29. What is the width of the rectangle written
as an exponential expression?
2-1 m
Area = 2-4 m²
? m
Answers
The width of the rectangle as an exponential factor whose length is 2^(-1) m and Area is 2^(-4) m^2 is 2^(-3) meter.
As per the question statement, we are given a triangle whose length is 2^(-1) m and Area is 2^(-4) m^2 is 2^(-3) meter. We are supposed to find out the width of the rectangle as an exponential factor.
Before solving the question, we should know the formula for calculating the area of the rectangle
Area = Length * Width
Given Area = 2^(-4) m^2
Given Length = 2^(-1) m
Let Width = "x" m
2^(-4) = 2^(-1) * x
2^(-4)/2^(-1) = x
2^(-4+1) = x
2^(-3) = x
Hence width of the given rectangle as an exponential factor is
x = 2^(-3) meter
Exponential factor: An exponential function is defined by the formula f(x) = a^x, where the input variable x occurs as an exponent.Area: The space occupied by any figure, object or body whether 2D or 3D.To learn more about exponential factor, click on the link given below:
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Related Questions
Identify rise over run (please!)
Answers
2- 3/1
3- 5/3
4- -3/2
5- 3/2
6- 3/1
The first three are the top row and 4,5, and 6 are the bottom row
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.
Answers
Answer:
Step-by-step explanation:
30 and 20
Write
24/25
as a percentage.
Answers
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%
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
Answers
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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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?
Answers
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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Evaluate each logarithm.
log₃9
Answers
The value of the expression log₃9 is 2.
The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.
Log a to the base b can be written as- log a/ log b.
Moreover, log [tex]a^{k}[/tex]= k log a, for all non negative values of a
Here, we are given a logarithmic expression- log₃9
We can expand this as-
log₃9 = log 9/ log 3
= log [tex]3^{2}[/tex]/ log 3
= 2 log 3/ log 3
= 2
Thus, the value of log₃9 is 2.
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4 metode la 381-(x+y)=15
Answers
Answer:
codec log 8x + y =15
Step-by-step explanation:
have a good day!
“Solve the equations”3x*3-9x^2-54x=0
Answers
x = 0
x = −5
Answer:x=6 x=-3
Step-by-step explanation:
3x(x^2-3x-18)=0
(X-6)(x+3)=0
X-6=0. X+3=0
+6=+6. -3=-3
X=6. X= -3
0.3596 is considered a rational number. What makes this number rational
Answers
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
Find the x-intercept and y-intercept
from the following linear equation:
8x - 9y = 144
Answers
Answer:
X intercept (18,0)
Y intercept(0,16)
Step-by-step explanation:
hope this was helpful!
2/3p - 11 = 1/3p -15
p=_
Answers
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!)
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.
Answers
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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Write 987.6 in scientific notation.
Answers
Decimal value Scientific Notation
987,650,000 9.8765 × 108
The function y = log(x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
Answers
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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Write each expression as a single natural logarithm. ln a-2 ln b+1/3 ln c
Answers
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 product of two factors is 1. One of the factors is 1. Can you tell what the other factor is? A. Yes; the other factor is 0 since 0 × 1 = 1. B. Yes; the other factor is 1 since 1 × 1 = 1. C. No; any number times 0 is 0, so there is no way to know what the other factor is. D. No; any number times 1 is 1, so there is no way to know what the other factor is.
Please help I have to turn in my homework by tonight at 11:00 PM!
Answers
The product of two factors is 1. One of the factors is 1. B. Yes; the other factor is 1 since 1 × 1 = 1.
How to calculate the value?From the information given, the product of two factors is 1 and one of the factors is 1.
Let the other number = y
The other number will be:
1 × y = 1
y = 1
Therefore, the other number is 1
In conclusion, the correct option is B.
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como se escribe la cantidad en letra de 855672019
Answers
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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A right triangle has a hypotenuse
with length 17 and a leg with
length 10. How long is the
triangle's other leg?
Answers
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]
how do you divide 1/2 by -4
Answers
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]
given f(x)=x-2, write the new function if the y-intercept is decreased by six units.
Answers
Answer:
f(x) = x - 8
Step-by-step explanation:
Solve each equation.
2x=8
Answers
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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Carson wants to divide 128 by 3.2. What is the place value of the first digit in his answer?
tenths
ones
tens
hundreds
Answers
Answer:Tenths
Step-by-step explanation:Hope it helps
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)
Answers
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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Classify each number as rational or irrational
Answers
11/3 [rational]
Sqrt 3/16 [irrational]
Sqrt 48 [irrational]
0.01045 [rational]
Sqrt 16/81 [rational]
16pi [irrational]
0.42 [rational]
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?
Answers
Answer: 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Find the degree measure of the indicated angle.
Answers
Answer:
75 degree
Step-by-step explanation:
35+70+75=180 degree
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
Answers
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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simply fully: square route 8 x square route 18
Answers
Answer:
12
Step-by-step explanation:
[tex]\sqrt{8} * \sqrt{18} =12[/tex]
help pleaseeeeeeeeeeeee
Answers
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
mile
long. You walk 3 laps around the lake in the morning
and 2 laps in the evening. Your friend walks the same
1
total distance as you on a 1--mile track. How many
2
laps does your friend walk?
Answers
The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 3/2 mile track.
The total laps of our friend runs is 3laps.Given that
The sidewalk around a lake is 9/10 mile long.You walk 3 laps around the lake in the morning and 2 laps in the evening.Your friend walks the same total distance as you on a 3/2 mile track.To find
How many laps does your friend walks?So, according to the question
we have,
The length of sidewalk around the lake = 9/10 miles.Total distance walk by you = 9/10 (3+2)= (9 ×5)/10
= 4.5 miles.
Now, from question
Your friend walk same distance travel by you on 3/2 mile track.So, Total laps walk by your friend
= ( Total distance walk by you)/(Total length of your friends track)
= [tex]\frac{4.5}{(\frac{3}{2}) }[/tex]
= [tex]\frac{4.5\times 2}{3}[/tex]
= 9/3 = 3
Answer:
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