A house increased in value by 36 percent since it was purchased. If thw current value is 306000 what was the value when it was purchased

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

From the question, we have the following function that can be used in our computation:

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

Read more about trigonometry functions at

https://brainly.com/question/24349828

#SPJ1

The solution to the equation given by M * M * M = 729 is 9

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Given the equation:

M.M.M = 729

This gives:

M * M * M = 729

M³ = 729

Taking the cube root of both sides:

∛M³ = ∛729

M = 9

The solution to the equation is 9

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

#SPJ1

We cannot conclude that there are more than 70,000 defined words in the dictionary.

To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.

Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.

So, sample mean

= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10

= 510 / 10

= 51.0

and, the sample standard deviation (s)

= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]

≈ 16.23

Next, we calculate the test statistic using the formula:

test statistic = (x - μ) / (s / √n)

In this case, μ = 48.0, s ≈ 16.23, and n = 10.

test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34

With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.

Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.

Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.

Learn more about test statistic here:

https://brainly.com/question/31746962

#SPJ1

ANSWER

A'(7, 2)

B'(2, 5)

C'(5, 8)

EXPLANATION

The vertices of ABC are A(4, -4), B(-1, -1) and C(2, 2).

The translation is given as T(3, 6).

This simply means that the triangle was translated 3 units to the right and 6 units up.

Therefore, we will add 3 to each x cordinate and 6 to each y cordinate.

=> A(4, -4) becomes A'(4 + 3, -4 + 6) => A'(7, 2)

=> B(-1, -1) becomes B'(-1 + 3, -1 + 6) => B'(2, 5)

=> C(2, 2) becomes C'(2 + 3, 2 + 6) => C'(5, 8)

Those are the cordinates of A'B'C'.

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

For more questions on  quadratic equation

https://brainly.com/question/30164833

#SPJ8

The first plane is farther from the airstrip after the second leg

The first plane

Initial distance = 150 miles west

Additional distance = 220 miles 30 degrees SW

This means that

Additional distance = 220 * cos(30) miles SW

Additional distance = 190.53 miles

Total distance = 150 + 190.53 = 340.53

The second plane

Initial distance = 220 miles east

Additional distance = 150 miles x degrees SE

This means that

Additional distance = 150 * cos(x) miles SW

Total distance = 220 + 150 cos(x)

Given that

x < 30

We have

Second plane < First plane

220 + 150 cos(x) < 340.53

Evaluate

cos(x) < 0.8035

Take the arc cos of both sides

x < 36

x < 36 is not the same as x < 30

Hence, the first plane is farther

Read more about bearing distance at

https://brainly.com/question/22518031

#SPJ1

Answer:

x = 6

Step-by-step explanation:

We want to solve:

\(\frac{-2}{3} x+9=\frac{4}{3} x-3\)

First, isolate the variable by moving all the terms with x to one side and all the constants to the other side:

\(\frac{4}{3}x +\frac{2}{3} x=9+3\)

Combining the fraction on the left, we get:

\(\frac{6}{3} x=12\)

6/3 = 2, so:

2x = 12

Dividing both sides by 2 yields:

x = 6

Answer:

X = 6

Step-by-step explanation:

Edge 2020

The value of x from the given proportion is 4.

The given numbers 12, 9 and 3 are proportions.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

To find the value of x:

So, 12:x::9:3

⇒ 12×3=x×9

⇒ 9x=36

⇒ x=36/9

⇒ x=4

Therefore, the value of x from the given proportion is 4.

To learn more about the proportions visit:

https://brainly.com/question/7096655.

#SPJ1

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

For similar question on projectile.

https://brainly.com/question/30695754

#SPJ11

Answer:

On Wednesday they sold 5, over the four days they sold 19, and the third I believe it is 26.32 . Please rate me and mark me brainliest!

Step-by-step explanation:

Answer:

height: 16 inch

length of base: 10 inch

width of base: 50 feet

Step-by-step explanation:

128*(1/8)=16 inch

80*(1/8)=10 inch

x*1/8=6.25

x=6.25*8=50 feet

The height and length of the model will be 16 in and 10 in respectively, and  the width of the building will be 50 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, the scale factor of the building and a model of it is 1/8.

Height of the model = 128/8 = 16 in

Length of the model = 80/8 = 10 in

Width of the model = 6.25*8 = 50

Hence, The height and length of the model will be 16 in and 10 in respectively, and  the width of the building will be 50 feet.

For more references on scale factor, click;

https://brainly.com/question/29464385

#SPJ5

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Answer:

c = (b+3a)/2

Step-by-step explanation:

Solve for c:

Multiply both sides by abc:

Hello

a=2, b=7, c= -30

ac=-60

-60= 12*(-5)

We can see that 12*(-5)=ac and 12-5=b=7

So

\(2x^2+7x-30=2x&2+12x-5x-30=2x(x+6)-5(x+6)=(x+6)(2x-5)\)

Thanks

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

More can be learned about extremas of a function at https://brainly.com/question/9839310

#SPJ1

Answer:

52

Step-by-step explanation:

you divide both sides of the equation by 8 to get x by itself so you do 416 divided by 8 which is 52

Answer: M = 52

Step-by-step explanation: 8m = 416, divide 416 by 8, get 52, Check and do 52 times 8, it equals 416, so M is definitely 52

The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

Learn more about amplitude on

https://brainly.com/question/3613222

#SPJ1

Answer:

-6387

Step-by-step explanation:

I have a feeling you're just giving away points :)

Answer:

Dilate, Reflect

Not congruent, dilations are used

Step-by-step explanation:

Dilate Figure K by a factor 3 to get the white shape.

Reflecting the resulting figure over the x-axis will give you Figure L

Step 1: Dilate by a scale factor of 3

Step 2: Reflect over the x-axis

Since dilations are used, the shapes are not congruent as they change the side lengths and area.

-Chetan K

Answer:

Step-by-step explanation:

87

Answer:

630 in.³

Step-by-step explanation:

To find the volume of a rectangular prism, you can multiply the height, times the width, times the length. So, let's go ahead and do that with the values of the given prism.

7 × 10 × 9 = 70 × 9 = 630

So, our volume is 630...but not so fast. We also have to put in our units. Our units are inches × inches × inches, or inches³. So our final value is 630 in.³

Hopefully that's helpful! :)

For the given two - dimensional function, we can write -

In mathematical analysis, the maximum and minimum of a function, known generically as extremum are the largest and smallest value of the function, either within a given range (the local or relative extrema), or on the entire domain.

Given is calculate the relative maxima and minima for the function -

2x⁴ + y² - 3yx²

For the given two - dimensional function, we can write -

Relative Maxima  →  No relative maxima.

Relative Minima  →  No relative minima.

Saddle Points  →  No saddle points.

Therefore, for the given two - dimensional function, we can write -

To solve more questions on maxima and minima, visit the link below-

https://brainly.com/question/30194223

#SPJ1

{Question in english -

Calculate the relative maxima and minima of the function.

f(x, y)=2x^4+y^2-3yx^2}

180

Step-by-step explanation:

the given condition formulate:

750-570

the sum or difference:180

get the result: 180

Answer: 180

The required value of percent is obtained as 24%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Suppose the required percent value be x.

Now, the following equation can be written as,

750 - x% of 750 = 570

=> 750 - 750x/100 = 570

=> 750x/100 = 180

=> x = 24

Hence, the percent difference with respect to 750 kg is 24%.

To know more about percentage click on,

brainly.com/question/29306119

#SPJ2

9514 1404 393

Answer:

  your marked choice is correct: x = e

Step-by-step explanation:

For the line to go through the origin, the ratio of ln(x) to x at the point must equal the slope at the point.

The slope of ln(x) is 1/x, so we require ...

  ln(x)/x = 1/x

  ln(x) = 1 . . . . . . multiply by x

  x = e . . . . . . . . take antilogs

Answer:

40 % dogs

Step-by-step explanation:

if ratio = 4:6

the store =10:0

10=100%

1=10%

4=40%

6=60%

40:60

40%:60%

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

For more such information on: expression

https://brainly.com/question/1859113

#SPJ8

9514 1404 393

Answer:

  (x, y) = (-7, 5)

Step-by-step explanation:

I find a graphing calculator to be useful for solving equations by graphing. The graph shows the solution to be ...

  (x, y) = (-7, 5)

__

In these equations, the y-coefficients are the same, so we can eliminate y by subtracting the first equation from the second.

  (4x -6y) -(-2x -6y) = (-58) -(-16)

  6x = -42 . . . . . . . . . simplify

  x = -7 . . . . . . . . divide by 6

Substituting into the first equation gives ...

  -2(-7) -6y = -16

  6y = 30 . . . . . . . . . . add 16+6y to both sides

  y = 5 . . . . . . . . .divide by 6

The solution is (x, y) = (-7, 5).

Step-by-step explanation:

the value of root three is given already so the question is asking you to round it of to the nearest 1000 which means there should be three numbers after the decimal point.

Okay, here we have this;

Considering the provided information, we are going to calculate the requested widths, so we obtain the following:

Let us remember that the volume of a box is equal to the multiplication of its three dimensions, so from the given information we obtain the following:

Kyle's box Volume=Long * High * Width

12 ft^3=2ft * 3ft * Width

12 ft^3=6 ft^2 * Width

Kyle's box Width =12 ft^3/6 ft^2

Kyle's box Width = 2 ft

Myla’s box Volume=Long * High * Width

16 ft^3=4ft * 2ft * Width

16 ft^3=8 ft^2 * Width

Myla’s box Width =16 ft^3/8 ft^2

Myla’s box Width = 2 ft

Finally we obtain that the widths of Kyle and Myla’s boxes are 2 ft.

Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

To solve more questions related to the Area

https://brainly.com/question/16519513

https://brainly.com/question/76387