According to the given the given logarithm log₃ 1/9 the value is = -2
What is Logarithmic functions?Logarithmic functions are significant due of their link to exponential functions. Logarithms are useful for solving exponential equations and investigating the properties underlying exponential functions.
According to the given information:log₃ 1/9
Can be written as:
log₃ (1/9) = x
using the log definition in exponential form. if x and b are positive real number and b dose not equal 1 then log_b (x) = y is equivalent to b^y = x.
3^x = 1/9
creating equivalent expression in the equation that all have equal base.
3^x = 3^-2
if the base are the same, two expression are only equal if the exponential are also equal
x = -2
the variable x is equal to -2
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Data points are considered to be unusual if they are more than two standard deviations
away from the mean. Which data points in each distribution are considered to be unusual?
Show all work.
Answer:
Step-by-step explanation:
30 and 20
Which sum or difference is equivalent to the following expression?
2x+3/4
A. x/2 + 3/4
B. x/2 - 3/4
C. 3x/4 + 3/4
D. 8x +24
The expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.
How to Find Expressions that are Equivalent?Express the given expressions in their simplest form to determine the expression that is equivalent to (2x + 3)/4.
A. x/2 + 3/4
Find the common denominator. The common denominator is 4. Therefore:
= 2(x) + 1(3)/4
= (2x + 3)/4
x/2 + 3/4 ≠ (2x + 3)/4
Thus, the expression, x/2 + 3/4 is equivalent to (2x + 3)/4.
B. x/2 - 3/4 = (2x - 3)/4
Therefore, x/2 - 3/4 ≠ (2x + 3)/4
C. 3x/4 + 3/4 = (3x + 3)/4
Therefore, 3x/4 + 3/4 ≠ (2x + 3)/4
D. 8x + 24 ≠ (2x + 3)/4
Therefore, 8x + 24 ≠ (2x + 3)/4
In summary, we can conclude that, the expressions, x/2 - 3/4, 3x/4 + 3/4, and 8x +24x/2 + 3/4 is not equivalent to (2x + 3)/4. Thus, the expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.
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Find the domain and the range of each function.
y=log₂(x-3)
The domain of the function is (3,∞) , {x|x>3}
and the range of the function is (−∞,∞), {y|y ∈ R}
given the function is y = log₂(x ₋ 3)
Set the argument in log₂(x ₋ 3) greater than 0 to find where the expression is defined.
x ₋ 3 > 0
Add 3 to both sides of the inequality.
x > 3
The domain is all values of x that make the expression defined.
Interval Notation:
(3,∞)
Set-Builder Notation:
{x|x>3}
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
(−∞,∞)
Set-Builder Notation:
{y|y∈R}
Determine the domain and range.
Domain: (3,∞) , {x|x>3}
Range : (−∞,∞), {y|y ∈ R}
Hence we get the required domain and range of the given function.
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0.3596 is considered a rational number. What makes this number rational
Answer:
see explanation
Step-by-step explanation:
a rational number has the form
[tex]\frac{a}{b}[/tex] , where a and b are integers
given
0.3596 ← with 6 in the [tex]\frac{1}{10000}[/tex] place
= [tex]\frac{3596}{10000}[/tex] = [tex]\frac{899}{2500}[/tex] ← a rational number
6) On a map scale 1cm to 250m the area of
a car park is 3cm². What is the actual
area of the care park in hectares? (1 hectare=10,000m^2)
The actual area of the care park in hectares is 18.75
As per the known fact, ratio of measurement on scale is equal to the ratio of measurement in real. So, writing the equation first -
Area of car park = 3 cm²
Keep the value of 1 cm in the above mentioned equation.
Area of car park = 3 × (250)²
Taking square
Area of car park = 3 × 62,500
Performing multiplication
Area of car park = 1,87,500 m²
Converting the area in hectares
10,000 m² = 1 hectare
1,87,500 m² = (1 ÷ 10,000) × 1,87,500
1,87,500 m² = 18.75 hectares.
Therefore, the actual area of the care park is 18.75 hectares.
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01.07 Operations with Scientific Notation
CCSS.Math.Content.8.EE.A.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Two random numbers 180000000 and 0.00000534 can be written as 1.8 x 10⁸ and 5.34 x 10⁻⁶.
What is a scientific notation?Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may be called scientific form.
When a number is written using only the digits of the number, that is considered standard notation. Since words are not used in conventional number notation, this is the way that numbers are typically written.
Let the bigger number by 180000000 and the smaller number be 0.00000534. The two numbers in scientific notations can be written as below:-
180000000 = 1.8 x 10⁸
0.00000534 = 5.34 x 10⁻⁶.
Therefore, two random numbers 180000000 and 0.00000534 can be written as 1.8 x 10⁸ and 5.34 x 10⁻⁶.
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A web designer charges customers an initial consultation fee plus an hourly rate. The table shows the linear relationship between x, the number of hours and y, the total cost of hiring the designer. a. Find the rate of change b. What does the rate of change represent in the context of the situation?
The rate of change means that the designer hourly charge is $55 per hour
Linear equation
A linear equation is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the total cost of hiring the designer after x hours.
From the table, using the point (0, 125) and (15, 950):
m = y₂-y₁/x₂-x₁= 950- 125/15-0 = 55The rate of change means that the designer hourly charge is $55 per hour
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how do you divide 1/2 by -4
Answer:
Step-by-step explanation:
1/2÷4 = 1/8 = 0.125.
[tex]\cfrac{1}{2}\div -4\implies \cfrac{1}{2}\div \cfrac{-4}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{-4}\implies {\LARGE \begin{array}{llll} -\cfrac{1}{8} \end{array}}[/tex]
Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%. How much state and local tax should be withheld from her weekly pay?
The state and local tax that will be paid by Mei will be $17 and $12.50 respectively.
How to calculate the tax?From the information, Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%.
The state tax that will be paid will be:
= Rate × Income
= 6.4% × $265.85
= 0.064 × $265.85.
= $17
The local tax that will be paid will be:
= Rate × Income
= 4.7% × $265.85
= 0.047 × $265.85.
= $12.50
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A cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F. The table shows temperature readings for the cake.
a. Given a room temperature of 70⁰F , what is an exponential model for this data set?
The exponential model for the given data set is [tex]y(x) = 70 + (110)e^{-0.135x}[/tex].
Given that cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F and the table shows temperature readings for the cake and the room temperature is 70°F.
Temperature at time = 0 min, y₀= 180° F
Ambient (room) tempertaure = y₁ = 70° F
Using Newton's cooling method,
y(x) = y₁ + (y₀ - y₁)e⁻ⁿˣ
y(x) = 70 + (180-70)e⁻ⁿˣ
y(x) = 70 + (110)e⁻ⁿˣ
Given, at x=5 min, y(5) = 126,
y(5) = 70 + (110)e⁻⁵ⁿ = 126
Solving, e⁻⁵ⁿ = (126-70)/110 = 0.5091
Taking and log and solving for n,
- 5n = log(0.5091)
-5n= -0.67511
n = 0.135
Thus, the exponential model is [tex]y(x)=70+(110)e^{-0.135x}[/tex]
Hence, an exponential model for given data set when a room temperature of 70°F is [tex]y(x)=70+(110)^{-0.135x}[/tex].
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Find the x-intercept and y-intercept
from the following linear equation:
8x - 9y = 144
Answer:
X intercept (18,0)
Y intercept(0,16)
Step-by-step explanation:
hope this was helpful!
Does the table represent a function? Why or why not?
X23345
45677
у
A. Yes, because every x-value corresponds to exactly one y-value.
OB. No, because one x-value corresponds to two different y-values.
C. Yes, because there are two x-values that are the same.
OD. No, because there are two y-values that are the same.
Based on table shown above, we have that: B. No, because one x-value corresponds to two different y-values.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Based on table shown above, we can reasonably infer and logically deduce that this table does not represent a function because one x-value corresponds to two different y-values.
In conclusion, this table is not a function because no function can have the same x-values (3) for different y-values (5 and 6).
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What is the slope of the line that passes through the points (2,8) and (-3,14)?
The slope of the line that passes through the coordinates is -6/5.
What is defined as the slope of the line?The slope of a line is a measurement of its steepness and direction. Whatever two distinct points on a line can be used to calculate the slope of that line. The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line. The net y coordinate change is Δy, whereas the net x coordinate change is Δx.The slope of the line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
Where, the coordinates are given.
(x₁ ,y₁) = (2, 8)
(x₂, y₂) = (-3, 14)
Put the value in the slope;
m = (14 - 8)/(-3 - 2)
m = 6/-5
m = -6/5
Therefore, the slope of line passing from the points is -6/5
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Write 987.6 in scientific notation.
Decimal value Scientific Notation
987,650,000 9.8765 × 108
Write each expression as a single natural logarithm. ln a-2 ln b+1/3 ln c
We have expression ln a-2 ln b+1/3 ln c as a single natural logarithm
㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to express ln a-2 ln b+1/3 ln c as a single natural logarithm.
⇒ ln a-2 ln b+1/3
⇒ ㏑ (a) - ㏑ (b²) + ㏑ [tex]c^{\frac{1}{3} }[/tex]
Use the quotient property of logarithms for ln a-2 ln b
⇒ ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]
Use the quotient property of logarithms for ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]
⇒ ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
Finally, we have expressed ln a-2 ln b+1/3 ln c as a single natural logarithm ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
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help pleaseeeeeeeeeeeee
Answer:
Inverse property
Step-by-step explanation:
3/4 is the reciprocal of 4/3 which means they would cancel each other out. So you would only be left with x=x
simply fully: square route 8 x square route 18
Answer:
12
Step-by-step explanation:
[tex]\sqrt{8} * \sqrt{18} =12[/tex]
The function y = log(x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
The function [y = log(x)] is translated 1 unit to the right and 2 units down, yielding [g(x) = log(x - 1) - 2] as the translated function. and this may be established by using the transformation's rules.
Given:
One unit to the right and two units down translate the function y=log(x).
The translated function's graph can be drawn using the procedures listed below:
First, write the function that is supplied.
y = log(x) (x)
Step 2: Multiply the given function in the right direction—that is, in the positive x-axis direction—by factor 1 in accordance with the data provided. The aforementioned function is now:
f(x) = lox (x - 1)
Step 3: Next, move the graph of the function f(x) in a downward direction, or in the opposite direction of the y-axis.
g(x) = log(x - 1) - 2
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Classify each number as rational or irrational
x+1, 2x-1 and 3x + 1 are the first three terms of a G.P. If x=0, find the common ratio.
Step-by-step explanation:
if that is a geometric sequence to find the common ratio
[tex] \frac{t2}{t1} [/tex]
you divide the exceeded term with the previous term
simply you can say
[tex] \frac{tn}{t(n - 1)} [/tex]
therefore now we have
[tex] \frac{2x - 1}{x + 1} or \\ \frac{3x + 1}{2x - 1} [/tex]
therefore you will substitute x=0 in any of the given equations they should give youbthe same answer
[tex] \frac{2(0) -1 }{0 + 1} = - 1[/tex]
or
[tex] \frac{3(0) + 1}{2(0) - 1} = - 1[/tex]
the common ratio is -1como se escribe la cantidad en letra de 855672019
La cantidad 855672019 descrita en palabras es Ochocientos cincuenta y cinco millones seiscientos setenta y dos mil diecinueve.
¿Cómo representar una cantidad mediante una frase?
En este ejercicio debemos representar en palabras la cantidad asociada al conjunto de dígitos descritos en el enunciado. Para leer y describir un número se lee de izquierda a derecha, en donde un dígito a la derecha tiene más magnitud que un dígito a la izquierda, de modo que se comienza con el dígito de mayor magnitud hasta alcanzar el de menor magnitud.
8 - Ochocientos millones
5 - Cincuenta millones
5 - Cinco millones
6 - Seiscientos mil
7 - Setenta mil
2 - Dos mil
01 - Diez
9 - Nueve
En consecuencia, la cantidad 855672019 es Ochocientos cincuenta y cinco millones seiscientos setenta y dos mil diecinueve.
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given f(x)=x-2, write the new function if the y-intercept is decreased by six units.
Answer:
f(x) = x - 8
Step-by-step explanation:
i dont know how if tried quite a few times and cant get it
Answer:
2/3 and 3/2
Step-by-step explanation:
→ Divide the smaller triangle by the larger one for the first one
8 ÷ 12 = 8/12 = 2/3
→ Divide the larger triangle by the smaller one for the second one
12 ÷ 8 = 12/8 = 3/2
find the missing terms
_,-9,_,3,9
Answer:
-15,-9,-3,3,9
Step-by-step explanation:
Write
24/25
as a percentage.
Answer: 96%
How to Solve
Formula:
y ÷ x *100
Substitute
=> 24 ÷ 25 * 100
Lets Multiply 24 * 100 (or you can divde 24 and 25 then multiply with 100. do as you're convenience, answer will remain)
Answer 2400
Now As our formula says divide 2400 by 25
Answer 96
Hence 96%
So, 24/25
as a percentage is 96%
All done!
Answer:
96%
Step-by-step explanation:
First, divide 100 but 25 (the denominator) and you get 4. This means that to get a number over 100, which is a percentage you need to multiply the initial fraction by 4. You get 96/100, and you can remove the 100 to get 96%
A hole the size of a photograph is cut from a red piece of paper to use in a picture frame. 5 4 3 2 photograph -5-4-3-2-1₁- 2/9 -2. -3- red paper -5 1 2 3 5 X What is the area of the piece of red paper after the hole for the photograph has been cut? O 17 square units 25 square units 39 square units 47 square units
Answer:57
Step-by-step explanation:
Find the area of a rectangle with a base of 2 and a height of 6.
Answer:
12
Step-by-step explanation:
2 x 6 = 12
to find area you multiply length x width or in this case base x height
6.5 * 5 3/4 that is my question
6.5 can be translated to 6 1/2 times 5 3/4 or 5 3/4 can be translated to 5.75 times 6.5 which equals 37.375
A right triangle has a hypotenuse
with length 17 and a leg with
length 10. How long is the
triangle's other leg?
Answer:
[tex]3\sqrt{21}[/tex]
Step-by-step explanation:
By the Pythagorean theorem,
[tex]\sqrt{17^2-10^2}=\sqrt{189}=3\sqrt{21}[/tex]
d=rt (Distance formula distance=rate•time)
t
if d=150 when r=60, find t
Answer:
25
Step-by-step explanation:
if the formula for distance is distance = rate times time then you have to divide the rate 60 by the distance 150 to get 25 .