Slope of (3,2) and (19,6)

Answer:

  16.8 hours

Step-by-step explanation:

An exponential population increase can be modeled by the function ...

  p(t) = a·b^(t/p)

where 'a' is the initial value (at t=0), b is the multiplier in time period p.

__

The colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.

  p(t) = 80·1.6^(t/3)

  1119 = 80·1.6^(t/3)

__

Solving this for t, we find ...

  1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80

  log(1119/80) = (t/3)log(1.6) . . . . . take logarithms

  t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t

  t ≈ 16.8 . . . . hours

It will take about 16.8 more hours for the population to increase from 80 to 1119.

The graph of the given quadratic equation is graph C.

Remember that for a quadratic equation with a vertex (h, k), the vertex form is given by:

[tex]y = a*(x - h)^2 + k[/tex]

Where a is the leading coefficient, in this case we have a = 1.

Here we have:

[tex]y = (x - 3)^2 - 25[/tex]

So the vertex is at (3, -25).

From that function we can also get the y-intercept, that is given by evaluating the function in x = 0, so we get:

[tex]y = (-3)^2 - 25 = -16[/tex]

So this function passes through (3, -25) and (0, -16). The sketch can be seen below.

Notice that from the given options only the third graph intercepts the y-axis on the negative region, so from that, we conclude that the third graph is the correct option.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Work Shown:

tan(angle) = opposite/adjacent

tan(61) = x/9

x = 9*tan(61)

x = 16.2364298 approximately

Your calculator needs to be in degree mode. One quick way to check is to type in something like tan(45) and the result should be 1.

Keys:

Step-by-step explanation:

[tex]\left(5\sqrt{3}-\sqrt{27}\right)^3\\\5\sqrt{3}-\sqrt{27}^3=\left(2\sqrt{3}\right)^3\\= 2\sqrt{3}\\\left(2\sqrt{3}\right)^3=2^3\left(\sqrt{3}\right)^3\\=2^3\left(\sqrt{3}\right)^3\\2^3=8\\=8\left(\sqrt{3}\right)^3\\=8\cdot \:3\sqrt{3}\\8\cdot \:3=24\\=24\sqrt{3}[/tex]

Answer:

It is not an integer.

Step-by-step explanation:

[tex](5\sqrt{3} -\sqrt{27} )^3\\\\=(\sqrt{3} *(5-3))^3\\\\=8*3*\sqrt{3} \\\\=24\sqrt{3} \\[/tex]

The correct solution method of Kendall's money is 7x = 98. Divide both sides by 7. Kendall had $14

x = Kendall's money

Mateo's money = $98

= 7 × x

The equation:

7 × x = 98

7x = 98

x = 98/7

x = $14

Therefore, the correct answer is option B

Learn more about equation:

https://brainly.com/question/2972832

#SPJ1

The number of quarts of paint did mieko use in the living room is A = 3 quarts

Given data ,

Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room

Now , on simplifying the equation , we get

Two gallons of paint is equal to 8 quarts (2 x 4 = 8)

Mieko used 1/4 of the paint on her bedroom, which is equal to 2 quarts (1/4 x 8 = 2)

She used 3 quarts of paint on the hallway

Thus, Mieko used a total of 2 + 3 = 5 quarts of paint on the bedroom and hallway

Therefore , she used 8 - 5 = 3 quarts of paint in the living room

Hence , the number of quarts is A = 3 quarts

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The purpose of knowing the angle of elevation and depression in relation to the field of surveyor, military/police, aeronautics (pilot), engineers, landscapers, and architects is discussed below

If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object. If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.

If the pilot looks straight out, that line of sight is horizontal (focused on the distant horizon). The pilot might see the airport's runway, distant buildings, or even mountains in her field of view.

If the pilot looks down at the ground, the one will see the ground crew. The angle of depression is the angle that is formed between the horizontal and the downward looking angle. It is always a downward view, an angle below the horizon.

For the ground crewmember, looking down would not be much help in communicating with the pilot in her cockpit seat. The crewmember will look up, above the horizontal line, to see the pilot. The ground crewmember's angle of vision if an angle of elevation, the angle above the horizon.

Angle of elevation or depression in a survey can be defined as the angle subtended between the line of sight passing through the scope and the horizontal axis of the instrument.

Engineers, landscapers, architects all use trigonometry in their everyday life to help them efficiently and safely create or design something new.

Learn more about angle of elevation and depression here:

https://brainly.com/question/18652056

#SPJ1

The area of sector EBR in the given diagram attached below is: 33.75π units².

Area = θ/360º × πr²

Given the following:

Measure of arc TE = 2(m∠TRE) = 2(15) [inscribed angle theorem]

Measure of arc TE = 30°

Arc RE = 180 - arc TE = 180 - 30 [semicircle]

Arc RE = 150°

m∠EBR = Arc RE = 150°

Area of sector EBR = m∠EBR/360 × π(BE²)

Area of sector EBR = 150/360 × π(9²)

Area of sector EBR = 33.75π units²

Learn more about the area of sector on:

https://brainly.com/question/22972014

#SPJ1

Step-by-step explanation:

Select four types of data demographers study to make predictions.

birth rate

death rate

employment

income

marriage

migration

The sum of the interior angles of a regular polygon of 12 sides is 1800°

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of the all the interior angles of a polygon with 'n' number of sides is given by the formula,

Sum of all the angles = (n-2) × 180°

Since the number of sides in the polygon is 12, the sum of the angles will be,

Sum = (12-2) × 180° = 10 × 180° = 1800°

Hence, the sum of the interior angles of a regular polygon of 12 sides is 1800°.

Learn more about Polygon:

https://brainly.com/question/10441863

#SPJ1

The properties used is [tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]

the correct option is (A).

power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

Given:

[tex]4^{\frac{5}{3} } = \sqrt[3]{4^{5} }[/tex]

We can use the following property

[tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]

By using the property we can find the answer.

Learn more about exponents and power here:

https://brainly.com/question/15722035

#SPJ1

Answer:

A

Step-by-step explanation:

If you draw all of the diagonals from one vertex of a regular hexagon we make 5 triangles. This is further explained below.

Generally, the hexagon is simply defined as the hexagon is a polygon with six sides. to be considered a hexagon, the form must have six sides, all of which must be closed.

In conclusion, We get five triangles if we draw the diagonals of a regular hexagon starting at a single vertex.

Read more about Trigonometry

https://brainly.com/question/8120556

#SPJ1

          [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

       Given f(x)=-x+5, find f(-3).

    [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

We have the function

[tex]\longmapsto\sf{f(x)=-x+5}[/tex]

We need to find

[tex]\longmapsto\sf{f(-3)=}[/tex]

[tex]\longmapsto\sf{f(x)=-(-3)+5}[/tex]

Simplifying,

[tex]\longmapsto\sf{f(x)=3+5}[/tex]

(which is the exact same thing as 5-3)

Henceforth, We conclude that the answer is

[tex]\longmapsto\sf{f(-3)=8}[/tex]

#TogetherWeGoFar ~

[tex]\rule{300}{1}[/tex]

Hey there!

Find f(-3) :

f(-3) = 8 ✅

f(x) = -x + 5

>> Substitute -3 for x in f(x) :

f(-3) = -(-3) + 5

f(-3) = 3 + 5

f(-3) = 8

Therefore, your answer is f(-3) = 8

Similar question :

↣ https://brainly.com/question/20922457

Answer:

Step-by-step explanation:

The length of the arc is 3.5 cm

The attached image completes the question

The given parameters are:

The length of the arc is calculated as:

[tex]L = \frac{x}{360} * \pi d[/tex]

So, we have:

[tex]L = \frac{25}{360} * 3.14 * 16[/tex]

Evaluate the product

L =  3.5cm

Hence, the length of the arc is 3.5 cm

Read more about arc lengths at:

https://brainly.com/question/2005046

#SPJ1

Answer:3.5

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

In a right triangle such as this one

 cos (angle) = adjacent leg  / hypotenuse

  cos(k) =   KL / 15

You will need to find the leg length KL using Pythagorean Theorem

 15^2 = 9^2 + (KL)^2             KL =  12

then cos k  = 12/15 = 4/5  

Answer:

The answer is 0.75

Hope this helps!

Answer:

Step-by-step explanation:

V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight

Answer:

"Find g to make this statement true".

12 > 4 • g

The answer of the given expression is 1 & 2.

Thus, the answer of the given expression is 1 & 2.

Learn more about expressions here:

https://brainly.com/question/723406

#SPJ2

answer this fully! i need to know what x equals

X equal minus 0.5

The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²

f(x) = 3x² + 4x³ + 8x⁴

g(x) = -3x + 12x² - 5x³

h(x) = 12x + 6

Therefore,

(f.h)(x) = f(x).h(x)

Hence,

f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)

f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴

(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ +  36x³ + 42x³ + 18x²

(f.h)(x) =  96x⁵ + 132x⁴ + 78x³ + 18x²

learn more on function here: https://brainly.com/question/7783704

#SPJ1

In the given diagram, the measure of angle B (m∠B) is 40°

From the question, we are to determine the measure of angle B

By the exterior angle theorem,

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Then, we can write that

m∠A + m∠B = 155° (Exterior angle theorem)

115° + m∠B = 155°

m∠B = 155° - 115°

m∠B = 40°

Hence, the measure of angle B (m∠B) is 40°

Learn more on Exterior angle theorem here: https://brainly.com/question/26772685

#SPJ1

The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)

Let the number of people be x, and the revenue function be F(x).

Using the assumed values, the revenue function is:

F(x) = (60 + 8x)(250 - 30x)

We have:

F(x) = (60 + 8x)(250 - 30x)

Expand

F(x) = 15000 - 1800x + 2000x - 240x²

Differentiate the function

F'(x) = -1800 + 2000 - 480x

Evaluate

F'(x) = 200 - 480x

Set to 0

200 - 480x = 0

This gives

480x = 200

Divide both sides by 480

x = 0.42

Substitute x = 0.42 in F(x)

F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)

Evaluate

F(x) = 18210

Hence, the maximum revenue is $18210, at a rate of $0.42 per person.

We start by setting F(x) to 5000.

So, we have:

15000 - 1800x + 2000x - 240x² = 5000

Evaluate the like terms

10000 + 200x - 240x² = 0

Using a graphing tool, we have:

x = 6.89

Hence, they would reach their goal at a rate of $6.89 per ticket.

We have:

People = x

Cost per person = 20

So, the cost function is:

C(x) = 20x

Profit is calculated using:

P(x) = F(x) - C(x)

So, we have:

P(x) = 15000 - 1800x + 2000x - 240x² - 20x

Evaluate

P(x) = 15000 + 180x - 240x²

This is the point where P(x) = 0.

So, we have:

15000 + 180x - 240x²  = 0

Using a graphing tool, we have:

x = 8.29

Hence, the break even price is $8.29

Read more about profit, cost and revenue at:

https://brainly.com/question/25623677

#SPJ1

[1] n = -2

       We will convert the words given into a mathematical equation and then solve by isolating the variable. Let n be "a number"

19 decreased by four times a number is 17

19 - four times a number is 17

19 - 4 n is 17

9 - 4n = 17

-

9 - 4n = 17

- 4n = 8

n = -2

[2] x = -1, y = 3, or (-1, 3)

      I will plug the first equation into the second from the system of equations given to us because it already has an isolated variable, y.

2y - 2x = 8

2(2x + 5) - 2x = 8

4x + 10 - 2x = 8

2x = -2

x = -1

      Now, I will plug this value back into the equation and solve for y.

y = 2x + 5

y = 2(-1) + 5

y = -2 + 5

y = 3

The scaled size of the thumbnails is 16 pixels per inch of painting

The given parameters are:

The space between adjacent images is 40 inches.

Given that there are two spaces, the remaining space is:

Remaining = 800 - 2 * 40

Remaining = 720

Given that there are three samples of image, the width of each image is:

Image = 720/3

Divide

Image = 240 pixels

The scaled size is then calculated using:

Scale = Image scale width/actual width

This gives

Scale = 240/15

Evaluate

Scale = 16

Hence, the scaled size of the thumbnails is 16 pixels per inch of painting

Read more about dilation at:

https://brainly.com/question/3457976

#SPJ1

Answer:

2677.4

Step-by-step explanation:

40161/15

The area of rectangle ABCD with side 6 unit by 8 units is  48 unit²

An equation is an expression that shows the relationship between two or more variables or numbers.

From the rectangle ABCD:

AB = 6 units, BC = 8 units

Hence:

Area of ABCD = 6 units * 8 units = 48 unit²

The area of rectangle ABCD with side 6 unit by 8 units is  48 unit²

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1