A house is purchased for $145,000 and each year increases in value by 6% of its value the previous year. (6 marks) Let be the value of the house in year . Write a difference equation which gives the value of the house after years. Solve the difference equation. Find the projected value of the house in 15 years.

Step-by-step explanation:

The trick here is to realize that this is not a sum of the money that the three people paid originally, as that would need to include the money the clerk has ($25). This is instead a sum of a smaller amount the people could have paid ($9 × 3 people = $27), added with the additional money that the clerk would not have needed had they paid that smaller amount ($27 paid - $25 actual cost = $2). Another way to say this is, the $27 already includes the bellhop's tip. To add the $2 to the $27 would be to double-count it. So, the three guests' cost of the room, including the bellhop's tip, is $27. Each of the 3 guests has $1 in his pocket, totaling $3. When added to the $27 revised cost of the room (including tip to the bellhop), the total is $30.

To obtain a sum that totals to the original $30, every dollar must be accounted for, regardless of its location.

Thus, the sensible sum can be expressed in this manner:

The mixture requires 200 ounces of 40% alloy.

A mixture is a physical combination of two or more substances that retain their identities and are blended as solutions, suspensions, or colloids.

x = amount of 40% copper

400 = amount of 70% copper

x + 400 = total amount of copper = amount of 60% copper

Set a correctly weighted mixture of x and 300 equal to the a weighted (x+300), in which the weights are decimal percentages;

0.4x + 0.7(400) = 0.6(x + 400)

Solve for x:

0.4x + 280 = 0.6x + 240

0.2x = 40

x = 200

x = 200 ounces of 40% copper.

Therefore, the amount of 40% alloy needed for the mixture is 200 ounces.

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Answer:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25

The solution of the geometrical system is (x, y) = (2.5, 48.5).

In this question we have a picture representing two lines and a semirray that brings out two formulae for supplementary angles, these are shown below:

(x + 10) + 30 + (3 · y + 2) = 180

x + 3 · y = 148         (1)

30 + (3 · y + 2) + (5 · x - 10) = 180

5 · x + 3 · y = 158    (2)

And now we resolve the entire system of linear equations by substitution:

By (1):

x = 148 - 3 · y

(1) in (2):

5 · (148 - 3 · y) + 3 · y = 158

740 - 15 · y + 3 · y = 158

12 · y = 582

y = 48.5

By (1):

x = 148 - 3 · 48.5

x = 2.5

The solution of the geometrical system is (x, y) = (2.5, 48.5).

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Answer:

[tex]V=lwh\\\frac{V}{lw} = \frac{lwh}{lw} \\\frac{V}{lw} = h[/tex]

The prove that the equation can be verified using the laws of exponents.

It follows from the task content that the equation given is; 2^(2x+4)= 16 • 2^(2x).

It follows from the laws of indices ; particularly, the product of same base numbers.

The evaluation is therefore as follows;

2^(2x+4)= 16 • 2^(2x)

2^(2x) • 2⁴ = 16 • 2^(2x)

2^(2x) • 16 = 16 • 2^(2x)

Hence, since LHS = RHS, it follows that the expression is mathematically correct.

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Given - F(x) = 5 × 3-x

F(-2) refers to x = -2

Therefore 5×3-(-2) = 5× (3+2) = 5×5 = 25

Hence 25 is the value of f(-2)

So probability that kayla rolls an even number on the red cube and a multiple of 3 on the blue cube is 16.66 ≈ 16%

Given that we have red number cube and blue number cube so as we all know that Probability is the ratio of the favourable number of outcomes to the total number of outcomes is known as Probability.

First, find the possible outcomes.

Kalya has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6

So, possible outcomes =6×6 =36

Let, S be the sample space.

Then, ⁿ(s) =36

Let, E = the event of getting an even number on the red cube and a multiple of  on the blue cube.

E = (2,3),(2,6),(4,3),(6,3),(6,6)

Then,  ⁿ(E)=6

Let, P  is the probability of the event .

So, P(E)= [tex]\frac{n(E)}{n(S)}[/tex] = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex] = 16.67 percent or 16[tex]\frac{2}{3}[/tex]  %

Thus, the probability Kayla rolls an even number on the red cube and a multiple of  on the blue cube is 16.66 percent.

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Answer:

16%

Step-by-step explanation:

Answer:

6x + 9 = 4

Step-by-step explanation:

There are 20 bicycles at the Main Street station.

According to question statement, A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the given two stations.

We are supposed to know the number of bicycles at the Main Street station.

Let us assume that the number of bicycles at the Park Avenue station is "x". Then, number of bicycles at the Main Street station will be "5x".

We will have to form a Linear Equation of single variable "x" as per the conditions based in the question statement, and solving for x, we will obtain our desired answer.

As there are 24 bicycles at the two stations therefore,

[tex]x + 5x = 24[/tex], will be our equation.

Solving the equation for x, we get

[tex]x + 5x = 24\\6x = 24\\x=\frac{24}{6} \\or x=4[/tex]

Therefore the number of bicycles at the Park Avenue station is 4.

And the number of bicycles at the Main Street station will be 5x i.e., [tex]5*4 = 20[/tex].

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Answer: -2.25

Step-by-step explanation:-2.25 because it is closer to 0

Answer:

the number is -1

Step-by-step explanation:

11 + 10x = 1  Subtract 11 from both sides

10x = -10  Divide both sides by 10

x = -1

Check:

11 + (10 x -1) = 1

11 + (-10) = 1

Answer:  1

Step-by-step explanation:

here only taking the power of x in account

we have

[tex]\frac{x}{y} + \frac{y}{x}-\frac{x}{y} - \frac{y}{x}[/tex]

=0

since  [tex]x^{0}[/tex] =1

so solution is 1

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Answer: B

Step-by-step explanation:

Answer: x = [tex]\frac{-31}{23}[/tex], y = [tex]\frac{-9}{23}[/tex], z = [tex]\frac{-83}{23}[/tex]

Step-by-step explanation :Solving system of equations

Given the following system of equation below

 - 4x + 2y + z =1 .......(1)

x − y + 3x =  −5 ........(2)

3x + y − 4z = 10.........(3)

first we solve eq 1 and eq 3:

we get, -13x + 9y = 14 ..........(4)

Now we solve eq 2 and eq 4 and get value of x and y:

we get,  x = [tex]\frac{-31}{23}[/tex] and y = [tex]\frac{-9}{23}[/tex]

finally we put value of x and y in eq 1 and get the value of z:

-4(-31/23) + 2(-9/23) + z = 1

106/23 + z = 1

z = 1 - 106/23

z =[tex]\frac{-83}{23}[/tex]

Hence the solution of equation is ([tex]\frac{-31}{23}[/tex], [tex]\frac{-9}{23}[/tex], [tex]\frac{-83}{23}[/tex])

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Answer:

  64

Step-by-step explanation:

You have the recursive formula f(1)=1; f(n)=4f(n-1) and you want f(4).

The value of f(4) can be found a couple of ways. Perhaps the simplest is to compute the first 4 terms of the sequence using the recursive formula.

  f(1) = 1

  f(2) = 4·1 = 4

  f(3) = 4·4 = 16

  f(4) = 4·16 = 64

The value of f(4) is 64.

The multiplying factor of 4 on the previous term tells you this is a geometric sequence with a common ratio of 4. The explicit formula is then ...

  f(n) = f(1)·r^(n-1) . . . . . n-th term of sequence with common ratio r

  f(n) = 1·4^(n-1) . . . . . . formula for f(1)=1 and r=4

For n=4, this is ...

  f(4) = 1·4^(4-1) = 4^3

  f(4) = 64

Answer:

radius

Step-by-step explanation:

Answer:

I don't get the question will please can u snap it so I can see it my self and I will help u

Answer: -2 1 over 2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Think of "f(a)" like "y" in this context.   You can set that equal to 11 and solve for a:

f(a) = 3a + 2

11 = 3a + 2

9 = 3a

3 = a

Answer:7

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

6+14=5x

Add 6 and 14 which is equal to 20.

You will get 20=5x which you will then divide by 5 inorder to solve for x.

X=4

Pull out like factors :

5x - 20 = 5 • (x - 4)

Solve : 5 = 0

This equation has no solution.

A a non-zero constant never equals zero

Solve : x-4 = 0

Add 4 to both sides of the equation :

x = 4

Answer:

Step-by-step explanation:

You want the exact values of sine and cosine of the angle whose terminal point is at x=2/5 on the unit circle in the first quadrant.

The coordinates of a point on the unit circle are (cos(θ), sin(θ)). You already know that the x-coordinate is 2/5, so ...

  cos(θ) = 2/5

The Pythagorean identity in trigonometric terms is ...

  sin²(θ) +cos²(θ) = 1

Then the sine of the angle is ...

  sin(θ) = √(1 -cos²(θ))

  sin(θ) = √(1 -(2/5)²) = √((25 -4)/25)

  sin(θ) = (√21)/5

The exact values of sine and cosine are ...

∑ Hey, shadowwolf9764 ⊃

Answer:

1.52545155993

Round if needed: 1.53

Step-by-step explanation:

Given:

[tex]\frac{0.128\div 3.2+0.86}{\frac{5}{6}\cdot 1.2+0.8}+\frac{\left(1\:\frac{32}{63}-\frac{13}{21}\cdot 3.6\right)}{0.505\cdot \frac{2}{5}-0.002}[/tex]

Solution:

Convert Mixed Number to a improper fraction:

[tex]1\frac{32}{63}=\frac{95}{63}[/tex]

Now we have;

[tex]=\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}+\frac{95}{63}[/tex]

Solving the first part:

[tex]\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}=\frac{0.128}{7.308}[/tex]

Then we have;

[tex]=\frac{0.128}{7.308}+\frac{95}{63}[/tex]

Least common factor: 460.404

[tex]=\frac{8.064}{460.404}+\frac{694.26}{460.404}[/tex]

Now using this formula: [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]

[tex]=\frac{8.064+694.26}{460.404}[/tex]

Adding the numbers:

[tex]=\frac{702.324}{460.404}[/tex]

Next divide the numbers:

[tex]1.52545155993[/tex]

Hence, the answer is:

[tex]1.52545155993[/tex]

Round if needed:

[tex]1.53[/tex]

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The final answer for 2211₃ to convert into base 10 is 76₁₀.

Given 2211₃

Expand the number as below

2211₃ = 2 * 3³ + 2 * 3² + 1 * 3¹ + 1 * 3⁰

To convert base 3 to base 10 we need to expand form numbers as

2211₃ = 2 * 3³ + 2 * 3² + 1 * 3¹ + 1 * 3⁰

         = 2 * 27 + 2 * 9 + 1 * 3 + 1 * 1

         = 54 + 18 + 9 + 1

         = 76₁₀

Therefore, the Correct answer for 2211₃ to convert into base 10 is 76₁₀

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