Consider an investment of $6000 that earns 4.5% interest


What is the value of the investment after
15 years if the interest is compounded
annually?

Answer: The second option, y = 3(1/3)^x

Step-by-step explanation: Input each equation into a graphing calculator (preferably GeoGebra online) and check the answer. I linked the equation, but make sure to check anyway just in case :)

[tex](a+b)(a-b) = a^2 - ab + ba - b^2 = a^2 - b^2[/tex]

Since the middle terms cancel each other out, what is left is the difference of two squares.

In your example (x+6)(x-6) = x² -36

Answer:

10.33332

Step-by-step explanation:

-6.77777 is 6.77777 units away from 0. So there's 6.77777+3.55555 which is 3.55555 units away from 0.

Add those two numbers together and it's 10.33332

Answer:

10.33332

Step-by-step explanation:

distance between -6.77777 and 3.55555 is 10.33332

Answer:

-5x-24

Step-by-step explanation:

3(2x-8)-11x

Use distributive property.

6x-24-11x.

Combine like terms.

6x-11x-24=-5x-24

-5x-24

Hope this helps!

If not, I am sorry.

Answer:

-5x - 24

Step-by-step explanation:

3(2x − 8) – 11x =

Distribute the 3, then combine like terms.

= 6x - 24 - 11x

= -5x - 24

If quadrilateral JKLM were in third quadrant then the coordinates will be (-1,0),(-4,-1),(-4,-2)(-1,-2)

Given Quadrilateral JKLM is in fourth quadrant and coordinates (1,0),(4,-1),(4,-2)(1,-2)

We know that the coordinates of x used to negative in third quadrant and positive in fourth quadrant. Coordinates of y used to negative in third and fourth quadrant.

So in order to change the coordinates from fourth to third we need to change the coordinates of x axis to negative and the coordinates will be :

Coordinates of J will change from (1,0) to (-1,0)

Coordinates of  K will change from(4,-1) to (-4,-1)

Coordinates of L will change from (4,-2) to (-4,-2)

Coordinates of M will change from (1,-2) to (-1,-2).

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Answer:

The answer is 90.

Thank you

Answer:

89.6

Step-by-step explanation:

The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32

F = [ C × (9/5) + 32 ]

Given that, C = 32

F = 32 × (9/5) + 32

F = 32 [ 1 + (9/5) ]

F = 32 [ 1 + 1.8 ]

F = 32 × 2.8

F = 89.6

Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.

Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.

Thus to solve the given question, let the required distance be represented by x.

Applying the cosine rule, we have;

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C

The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;

C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]

C = [tex]50^{o}[/tex]

Thus,

[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]

  = 1296 + 729 + 1944(0.6429)

  = 2025 + 1249.8

[tex]c^{2}[/tex] = 3274.8

c = [tex]\sqrt{3274.8}[/tex]

  = 57.2259

c = 57.23

Therefore, the distance from the ship to the yacht is 57.23 km.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

Step-by-step explanation:

A function is continuous at x is

Limit as x approaches c= f(c).

Step 1: Find f(4).

4 is defined for 2x-1 so plug in. 4 for x.

[tex]2(4) - 1 = 7[/tex]

Note that what we just calculated was not only f(4) but also the left sided limit of f(x).

Step 2: Make sure the left sided and right sided limit are equal to 7.

[tex]a + 5x = 7[/tex]

Plug in 4 for x

[tex]a + 5(4) = 7[/tex]

[tex]a = - 13[/tex]

The trigonometric ratios shows that the cos M is 4/5.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: [tex]hypothenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin [tex]\alpha[/tex],  cos [tex]\alpha[/tex] and tan [tex]\alpha[/tex], where:

[tex]sin \alpha =\frac{opposite\;leg}{hypotenuse} \\ \\ cos \alpha =\frac{adjacent\;leg}{hypotenuse} \\ \\ tan \alpha =\frac{opposite\;leg}{adjacent\;leg}[/tex]

For finding the cos M, firstly, you should find the side MN from Pythagorean Theorem.

[tex]hypothenuse^2=(leg_1)^2+(leg_2)^2\\ \\\ 30^2=18^2+(MN)^2\\ \\ 900=324+(MN)^2\\ \\(MN)}^2=900-324\\ \\ (MN)^2=576\\ \\ MN=24[/tex]

If MN=24, the cos M will be

[tex]cosM =\frac{adjacent\;leg}{hypotenuse} =\frac{24}{30} =\frac{4}{5}[/tex]

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Answer:

8

Step-by-step explanation:

If the only zero for this function is at x = - 4 it looks like this:

f(x)  = (x+4)(x+4)        =    x^2 +8x + 16         so j = 8

Answer:

Step-by-step explanation:

x² +jx +k = 0

If there is only one root ( - 4 ), then (x + 4)² = 0

or

x² + 8x + 16 = 0

j = 8 and k = 16

The paint that the farmer needs to paint his Silo will cost $152.75.

To calculate the value of the total paint that the farmer will require, we must carry out the following procedure:

1. Identify the area you need to paint

2. Find how many cans of paint he needs.

That is, he will need 13 cans of paint.

3. Find the price of 13 cans of paint.

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The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.

A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.

Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.

Now, in terms of direction;

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a)

x×3+4=22

b)

x×3+4=22

x×3=22-4

x×3=18

x=18÷3

x=6

Hope it helps

Answer:

x=6

Step-by-step explanation:

your equation would be X * 3 + 4 = 22

to solve you subtract four from both sides then divide three by both sides because you do the opposite of the sign thats there and you get x= 6! i hope this helped

Answer: cosecant

Formula's are:

Secant:

1/cos(x) = sec(x)

Cosecant:

1/sin(x) = cosec(x)

Cotangent:

1/tan(x) = cos(x)/sin(x) = cot(x)

Answer:

The answer is 105.

Step-by-step explanation:

Answer:

∠ABC =   52°

∠BCA =  48°

∠CAB = 80°

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180.

13x² + 12x² + 20x² = 180

Combine like terms,

                 45x²  = 180

                     x² = 180 ÷ 45

                     x² = 4

                     x = √4

                     x = ± 2

x = 2 ; -2

∠ABC = 13x² = 13*4 = 52°

∠BCA = 12x² = 12 *4 = 48°

∠CAB = 20x² = 20 *4 = 80°

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

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The equation of the appropriate line of best fit is y = 1.25x + 2

Start by drawing a line through the points (see attachment)

From the attached graph, we have:

(x, y) = (0,2) and (4,6.5)

Calculate the slope (m) using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (6.5 - 4)/(2 - 0)

Evaluate

m = 1.25

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1.25(x - 0) + 2

Expand

y = 1.25x + 2

Hence, the equation of the appropriate line of best fit is y = 1.25x + 2

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Answer:

[tex]ME =\frac{z*s}{\sqrt{n}}[/tex]

Step-by-step explanation:

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings

To find margin of error, you need

        n = sample size

        z = z-score

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Answer: B. 4x-2y=2

Step-by-step explanation:

We will work this out one by one. Plug in the x and y values of the solution to the equations and you will see which one is true or false.

A. [tex]2(1)+y(1)=2\\2+1\neq 2[/tex]     B. [tex]4(1)-2(1)=2\\4-2=2[/tex]

C. [tex]2(1)-2(1)=2\\2-2\neq 2[/tex]     D. [tex]x(1)+y(1)=4\\1+1\neq 4[/tex]

With this information, we see that B is the correct answer.

I hope this helped!! Pls mark brainliest!! :))

Answer:

The LCM is made by multiplying all factors included in the factoring of the given expressions. Common factors are used once only and the one with the highest power is used. x + 3 is a factor in the first expressions is therefore used.

Step-by-step explanation:

Answer:

90 liters

Step-by-step explanation:

According to the graph in order to gain $36 you must sell 90 liters. Hope this helps :)

The equation will be 12a – 360 = 216. Then the value of the variable a will be 48.

The solution of the equation means the value of the unknown or variable.

When you multiply a number by 12 and subtract the product from 360, the difference is 216.

Let the number be a.

Then we have the equation

12a – 360 = 216

By solving the equation, we have

12a = 216 + 360

12a = 576

   a = 576/12

   a = 48

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Using the given information, the smallest possible value of x - z is 12

From the question, we are to determine the smallest possible value of x - z

From the given information,

w and x are whole numbers

and

w > 60

x < 50

∴ w = 61, 62, 63, 63, 65, ...

x = 49, 48, 47, 46, 45, ...

Then,

The smallest possible value of x - z is

x - z = 61 - 49

x - z = 12

Hence, the smallest possible value of x - z is 12

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Answer:

[tex]1\frac{1}{5}[/tex]

Step-by-step explanation:

3 = 3/1

(multiply top and bottom separately for fractions)

[tex]\frac{3}{1}[/tex] × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex]

[tex]\frac{6}{5} = \frac{5}{5}+\frac{1}{5}= 1\frac{1}{5}[/tex]

Answer:

Step-by-step explanation:

multiplying three (3) and two(2) and express the product of three and two over five.

five can enter in six three times , remainder 1

The fraction in lowest terms is one whole number , one over five.

The attached graph represents the function h(x), where h(x) = f(x)g(x)

Consider the functions f(x) = x - 6 and g(x) = x + 6. Which graph shows h(x) = f(x)g(x)?

We have

f(x) = x - 6

g(x) = x + 6

The equation h(x) = f(x)g(x) means

h(x) = f(x) * g(x)

So, we have:

h(x) = (x - 6) * (x + 6)

Expand

h(x) = x² - 36

See attachment for the graph of function h(x)

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Answer:

A on edg. 2020

Step-by-step explanation:

Which graph shows h(x) = f(x)/g(x)

Answer:

(49p2–490p) ÷(p–10)

Step-by-step explanation:

Answer:

8 is correct.

Mark as brainlist, thanks me, and rate. Hope it helps you!!!

The complete sentence is as follows:

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.

The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.

Given, An amusement park prices tickets at $55 and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.

Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.

[tex]P(x) = -40x^2- 100x + 27,500[/tex].

In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

We need to use the given information to complete the sentences.

The complete sentence is as follows:

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.

The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.

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The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

An amusement park prices tickets at $55 and sells an average if 500 tickets daily.

The function P(x) represents the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.

Plug x = 0

P(0) = 27500

The above value is the constant of the polynomial function.

The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increases in the price of a ticket.

As the x is the number of $2 increases in the price of a ticket.

Then,

= (500 - 20x) is the binomial that represents the number of tickets sold after x increases by $2

Thus, the constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.

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The number of the specimens would be in the culture after 5 minutes will be 7,962.62.

Consider the function:

y = a (1 + r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

A bacteria culture grows at a rate of 20% per minute.

If the culture initially has 3,200 bacteria specimens.

Then the equation will be

y = 3200 (1 + 0.2) ˣ

y = 3200 (1.20) ˣ

Then the number of the specimens would be in the culture after 5 minutes will be

y = 3200 (1.20)⁵

y = 7962.62

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The area of triangle ABC from the given vertices is gotten as; 7.5

We are given the vertices of the triangle as;

A(1, 2)

B(4, 0)

C(1,-4)

The formula for area of a triangle with 3 vertices is;

Area = ¹/₂[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Thus;

Area = ¹/₂[1(0 + 4) + 4(-4 - 1) + 1(1 - 0)]

Area = ¹/₂(4 - 20 + 1)

Area = -7.5

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