Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?

Answer:

The area of rectangle =21 sq units .

Step-by-step explanation:

Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.

Consider ABCD is  a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.

First we find sides of rectangle

AB=vertices of B- vertices of A

AB= -2+4i-(1+4i)=-3

BC= Vertices of C - vertices of B

BC=-2-3i-(-2+4i)=-7i

Length of BC=[tex]\sqrt{(-7)^2}[/tex]=7 ( Magnitude always positive)

CD= vertices of D- vertices of C

CD= 1-3i-(-2-3i)=3

Length of CD= [tex]\sqrt{3^2}[/tex]=3 ( Magnitude  always positive)

DA= vertices of A - vertices of D

DA= 1+4i-(1-3i) =7i

Length of DA= [tex]\sqrt{7^2}[/tex]=7 ( Magnitude always positive)

AB=CD and DA= BC

Length BC=7 units

Breadth AB=3 units

Area of the rectangle = [tex]length\times breadth[/tex]

Area of rectangle =[tex]AB\times BC[/tex]

Answer:

x = ± 3 and ± 2

Step-by-step explanation:

The given quadratic equation is

[tex](x^{2}-1)^{2}-11(x^{2}-1)+24=0[/tex]

To make this question easier we will consume ( x² -1 ) = a

a² - 11a + 24 = 0

Now we can factorize this equation easily

a²- 8a - 3a + 24 = 0

a (a-8) - 3 ( a-8) = 0

( a-3 ) ( a-8 ) = 0

Therefore, a - 3 = 0 ⇒ a = 3

or               a - 8 = 0 ⇒ a = 8

Now we put the value a

when a = 3    (x² - 1) = 3

                     x² = 3 + 1 = 4

                    x = √4

                       = ± 2

when a = 8   (x² - 1) = 8

                     x² = 9

                     x = √9

                        = ± 3

Therefore, x = ± 3 and ± 2 will be the answer.

Answer:

Step-by-step explanation:

"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.

A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.

The geometry of lines on a plane comes into play with regard to solutions.

Answer:

D.

Step-by-step explanation:

Answer:

Option C. Obtuse

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

If [tex]c^{2}=a^{2} +b^{2}[/tex] ----> is a right triangle

If [tex]c^{2}>a^{2} +b^{2}[/tex] ----> is a obtuse triangle

If [tex]c^{2}<a^{2} +b^{2}[/tex] ----> is an acute triangle

where

c is the greater side

Verify

[tex]c^{2}=26^{2}= 676[/tex]

[tex]a^{2} +b^{2}=7^{2} +24^{2}=625[/tex]

therefore

[tex]676>625[/tex]

[tex]c^{2}>a^{2} +b^{2}[/tex] -----> is a obtuse triangle

Answer:

its really  History and Mystery hope i hlaaaaaaaaaaaaaaaaped

Final answer:

To solve for 'r' in the given equation, add 9s to both sides and then divide by 4, resulting in r = (9s + K) / 4.

Explanation:

To solve for r in the equation 4r - 9s = K, we need to isolate r on one side of the equation. Here's how we can do this:

Answer:

$20.00 is the correct answer

Step-by-step explanation:

I promise this is correct

The inverse function of f(x) = 5x - 3 is found by switching x and y to solve for x, resulting in the inverse function f⁻¹(x) = (x + 3) / 5. This process is part of understanding function transformations that change a function's graph.

Finding the Inverse Function

Find the inverse function of f(x) = 5x - 3. To find the inverse, we need to switch the roles of x and y. So we first write  y = 5x - 3. We then solve this equation for x to get x as a function of y. Performing the steps:

Add 3 to both sides: y + 3 = 5x.

Divide both sides by 5: (y + 3) / 5 = x.

This new equation x = (y + 3) / 5 represents the inverse function. To use the proper notation, we replace y with f⁻¹(x) and x with y, giving us f⁻¹(x) = (x + 3) / 5.

Understanding Function Transformations

When considering transformations such as f(-x) or f(2x), these changes to the independent variable result in specific alterations to the graph of the function, such as reflections across the y-axis or horizontal shrinkage by half.

Answer:

The answer is D. 52

Step-by-step explanation:

edg 2020

The horizontal distance between the balloon and the ship can be calculated using the tangent function is 1639 feet.

To find the horizontal distance between the balloon and the ship, we can use the tangent function in trigonometry. Let's denote the horizontal distance as x, and the distance between the balloon and the ship along the ground as y.

We have the angle of depression (21°) and the altitude of the balloon (2,000 feet). We can set up the equation:

tan(21°) = y / (2,000 + y)

Now, we need to solve for y:

tan(21°) * (2,000 + y) = y

y * tan(21°) = 2,000 * tan(21°) - y * tan(21°)

y * (1 - tan(21°)) = 2,000 * tan(21°)

y = (2,000 * tan(21°)) / (1 - tan(21°))

Now, calculate the value:

y ≈ (2,000 * 0.364) / (1 - 0.364)

y ≈ 728 / 0.636

y ≈ 1,148.17

Now that we have the value of y, we can find the horizontal distance x using the Pythagorean theorem:

[tex]x^2 + y^2 = (2,000)^2\\x^2 + (1,148.17)^2 = 4,000,000\\x^2 = 4,000,000 - 1,319,441.98\\x^2 = 2,680,558.02\\x = 1,638.84 (rounded)[/tex]

The horizontal distance between the balloon and the ship is approximately 1,639 feet.

Horizontal distance = height of balloon / tangent(angle of depression) = 2000 / tan(21°) ≈ 5243.87 feet.

To find the horizontal distance between the balloon and the ship, we can use trigonometry, specifically the tangent function.

Let's denote:

- [tex]\( h \)[/tex] as the height of the balloon above the ground (2,000 feet in this case).

- [tex]\( \theta \)[/tex] as the angle of depression (the angle formed between the line of sight from the balloon to the ship and the horizontal ground).

Given that the angle of depression [tex]\( \theta \)[/tex] is 21°, we can use the tangent function:

[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]

In this case, the opposite side is the height of the balloon above the ground (2,000 feet), and we want to find the adjacent side, which represents the horizontal distance between the balloon and the ship.

So, we have:

[tex]\[ \tan(21°) = \frac{2000}{\text{horizontal distance}} \][/tex]

To find the horizontal distance, we rearrange the equation:

[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \][/tex]

Now, we can calculate this:

[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \approx \frac{2000}{0.381} \approx 5243.87 \text{ feet} \][/tex]

So, the horizontal distance between the balloon and the ship is approximately 5243.87 feet.

The [tex]95\%[/tex] confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.

Further Explanation:

Explanation:

The formula for confidence interval can be expressed as follows,

[tex]\boxed{{\text{Confidence interval}}=\left( {\overline X  \pm ME} \right)}[/tex]

ME represents the Margin of Error.

The confidence interval has two limits.

(1). Upper Limit

(2). Lower Limit

The upper limit can be calculated as follows,

[tex]{\text{Upper limit}}=\left( {X + ME}\right)[/tex]

The lower limit can be calculated as follows,

[tex]{\text{Lower limit}} = \left( {X - ME}\right)[/tex]

The given confidence interval is [tex]\left( {6.93,11.45}\right).[/tex]

The upper limit of the confidence interval is 11.45.

The lower limit of the confidence interval is 6.93.

The 95\% confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949

2. Learn more about standard normal distribution https://brainly.com/question/13006989

3. Learn more about confidence interval of mean https://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: Z-score, Z-value, confidence interval, confidence limit, 95 percent, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.

Answer:

2%

Step-by-step explanation: