A couple took a small airplane for a flight to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 233 miles. If the plane was flying at 170 miles per hour, what was the speed of the wind that affected the plane?

Types of correlation:

Based on the types of correlation, we can see that the best description of the data given is a positive correlation.

Answer: A positive correlation.

We have a 345 gallon hot tub that fills at a rate of 3.61 gallons/min.

To calculate filling time, we need to divide as it follows:

in that way we can find how much time does it take in minutes

now, if we want to determine time in hours, we must divide by 60, because there are 60 min. in one hour.

Then, it would take approximately 1.59 hours to fill the hot tub.

Answer:

Given that,

To find,

where,

Simplifing f(x) and g(x), we get

This is the simplified form of f(x).

For g(x) we get,

Now To find R(x), we get

we get,

Answer is:

we have that

interval (-infinite,0) ------> f(x)=5x+4

interval [0, infinite) ------> f(x)=x+7

Part B

f(0)

For x=0 ------> belong to the interval [0, infinite)

so

f(x)=x+7

substitute

f(0)=0+7

Part C

f(3)

For x=3 ---> belong to the interval [0, infinite)

so

f(x)=x+7

substitute

f(3)=3+7

OPTION C

A quartic function is a fourth-degree polynomial: a function that has, as its highest order term, a variable raised to the fourth power.

From our question, it was easy to

the graph of this equation is:

Let us make part of the table corresponding to this graph

Let:

A = Getting a 7

a = Number of sides with 7

N = Number of sides

so:

The daily rate can be found by dividing the total number of books over the number of calendar days.

15,260 / 28 = 545

545 books per day

To find the angles 1 and 2:

In the above triangle, the angles opposite to the equal sides are equal.

Let us take,

So, using the angle sum property of a triangle

Hence, the angles are

3)

- 18/(- 6)

This can be written as

- 18/- 6

Recall, if a negative number divides a negative number, the result is positive. Thus, the answer is 3

Using the distributive property, the maximum number of players that can be in the NBA is; 450 players

The distributive property is a property of algebra that states that you can distribute the contents of one parentheses into another to find an answer. For example;

a(b + c) = ab + ac

Now, we are told that there are 30 teams in the national basketball association and that each team has 12 healthy players plus three on injured reserve. Thus;

Number of players on each team = (12 + 3)

Now, for the 30 teams;

Total number of players for the teams = 30(12 + 3)

Applying distributive property, we have;

(30*12 + 30*3) = 450

Read more about distributive property at; https://brainly.com/question/2807928

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ANSWER and EXPLANATION

The recipe calls for 0.5 quart of milk and 2.5 cups of flour.

She has 3/8 quart of milk and 18/8 cups of flour.

To know the error she made, we have to find the ratio of milk to flour in the recipe and the ratio of milk to flour that she used and see if the ratios are the same.

RECIPE

Ratio of milk to flour is:

That is the ratio of milk to flour.

USED BY OLIVIA

Ratio of milk and flour that she used is:

We can already see that the ratios are not the same.

By comparing the ratios, we see that she actually used more flour than she was supposed to.

One way to find the least common multiple of two numbers is to first list the prime factors of each number.

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.

Let the number of attendees be a.

ak=c , where k=constant of variation.

6k=30

k=30/6

k=5

Find a when c=$50

5a=50

a=50/5

a=10

There will be 10 attendees for a bu

Answer:

To graph a line you have to find two points on the line, one way of doing this is first setting x=0 and solving for y, as follows:

With the above calculations, we got that the point (0,-1) is on the line.

Now, to find another point on the line we set y=0 and solve for x:

With the above calculations, we got that the point (-4/3,0) is on the line.

Once we have those points we draw the line that passes through those points.

The graph of the given equation is:

Answer:

(x+4)(x-5)

Step-by-step explanation:

Second order polynomial in the following format:

ax² + bx + c = 0

Has roots x¹ and x².

Can be factored as:

(x - x¹)(x - x²)

So, we have to find the roots.

Finding the roots:

Bhaskara formula, which is:

In the polynomial given in this question:

a = 1, b = -1, c = -20

So

The roots are:

The factored form is:

(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)

The square root of 2 is irrational

Here, we want to check if the square root of 2 is rational or not

When we talk of rational numbers, we mean numbers that can be expressed as the ratio of two integers

Roots of non-perfect squares such as two are not rational. They are referred to as irrational numbers. The special name they are called is surd

Answer:

which question you want to be answered

Answer:

[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]

[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]

Step-by-step explanation:

The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:

[tex]\boxed{P=0.5 \pi d+d}[/tex]

Part (a)

To express d in terms of P, rearrange the equation to isolate d.

Factor out the common term d from the right side of the equation:

[tex]\implies P=d(0.5 \pi +1)[/tex]

Divide both sides by (0.5π + 1):

[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]

[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]

[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]

Part (b)

Given:

Substitute the given values into the equation derived in part (a) and solve for d:

[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]

[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]

[tex]\implies d=36 \times \dfrac{7}{18}[/tex]

[tex]\implies d=\dfrac{252}{18}[/tex]

[tex]\implies d=14[/tex]

Therefore, the diameter is 14 inches.

a For any relation to be a function, an independent variable x cannot produce different dependent varible y

From the table,

when x = 5, y = 2

Also, when x = 5, y = 5

and when x = 5, y = 7

We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function

Hence, the table is not a function

The answer is False

ANSWER

EXPLANATION

Given;

Recall, the general formula for slope - intercept form is;

comparing the given equation with the standard slope intercept form formula;

Hence, the graph of the given equation is;

The I and II are linear function, so those have the same domain and the same range always. So the answer is B

we have the following:

solving for x:

Question:

Solution:

Let the following trigonometric equation:

Subtract the root of 3 from both sides of the equation:

solve for sin(x):

Applying the trigonometric circle on the given interval, we obtain that the correct answer is:

Answer:

ok you can ask

Step-by-step explanation:

don't forget to follow rate like

SOLUTIONS

What is the multiplicity of each of the roots of this graph?

Factorise f(x) by the options

(a) According to the option we have -3 is a root of so x+3 is a factor

(b) 1 is a root too so x - 1 is a factor

Therefore the correct answer = Option A

To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:

Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:

Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:

Finally, we have that the ball will go 59 feet from the child

we have:

h = hour

the equation is

answer: 3 hours

Here we have the following parabola:

To find the vertex, we could use the following formula:

Where a, b and c are the coefficients of the quadratic function:

As you can see, in this problem a = -1 , b = -4 and c = -8. Thus,

This is:

Then, the vertex of the parabola is (-2,-4)

The axis of symmetry of the parabola is the line x=-2. Since the vertex is situated at the coordinates (-2,-4), that means that the parabola is symmetrical around this line.

The vertex is maximum point of the parabola.

The range, is defined as all the values that the y-axis could take. If we notice, that is:

I'm going to upload a picture of the parabola: