An airplane flies six hundred miles to the south; then, after landing and refueling, it flies due north for three hundred miles. What is the airplane's displacement? (Remember, displacement is a vector, so direction needs to be indicated in your answer).

Answers

Answer 1

Answer:
Displacement =

   (distance between the start-point and the end-point)
in the direction of
   (direction from the start-point to the end-point).

For the entire story, the displacement is

   300 miles south .

Answer 2

Answer: If it's going 600 miles S, and 300 miles N, the displacement is 300 miles S

Answer:

The expression for f(x) is:

f(x) = (x+5)(x+5)(x+5)(x+4)(x-2)(x-9)

Step-by-step explanation:

We know that for any polynomial equation with roots:

$a_1,a_2,a_3,...$ with multiplicity:

$m_1,m_2,...$

the equation for the polynomial is given by:

$f(x)=(x-a_1)^(m_1)(x-a_2)^(m_2)......$

if the leading coefficient is negative we may take '-' sign in the starting of the expression.

Here we are given that :

f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3

Hence, f(x) is given by:

$f(x)=(x-(-4))^(1)(x-2)^(1)(x-9)^(1)(x-(-5))^(3)\n\n\ni.e.\n\n\nf(x)=(x+4)(x-2)(x-9)(x+5)^3\n\n\nf(x)=(x+5)(x+5)(x+5)(x+4)(x-2)(x-9)$

Hence, the expression for f(x) is:

$f(x)=(x+5)(x+5)(x+5)(x+4)(x-2)(x-9)$

"polynomial function f(x) has a leading coefficient of 1"

So because of that, we can eliminate A and B.

Now we have "root –5 with multiplicity 3"

That's just product of three factors (x+5)

So D is wrong.

We are left with the only possible correct option C.

Classify the following triangle. Check all that apply.

Answers

Triangle is both acute and scalene.

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

here, we have,

we know that,

A scalene triangle has three unequal sides and angles, whereas an acute triangle has three acute angles (measured fewer than 90 degrees). Consequently, the characteristics of an acute scalene triangle are as follows: three lines that cross each other. a trio of sharp angles All sides are not equal.

Given

All angles are less than 90 degrees so it is acute. The sides are of difference lengths so it is scalene.

To know more about acute triangles refer to :

brainly.com/question/1368335

#SPJ7

It has 90 degrees so it's right
And none of the sides are equal so it's scalene

Which is the solution to the equation 3.5 (2 h + 4.5) = 57.75? Round to the nearest tenth if necessary.

Answers

Answer:

h = 6

Step-by-step explanation:

Step 1: Distribute

7h + 15.75 = 57.75

Step 2: Subtract 15.75 on both sides

7h = 42

Step 3: Divide both sides by 7

h = 6

Matthew is driving his car to visit a farm. He covers a distance of 112.25 miles in 60 minutes. He visits a friend on the way, and thereafter drives 45 miles at the same speed. He estimates that he took 30 minutes to cover the last distance. Is this a reasonable estimate?

Answers

Answer: His estimate is not reasonable because the time it took to cover the last distance is 24.1 minutes and it is below his estimate

Step-by-step explanation:

On his way to the farm, he covered a distance of 112.25 miles in 60 minutes.

Speed = distance/time.

So his speed is 112.25/60 = 1.87 miles per hour.

He visits a friend on the way, and thereafter drives 45 miles at the same speed. So he covered 45 miles at a speed of 1.87 miles per minute.

Time taken = distance / speed

Time it took him to cover 45 miles = 45/1.87 = 24.1 minutes

The surface area covered by a rectangular playground is 200 yards. The width of the playground is twice as long as it's length. Using factors, find the length and the width of the playground