After solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.
What is an equation?A mathematical statement made up of two expressions joined by an equal sign is called an equation.An equation is 3x - 5 = 16.We obtain the value of the variable x as x = 7 after solving this equation.So,
Given equation: log9-log x+1=6Then,
log9-logx+1=69log-logx+1=6(9log-logx+1)+(-9log-1)=6+(-9log-1)x=(-9log+5)/logTherefore, after solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.
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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
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:
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
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]
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:
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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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 -1Find 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!
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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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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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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como 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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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%
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
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
Classify each number as rational or irrational
Write 987.6 in scientific notation.
Decimal value Scientific Notation
987,650,000 9.8765 × 108
find the missing terms
_,-9,_,3,9
Answer:
-15,-9,-3,3,9
Step-by-step explanation:
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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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
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]
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 .
Find the degree measure of the indicated angle.
Answer:
75 degree
Step-by-step explanation:
35+70+75=180 degree
Solve each equation.
2x=8
Solution of this polynomial equation is x = 4
What are polynomial equations ?In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
2x = 8
=> 2x / 2 = 8 /2
=> x = 4
Thus solution for given equation is x = 4.
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2/3p - 11 = 1/3p -15
p=_
Answer:
p = - 12
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] p - 11 = [tex]\frac{1}{3}[/tex] p - 15
multiply through by 3 to clear the fractions
2p - 33 = p - 45 ( subtract p from both sides )
p - 33 = - 45 ( add 33 to both sides )
p = - 12
Answer:
-12
Step-by-step explanation:
(sorry its a bit messy - hope it helps though!)
simply fully: square route 8 x square route 18
Answer:
12
Step-by-step explanation:
[tex]\sqrt{8} * \sqrt{18} =12[/tex]
In a survey, respondents were asked which type of activity they enjoyed most while on vacation. The bar graph shows the responses of males and females.
How many more males than females said that bike riding was their favorite activity?
Answer: 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
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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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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Question 6(Multiple Choice Worth 2 points)
(Linear Relationships MC)
At a restaurant, hot chocolate can be purchased in three different cup sizes. A 12-ounce cup costs $1.97, a 16-ounce cup costs $2.62, and a 20-ounce cup costs $3.27.
Which statement is true based on the given description?
O The description shows a linear relationship, but not a proportional relationship.
O The description shows a linear relationship and a proportional relationship.
O The description does not show a linear relationship or a proportional relationship.
O The description shows a proportional relationship, but not a linear relationship
We need to know about linear and proportional relationship to solve this problem. Statement 2 is true, the description shows a linear relationship and a proportional relationship.
Linear relationship is a relationship between two variables where if one increases the other increases or if one decreases the other decreases. The varibales in a linear relationship form a straight line on graph. Proportional relationship is the relationship between two variables where the ratio between pairs of different data always remains constant. In the given question, a 12 ounce cup costs $1.97, a 16 ounce cup costs $2.62 and a 20 ounce cup costs $3.27. The price of each cup increases with increase in capacity of the cup, so we can say that the cup capacity and price have a linear relationship. The ratio between each pair can be given by
12/1.97=6.10
16/2.62=6.10
20/3.27=6.10
The ratios between every pair is same, so it is a proportional relationship.
Thus we found that the description shows a linear relationship and a proportional relationship between the cup capacity and it's price, statement 2 is the right option.
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