Solve for x
80°
45°
11x
Given two parallel lines. Solve for x.

The stock was worth 40000 dollars in 1998.

Stocks, also known as equities, are securities that represent ownership in a corporation.  The value of your stock holdings is directly tied to the performance of the company and its financial health.

There are two main types of stocks: common stocks and preferred stocks. Common stocks typically offer voting rights, while preferred stocks generally do not. Preferred stocks often offer a fixed dividend, while common stock dividends can vary.

Stocks are bought and sold on stock exchanges, such as the New York Stock Exchange (NYSE) and the NASDAQ.

The value of the stock quintupled every 9 years, which means it increased by a factor of 5 every 9 years. To find the value of the stock in 1998, we need to divide the value in 2016 by 5 raised to the power of the number of 9-year intervals that have passed.

Let's call the value of the stock in 2016 x. Then:

x = million dollars = 1000000

The number of 9-year intervals that have passed is (2016 - 1998) / 9 = 18 / 9 = 2

So, the value of the stock in 1998 is x / (5^2) = 1000000 / (5^2) = 1000000 / 25 = 40000.

Therefore, the stock was worth 40000 dollars in 1998.

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Answer:

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

Step-by-step explanation:

To find the inverse of F(x), we need to follow these steps:

Step 1: Replace F(x) with y:

y = 5x^2 - 10x + 7

Step 2: Solve for x in terms of y:

y = 5x^2 - 10x + 7

y - 7 = 5x^2 - 10x

5x^2 - 10x = y - 7

5(x^2 - 2x) = y - 7

Completing the square:

5(x^2 - 2x + 1) = y - 7 + 5

5(x - 1)^2 = y - 2

x - 1 = ±sqrt((y-2)/5)

x = 1 ± sqrt((y-2)/5)

Step 3: Replace x with F^-1(x):

F^-1(x) = 1 ± sqrt((x-2)/5)

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

Answer:

  (d)  x-axis

Step-by-step explanation:

You want the line of reflection that transforms Z(10, -8) to Z'(10, 8).

The line of reflection is the perpendicular bisector of the segment between a point and its image.

Here, the segment ZZ' is on the vertical line x=10, so the bisector will be a horizontal line whose y-value is the average of the y-values of Z and Z':

  y = (-8 +8)/2 = 0/2 = 0

The line y=0 is the x-axis. The line of reflection is the x-axis.

__

Additional comment

Rather than go to the trouble of considering perpendicular bisectors, you can simply make use of your knowledge of reflection over the axes:

  (x, y) ⇒ (-x, y) . . . . reflection over the y-axis

  (x, y) ⇒ (x, -y) . . . . reflection over the x-axis   ←

  (x, y) ⇒ (-x, -y) . . . . reflection over both axes, or reflection across the origin

Answer:

 (d)  x-axis

Step-by-step explanation:

Answer:

  T = 79e^(-kt) +60

Step-by-step explanation:

You want the particular solution to the differential equation ...

  dT +k(T -60)dt = 0 . . . . T(0) = 139

This is a separable differential equation, so we can solve it by separating the variables and integrating each side:

  [tex]\dfrac{dT}{T-60}=-k\,dt\\\\\displaystyle \int{\dfrac{dT}{T-60}}=\int{-k}\,dt\\\\\ln{(T-60)}=-kt+C\\\\T-60=e^{-kt+C}=Ce^{-kt}\qquad\text{take antilogs; values of $C$ are different}[/tex]

Applying the initial condition, we have ...

  139 -60 = C = 79

Then the particular solution is ...

  [tex]\boxed{T=79e^{-kt}+60}[/tex]

No. A triangle cannot be formed with side lengths of 2, 4, and 5. option (d)

The sum of the lengths of the two shorter sides (2 + 4 = 6) must be greater than the length of the longest side (5). This is known as the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side. In this case, the two shorter sides do not meet this requirement, so it is not possible to form a triangle with these side lengths.

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Complete Question:

Is it possible to form a triangle with side lengths 2, 4, and 5? If so, will it be scalene, isosceles, or equilateral?

A.Yes; scalene

B. Yes; isosceles

C. Yes; equilateral

d. no

The options which are equal to, or a good estimate of the ratio include:

8 out of 1, 000 :

8 / 100 :

8 out of 1, 000 is a ratio that can be shown to be :

= 8 / 1, 000 x 100 %

= 0. 008 x 100 %

= 0. 8 %

0. 8 % is less than 1 %.

8 / 100 is a ratio that would be:

= 8 / 100 x 100 %

= 8 %

This is almost 10 % as it is 2 % away.

8 / 100 = 0. 08

2 / 25 = 0. 08

These two ratios are therefore equal.

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The student can take 8 months of lessons if he has $649 to spend on lessons and the book.

The arithmetic action of division is the opposite of multiplication. It is employed to determine how frequently one quantity is included within another. Divide the dividend by the divisor to execute a division, which can be represented with the division symbol () or a fraction bar (/). The outcome of division is the quotient, which shows how many times the dividend can be divided by the divisor. For instance, if you divide 8 apples into 4 equal portions, each portion would include 2 apples.

First, let's find the total cost of the lessons by multiplying the cost per month by the number of months:

$78/month × n months = $78n, where n is the number of months of lessons.

Next, we add the cost of the book to find the total cost:

$78n + $25 = $649.

Now, we can solve for n by subtracting the cost of the book from both sides of the equation:

$78n = $649 - $25 = $624.

Finally, we divide both sides of the equation by 78 to find the number of months of lessons:

n = $624 ÷ $78/month = 8 months.

So, the student can take 8 months of lessons if he has $649 to spend on lessons and the book.

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Based on the information provided, it can be concluded they will not save enough money to cover their camping site charges.

Charge per person: 6 (charge per person) x 2 = 12 x 10 (number of days) = 120

Tenth charge per night: 18 x 8 (They will stay for 10 days but due to the offer pay for 4 nights if you stay 5, they will pay only 8 nights) = 144

Total: 264

13 x 9 weeks = 117 x 2 (two people are saving) = 234

Based on this, the amount of money they will save is not enough as they will need $30 more to cover their expenses.

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The distance, that car will travel in 15 minute, is 28 km.

The formula used to explain the relationship between speed, distance, and time is speed distance time.

That is speed = distance/ time

So, distance = speed * time

Alternatively, you can calculate the time by dividing the distance traveled by the speed. You can figure out the third input if you know two of the inputs.

Given Speed of car = 112 km per hour

Time = 15 minutes = 15/60 hour

Time = 1/4 hour

Distance traveled by car in 15 minute = Speed of car * time

Distance = 112 * 1/4

Distance = 28 km

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Answer:

4 Lessons

Step-by-step explanation:

55 * 4 = 220   +     140    =    360

75 * 4 = 300   +      60    =     360

Price per lesson, times number of lessons, plus deposit cost, equals total amount when the lessons will be the same price.

Hope this helps!

Answer: 7

Step-by-step explanation: 13 + 7 = 20

Answer: 7

Step-by-step explanation:

q+13=20

subtract 13 on both sides and you get

q=7

The probability of winning the quiz is 0.19 or 19% when the contestant answers randomly to each question.

The number of possible outcomes for answering 3 multiple-choice questions with 3 choices each is [tex]3^3[/tex] = 27. Out of these 27 possible outcomes, 9 of them result in the contestant getting 2 or more questions correct.

So, the probability of winning the quiz can be calculated as follows:

P(Winning) = 9/27 = 1/3 = 0.3333...

Rounding to two decimal places, the probability of winning the quiz is approximately 0.33 or 33%.

However, since the contestant is answering randomly to each question, the probability of winning can also be expressed as the sum of the probabilities of getting exactly 2, or 3 questions right. This is calculated using the binomial distribution. The probability of getting exactly 2 questions right is:

The probability of getting exactly 3 questions right is:

The sum of these probabilities gives the total probability of winning:

Rounding to two decimal places, the probability of winning the quiz is approximately 0.19 or 19%.

Since the contestant is answering randomly to each question, the probability of winning is approximately 0.19 or 19%.

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Triangle STV is congruent to triangle UTW by SSS congruence postulate

SSS congruence postulate is a statement in geometry that says if three sides of one triangle are equal in length to the corresponding three sides of another triangle, then the two triangles are congruent.

In other words, if the lengths of the sides of two triangles are the same, then the triangles are the same shape and size. The acronym SSS stands for "side-side-side."

Corresponding Parts of Congruent Triangles are Congruent is abbreviated as CPCTC.

According to the CPCTC theorem, every corresponding component of one triangle is congruent to the other when two triangles are congruent.

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Answer:

50% or 1/2

Step-by-step explanation:

Because there are 4 animals in the barn, if two animals leave (out of 4), then there are 50% of the animals in the barn and 50% of the animals leaving the barn.

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The probabilities are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of students in the problem is given as follows:

17 + 25 + 21 + 37 = 100.

Hence the probabilities are given as follows:

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the ordered pair will be (3,-1) lies in the inverse function.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

function g(x)=∛(x−4)

So the inverse of the function

g ¬(x) = x³+4

So the ordered pair will be (3,-1)

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Answer: 8.9 and 6.7

Step-by-step explanation:

These are right triangles, so you can use the Pythagorean theorem, a² + b² = c², where a and b are the legs, or shorter sides, of the triangle and c is the hypotenuse, or the longest side.

1. 4² + 8² = c²

16 + 64 = c²

80 = c²

c = √80

c = 8.9

2. 6² + 3² = c²

36 + 9 = c²

45 = c²

c = √45

c = 6.7

Answer: 10π + 20, or 51.4159, cm

Step-by-step explanation:

The circumference of a circle is calculated using πd. Our d, or diameter, is 20, so the circumference of a full circle would be 20π. However, we only have half of a circle, so that number is halved, resulting in 10π. Now, we just have to add on the cross section, which is equal to the diameter, giving us 10π + 20, or 51.4159, cm.

The balance after 6 years is $2108.

percentage, a relative value indicating hundredth parts of any quantity.

Given that savings account earns 4% annual simple interest.

The principal is $1700.

We need to find the balance after 6 years.

The formula for simple interest I=Prt

I = interest

P = principal ($1700)

r = annual interest rate (4%)

t = time in years (6)

So the interest earned in 6 years is:

I = 1700× 4×6 / 100 = $408

The balance after 6 years is the sum of the principal and the interest earned:

1700 + 408 = $2108.

Hence,  the balance after 6 years is $2108.

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Answer:

2793.75

Step-by-step explanation:

1350 - 175 = 1175

1175 / 4 = 293.75

The test does not prove the alternative hypothesis correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.

The test does not prove the alternative hypothesis correct, because when performing a hypothesis test, the null hypothesis is rejected in favor of the alternative hypothesis. However, rejecting the null does not necessarily mean that the alternative hypothesis is true. It is possible for the null hypothesis to be rejected even when it is true, due to the occurrence of random fluctuations. Therefore, the test does not prove that the alternative hypothesis is correct, as there is always a possibility that the null hypothesis is true despite being rejected. To prove that the alternative hypothesis is correct, a series of hypothesis tests must be conducted to show that the population parameter is consistent with the alternative hypothesis.

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a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.

b) The rider's minimum height above the ground is of: 5 meters,

c) The horizontal distance is given as follows: x = 0 m and x = 6 m.

The quadratic function in the context of this problem is defined as follows:

y = x²/3- 2x + 8.

In which:

The coefficients are given as follows:

a = 1/3, b = -2, c = 8.

The x-coordinate of the vertex is given as follows:

x = -b/2a = -(-2)/(2/3) = 3.

Hence the y-coordinate of the vertex is given as follows:

y = (3)²/3 - 2(3) + 8 = 5 meters.

Hence the vertex-form definition of the equation is given as follows:

y = 1/3(x - 3)² + 5.

As the function is concave up, the minimum height is of 5 meters.

For the horizontal distance at a height of 8m, we have that:

x²/3 - 2x + 8 = 8

x²/3 - 2x = 0

x(x/3 - 2) = 0.

Hence:

x = 0 m and x = 6 m.

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Answer:

3.41

Step-by-step explanation:

41/12

Answer:

Step-by-step explanation:

The tree is .0564 meters

Answer:

Step-by-step explanation:

de chill de chill

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

the geometric mean of 2 numbers a and b is [tex]\sqrt{ab}[/tex]

the geometric mean of 6 and 8 is then

[tex]\sqrt{6(8)}[/tex]

= [tex]\sqrt{48}[/tex] ← express as factors

= [tex]\sqrt{16(3)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex]

The cost price of cloth that John bought per meter is Php 46.00 (Option C). To find the cost price per meter, divide the total cost by the number of meters of cloth.

In this case, the total cost is Php 425.50 and the number of meters is 9.25. By dividing the total cost by the number of meters, we get Php 46.00 per meter. This means that John paid Php 46.00 for every meter of cloth he bought. This is the cost price per meter and it is option C, Php 46.00.

The specific value that corresponds to the unit price that was purchased is reflected in retail systems by the cost price. In some stock market theories, this value is used to determine the value of stock holdings, and it is used as a key factor in determining profitability.

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Answer:

0.2x-0.8

Step-by-step explanation:

In 0.2(x-4), you can multiply 0.2(The number outside of the parentheses) by the numbers inside the parentheses. So, it would be 0.2*x-0.2*4, which is 0.2x-0.2(4), which is 0.2x-0.8.

Answer:

see below

Step-by-step explanation:

(1+20%) * (1-20%) =1.2 *0.8 = 0.96

so it's the same as 1- 4% = 0.96

no