The annual average price per square foot for office space in a city was $30.18 in 2004, and it was $66.85 in 2015.
(a) Find an exponential function of the form f(t)=y0b^t to model these data in which t=0 corresponds to 2004.

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.

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.

To know more about equation here

https://brainly.com/question/3162971

#SPJ1

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!

Answer:

143

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.

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.

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.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ2

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:

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]

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.

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

To learn more about the factorization from the given link

https://brainly.com/question/25829061

#SPJ13

The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

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.

To solve more questions on Arithmetic and Geometric sequences, visit the link below -

brainly.com/question/13817006

#SPJ2

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.

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.

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

For more references on equation, click;

https://brainly.com/question/10413253

#SPJ1

The shape has a surface area of: Surface Area = 282.6 in²

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

Read more about surface area at

https://brainly.com/question/10254615

#SPJ1

Answer:√53 or 7.28010988928

Step-by-step explanation:

Answers:

A. 79 − 3x = 12x + 19

B. 7 − x = 12/x

C. x^2 + 3 = 10x − 21

The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)

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)

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

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

The height of a person is 5.2ft in centimeter: 158.49cm

So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.

Approximately 30.48 cm makes up one foot.

1 ft = 30.48 cm

Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.

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.

To learn more about Factor click on the link

brainly.com/question/25829061

#SPJ1

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

Learn more about slope here:

https://brainly.com/question/3493733

#SPJ9

If you multiply by 12 you will get rid of all your fractions.

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.

To know more about linear equations, visit:

brainly.com/question/13955204

#SPJ1

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

On solving for [H], we get -

H = (T - Ga)/y

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

To solve more questions on Equation Modelling, visit the link below -

brainly.com/question/14441381

#SPJ1

The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).

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:

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.

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

The length of each factory worker on average is 25.57 lengths

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

Read more about average at

https://brainly.com/question/548811

#SPJ1