The exponential model of the given data is f(t) = 30.18 × 1.06^t.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
Given that,
The average price for office space in 2004 is $30.18.
The average price for office space in 2015 is $66.85.
Suppose the average price in 2004 is taken as y₀.
The given situation can be represented in the form of exponential function f(t) = y₀b^t as,
Take t = 0 for 2004
Then, f(0) = y₀b^0
⇒ f(0) = y₀ = $30.18.
Then, at 2015, t = 12. Substitute the respective values to get,
f(12) = 30.18 × b^12
⇒ 66.85 = 30.18 × b^12
⇒ b^12 = 66.85 / 30.18
⇒ b = 1.06
Thus in exponential form the given situation can be written as,
f(t) =30.18 × 1.06^t
Hence, the given data can be modeled in exponential function as f(t) =30.18 × 1.06^t.
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Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of a person is 5.2ft in centimeter: 158.49cm
What are the Factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.
The letters "ft" and "cm" stand for feet and centimeters, respectively. The centimeter is used in the International System of Units and is regarded as a component of the metric system. The US customary measurement system uses the unit foot.Approximately 30.48 cm makes up one foot.
1 ft = 30.48 cm
Now, the formula for 5.2 feet to centimeters is as follows:We are aware that 1 foot equals 30.48 centimeters.Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.
5.2 ft = 158.49 cm.5.2 feet is therefore equal to 158.49 cm in centimeters.
Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.
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Select all the equations that have {4} as its solution set.
Responses
79−3x=12x+19
7−x=12x
x2+3=10x−21
5 + 2x = 3x + 3
SELECT ALL, THIS IS MULTIPLE CHOICE.
Answers:
A. 79 − 3x = 12x + 19
B. 7 − x = 12/x
C. x^2 + 3 = 10x − 21
Write the number in standard form.
5.01 times 10 superscript negative 3 baseline
A. 5,010
B. 0.501
C. 0.0501
D. 0.00501
Answer:
The correct answer is D
Step-by-step explanation:
the negative power shows that on the exponent shows that the value is small and is being simplified.
When ever there is a negative power we increase zeros with respect to the exponent value.
A movie theater sends out a coupon for 54% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation for the representation of the given situation will be
y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.
What is an equation?An equation is a statement that says that the value of two mathematical expressions is equal.
Given that, a cinema sends out a coupon for 54% off the price of a ticket.
The equation for this situation will be y = x - 0.54x,
And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.
Hence, the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be
y = x - 0.54x
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An orange grove manager uses two different sized buckets to load oranges into a truck. The first bucket can transport a pound of oranges, and the second bucket can transport
y pounds of oranges. The first bucket is filled up G times and the second bucket is filled up I times The total amount of oranges. I that have been loaded can be found usina
the equation T = Ga + Hy.
Solve for H.
T + Ge
O H
y
O H= y(T - Gx)
T
0 H = Gx+y
T_ Cr
O H
2
On solving for [H], we get -
H = (T - Ga)/y
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
T = Ga + Hy
We have -
T = Ga + Hy
Solving for [H], we get -
Hy = T - Ga
H = (T - Ga)/y
Therefore, On solving for [H], we get -
H = (T - Ga)/y
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use eulers method with step size 0.5 to compute the approximate y values y1 y2 y3 and y4 of the solution of the intitial value problem y'=y 2x y(3)=0
Answer:
[tex]y_1=\boxed{-3}[/tex]
[tex]y_2=\boxed{-8}[/tex]
[tex]y_3=\boxed{-16}[/tex]
[tex]y_4=\boxed{-28.5}[/tex]
Step-by-step explanation:
Given:
[tex]y'=y-2x, \;\;y(3)=0[/tex][tex]h=0.5[/tex]Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:
[tex]y'=y-2x, \;\;y(3)=0[/tex]
at x = 3.5, 4, 4.5, 5.
Therefore:
[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]
Euler's Method
[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]
[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]
[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]
Which of the following (x,y) coordinates are solutions to the inequality 2x+5y<1?
The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)
How to determine the coordinates of the solution of the inequality?From the question, we have the following inequality that can be used in our computation:
2x+5y<1
Solving further, we need to collect the like terms
Since there are no like terms in the expression, it remains unchanged
So, the inequality becomes
2x + 5y < 1
Subtract 5y from both sides of the inequality
This gives
2x < 1 - 5y
Divide both sides by 2
The expression becomes
x < 1/2 - 5/2y
Evaluate
x < 0.5 - 2.5y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x < 0.5 - 2.5 * 4
Evaluate the products
x < -9.5
This means that x is less than -9.5 when y is 4
-10 is less than -9.5
So, we have
x = -10 and y = 4
Express as ordered pairs (i.e. coordinates)
(x, y) = (-10, 4)
Hence, the coordinates of the solution is (-10, 4)
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How can you determine if an inverse is a function?
Solve. 4x+2=(1/8)x-2
_______
Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
The slope of the line is - 2 with the equation as 2 x + y - 2 = 0
We are given that:
y intercept of the line = 2
Point is (0, 2)
It is parallel to the line 2 x + y = - 5
Slope of line 2 x + y = - 5:
y' = - 2
m = - 2
Slope of parallel lines are equal
m = m'
m' = - 2
Equation of the line:
y - y₁ = m( x - x₁)
y - 2 = - 2( x - 0)
y - 2 = - 2 x
2 x + y - 2 = 0
a) standard form of the equation = 2 x + y - 2 = 0
b) slope of the line = m' = - 2
c) point-slope form = (y - 2) / (x - 0) = - 2
d) Properties of algebra used = cross multiplication and simplification.
Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0
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solve the following inequality
x³-5x² < 4x-20
The final solution is all the values that make (x+5) (x+2) (x−2)=0 true.
x = −5,−2,2
What is factorization?
Factorization, also known as factoring, is the process of breaking down an object (such as a number, a matrix, or a polynomial) into a product of another object, or factors, which when multiplied together yield the original object (such as the number or matrix) in question.
What is inequality?
A relationship between two expressions or values that are not equal to each other is called an inequality.
Here, we have
Factor out the greatest common factor from each group
x²(x+5) - 4(x+5) = 0
Factor the polynomial by factoring out the greatest common factor, (x+5)
(x+5)(x²-4) = 0
Rewrite 4 as 2².
(x+5)(x²-2²) = 0
(x+5)(x+2)(x-2) = 0
Now,
x+5 = 0
x-2 = 0
x+2 = 0
set x+5 =0 then we get
x = -5
set x+2 =0 then we get
x = -2
set x-2 =0 then we get
x = 2
Hence, the final solution is all the values that make (x+5) (x+2) (x−2)=0 true.
x = −5,−2,2
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WILL GIVE BRAINLiST, RATE IT 5 STARS, AND HEART IT FOR CREATIVE WRITING HELP. PLEASE ANSWER BOTH QUESTIONS, IF ITS ONE QUESTION I CAN DO THAT TOO!
1. What are 5 observations you made about the setting of “Avatar” after watching the trailer? (Play the first avatar movie trailer)
2. Based on the trailer, what is one central theme of the movie? How does the setting contribute to this theme? (Play the first avatar movie trailer)
when answering, answer it like 1= and 2=
Answer: Read explanation
Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.
Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.
Make any corrections if you want! Make it more comfortable to your style!
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3x+=x+5
4
2
6
12
10
If you multiply by 12 you will get rid of all your fractions.
What are linear equations?In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
The given linear equation is
6 - (3/4)x + (1/3) = (1/2)x + 5
In this equation the fractions are
(3/4), (1/3) and (1/2)
Take the LCM of 4, 3, and 2
LCM(4, 3, 2) = 12
So, if we multiply the equation with the number 12 we can eliminate the fractions.
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4x + 10y = 2
x - 10y = 13
Answer:
x = 3
y = -1
Step-by-step explanation:
4x + 10y = 2 Eq. 1
x - 10y = 13 Eq. 2
The result of the sum of Eq. 1 and Eq. 2 is:
4x + x = 5x
10y - 10y = 0y = 0
2 + 13 = 15
Then the result is:
5x = 15
x = 15/5
x = 3
From Eq. 2:
x - 10y = 13
3 - 10y = 13
-10y = 13 - 3
-10y = 10
y = 10/-10
y = -1
Check:
From Eq. 1:
4x + 10y = 2
4*3 + 10*-1 = 2
12 - 10 = 2
The solution of the equation is that the value of x = 3 and y = -1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The equation will be solved as,
4x + 10y = 2 Eq. 1
x - 10y = 13 Eq. 2
The result of the sum of Eq. 1 and Eq. 2 is:
4x + x = 5x
10y - 10y = 0y = 0
2 + 13 = 15
Then the result is:
5x = 15
x = 15/5
x = 3
From Eq. 2:
x - 10y = 13
3 - 10y = 13
-10y = 13 - 3
-10y = 10
y = 10/-10
y = -1
Therefore, the solution of the equation is that the value of x = 3 and y = -1.
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A Not secure admin248 acellus.com/StudentFunctions/interface/acell
Parallel Lines
Inear Functions and Systems
A line is parallel to y = -2x - 3 and
intersects the point (5, 4). What is
the equation of this parallel line?
Start by entering this into point-slope form.
y -4 = -2(x-[?])
In a geometric sequence, the difference between each pair of consecutive terms must be the same.
The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
What is a Sequence?Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -
3, 6, 9, 12, 15
x, x + 2, x + 4, x + 6
Given is the following statement -
"In a geometric sequence, the difference between each pair of consecutive terms must be the same"
The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -
a[n + 1]/a[n] = r {constant}
Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
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Which equation is equivalent to the given equation?
x²- 10x = 14
-
(x - 10)² =-86
(x - 5)² = 39
(x - 5)²= = -11
(x-10)²= 114
Can you answer this question?
Answer: y= 3 times 2 to the power x. Second answer
Step-by-step explanation:
if you plug in 0 for x, y= 3x 1= 3
if you plug in 1 for x y= 3 x 2 = 6
Look at the x values and y values
(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.
Seven factory workers take part in a charity swim. Altogether they swim 179 lengths of a pool. How many lengths does each worker swim on average?
The length of each factory worker on average is 25.57 lengths
How to determine the length of each on average?From the question, we have the following parameters that can be used in our computation:
Total length of the pool = 179 lengths
Number of workers = 7
The length of each on average is calculated as
Average length = Total length of the pool/Number of workers
Substitute the known values in the above equation
So, we have the following equation
Average length = 179/7
Evaluate the quotient
Average length = 25.57
Hence, the average length is 25.57 lengths
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Find the Surface Area for the following:
(Use 3.14 for . Do not round and do not type your units.)
Surface Area = ______ in²
The shape has a surface area of: Surface Area = 282.6 in²
How to determine the surface area?The given parameter is represented on the figure
In this case, the figure is a cone with the following parameters
Radius, r = 5 inches
Height, h = 12 inches
The surface area of the cone is then calculated as
A = πr * (r + √(h² + r²))
Substitute the known values in the above equation, so, we have the following representation
A = 3.14 * 5 * (5 + √(12² + 5²))
Evaluate the expression
A = 282.6
Hence, the surface area is 282.6 square inches
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consider the line y= 5/2x+5
1. find the equation of the line that is perpendicular to this line and passes through the point (-5,6)
2. find the equation of the line that is parallel to this line and passes through the point (-5,6)
Answer:
Step-by-step explanation:
1
y-6 = -2/5(x-(-5)
y - 6 = -2/5(x+5)
y -6 = -2/5 x -2
y = -2/5 x -2 + 6
y = -2/5 x + 4
2
y-6 = 5/2 (x-(-5)
y-6 = 5/2 (x+5)
y - 6 = 5/2 x + 25/2
y = 5/2 x + 25/2 + 6
y = 5/2 x + (25+12)/2
y = 5/2 x + 37/2
Which model represents the sum of 4 + 12?
Answer: 16
Step-by-step explanation:
Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.
Is f = 9 a solution to this equation?
4f = 36
Yes or no
ASAP Write an equation of a quadratic formula with the given properties: f(3)=f(-5)=0;f(-6)=-36
The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).
How to derive a quadratic equation that contains three points
In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:
y = a · x² + b · x + c
Where:
x - Independent variable.y - Dependent variable.a, b, c - Real coefficients.We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:
9 · a + 3 · b + c = 0
25 · a - 5 · b + c = 0
36 · a - 6 · b + c = - 36
Then, the solution to the system is found by numerical methods:
(a, b, c) = (- 4, - 8, 60)
The equation that contains the three points is y = - 4 · x² - 8 · x + 60.
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please help me and please hurry. also please show working clearly!!
Answer:
The limit does not exist
Step-by-step explanation:
This is because the left hand limit is 3,we know this because as the graph approaches from the left side of the Cartesian plan the open dot is on 3
and the right hand limit is 1 because as the graph approaches the X=1 from the right hand side the open dot lands on 1
Since the left hand limit doesn't equal to right hand limit,the overall limit of x=1 doesn't exist.
Simplfy and solve 13+7x66
Have someone read this to you while your eyes are closed and answer the question in the end. 8 x 5 - 23 + 21 x 6 + 100 - 20 x 5 = ????
Answer:
143
Step-by-step explanation:
Factorise this expression as fully as possible
2xy^2 + 8y
2y(xy+4)
Hope this answers your question!
Answer:
2y(xy+4)
Step-by-step explanation:
First, Distribute
you get 2y(xy+4) because you have to isolate the like terms than find a gcf of the terms
Anthony claims that A KLM is an isosceles triangle. Find the length of KM using the distance formula.
Answer:√53 or 7.28010988928
Step-by-step explanation:
Solve the equation below for x
Cx — 4 = 7
The equation for the value of x will be 11/C.
According to the question,
We have the following equation:
Cx — 4 = 7
Now, we can easily find the value of x from this equation by following the given steps.
We will first add 4 on both sides of the equation:
Cx = 7+4
Adding the two numbers on the right hand side:
Cx = 11
Dividing by C on both sides of the equation:
x = 11/C
(More to know: we can now find the value of x if the value of C is given.)
Hence, the equation for the value of x will be 11/C.
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