4)[/tex]
Step-by-step explanation:
Careful with simplifying every step.
Bubba's Boot is a favorite stop of visitors to Nashville's downtown shopping
area. Last year 2.42 x 105 people visited Bubba's. This year it has become an even
more popular venue with 2.53 x 106 visitors. About how many more visitors have
been to Bubba's this year than last year?
Scientific Notation: 2.29 × [tex]10^6[/tex]
Standard Form: 2288000
I hope this helps you
:)
Answer:
About 12 more visitors ( 12.08 to be exact)
Bob is solving the following linear equation. 17 - 4x - 4= - 10x + 13 + 6x His final two steps are: : 13- 4x = - 4x + 13 = 13= 13 Select the statement that correctly interprets Bob's solution. A The solution is x = 0. ® The solution is the ordered pair (13, 13). © There is no solution since 13 = 13 is a true statement. © There are infinitely many solutions since 13 = 13 is a true statement.
The equation 17 - 4x - 4= - 10x + 13 + 6x is a linear equation
The true statement about Bob's solution is (d) There are infinitely many solutions since 13 = 13 is a true statement.
How to determine the true statement?The equation and the steps are given as:
17 - 4x - 4= - 10x + 13 + 6x
13 - 4x = -4x + 13
13 = 13
The final step where both sides of the equation are represented by the constant value 13 means that:
The equation has infinitely many solutions
Hence, the true statement about Bob's solution is (d) There are infinitely many solutions since 13 = 13 is a true statement.
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A store sells an 8-pound bag of flour for $18.80. If larry can buy a 2-pound bag of flour at the same rate, what would be the price of the 2-pound bag?
Answer:
$4.70
Step-by-step explanation:
First, you need to divide 18.80 by 8.
18.80/8 = 2.35
2.35 is the unit price for one (1) pound bag of flour,
Multiply by 2 to find the price of a two (2) pound bag.
2.35 * 2 = 4.7
$4.70 is the price of a two-pound bag.
hope this helps :)
What is the slope of the line that contains the points (13, -2) and (3, -2)?
Answer:
the slope = 0
Step-by-step explanation:
we notice that the points (13, -2) and (3, -2) have the same y-coordinate -2
Then
the slope = 0
Given X(4, -7). what are
the coordinates of X" 1EX - R,ax(R, axi, (X)),
A
(4,7)
B
(0,9)
C
(-4, -7)
D
(-4, 7)
5) WILL GIVE BRAINIEST TO BEST ANSWER
find the equations use to solve
Graphing!
Answer:
A: y= 3x-4
B: y= -2/4x+3
Step-by-step explanation:
slope intercept form: y=mx+b
m = slope
slope = rise/run
b = y-intercept
Answer:
A: y = 3x - 4
B: y = -1/2x +3
Step-by-step explanation:
First, lets find the slope of line B. We need to find two coordinates on the line that coincide with points on the grid. We see that (2, 2) and (4, 1) are two points that match the criteria, so we can use both points. You can use any two points, I just randomly chose these two. Slope is nothing but the Y coordinate of the first point subtracted from the Y coordinate of the second point. We do 2 - 4 and get -2. Next, we do the same thing but with the X coordinates to get 2 - 1, which is 1. We do 1 over -2 to get negative 1/2 for our slope. The last variable in the equation is just where the line hits the Y axis, which is 3. So, the final equation is y = -1/2x + 3. Rinse and repeat for the next question.
Jacinta compares the volume of two boxes. Both boxes have a width of
2. 5
2. 5 inches, and a height of
10
10 inches. The larger box has a length of
8
8 inches. The smaller box has a length that is
75
%
75% of the length of the larger box.
Answer:200 in ^3
Step-by-step explanation:
Im trying to help my sis but i cant remember :/
428.5oz (total amount she had to put out)÷ 5(amount of bowls she wanted to use) = 85.7oz
Drink A is 20% water by weight, and drink B is 35% water by weight. How many fluid ounces of drink A must be added to 80 oz of drink B to have a drink whose final proportion of water is 30%
Answer:
40 fluid ounces of drink A must be added to 80 oz of drink B to have a drink whose final proportion of water is 30%
Step-by-step explanation:
35% of 80 oz of drink B = 0.35(80) = 28 oz
0.20(A) + 0.35(80) = 0.30(A + 80)
0.20A + 28 = 0.30A + 24
A = 40Is the function F(x)=5x2
Solve the system of equations (1 point)
y = 2x(squared) – 3
y = 3x - 1
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
════════════════════
1.
[tex]y = {2x}^{2} - 3[/tex]
[tex] {2x}^{2} - 3 = y[/tex]
[tex] {2x}^{2} = y + 3[/tex]
[tex]\frac{2x^{2}} {2} = \frac{y + 3}{2}[/tex]
[tex] {x}^{2} = \frac{y + 3}{2} [/tex]
[tex]x = \sqrt \frac{2y + 6}{2}[/tex]
───────────────────
2.
[tex]y = 3x - 1[/tex]
[tex]3x - 1 = y[/tex]
[tex]3x = y + 1[/tex]
[tex] \frac{3x}{3} = \frac{y+1}{3}[/tex]
[tex]x = \frac{y + 1}{3}[/tex]
═══════════════════
Explanation:
#Carry on learning
let p be a polynomial function where p(x)=x4- dx3 + 8x2 - 10x + 4 if (x-2) is a factor of the polynomial, what is the value of d?
Answer:
d = 4
Step-by-step explanation:
If (x -2) is a factor of polynomial p(x), then the remainder will be zero.
⇒ p(2) = 0
[tex]\sf \bf 2^4-d*2^3 + 8*2^2 -10*2 + 4 = 0\\\\[/tex]
16 - 8d + 8*4 - 20 + 4 = 0
16 - 8d + 32 - 20 + 4 = 0
-8d + 32 = 0
-8d = - 32
d = -32/(-8)
[tex]\boxed{d = 4}[/tex]
The price of an item has been reduced by 80% . The original price was $85. What is the price of the item now?
and fast pls it is due today and thx u!.
Let the price be x
x=85-80% of 85x=85-0.8(85)x=85-68x=$17Price is $17 now
PLS HELP 45 POINTS whats the answer?
Answer:
Step-by-step explanation:
d or b
If 2/5 of the judges were wearing their powdered wigs, what fraction of the judges were not wearing their powdered wigs?
Answer: [tex]\frac{3}{5}[/tex] of the judges were not wearing their powdered wigs.
Step-by-step explanation:
[tex]\frac{2}{5}[/tex] out of the whole [tex]\frac{5}{5}[/tex] were wearing a wig. So subtract [tex]\frac{2}{5}[/tex] from [tex]\frac{5}{5}[/tex] to see the fraction that wasn't wearing a wig.
[tex]\frac{5}{5} -\frac{2}{5} =\frac{3}{5}[/tex]