11×+2-4x-x-2 16-13x+24-39

A function is created to represent the miles per gallon your car gets. What restrictions would be made to the domain ?

STatiana [176]

D. The domain would only include positive numbers

7 0

3 years ago

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Which monomial is a perfect cube? 16x6 27x8 32x12 64x6

miss Akunina [59]

The fastest way is to just use a scientific calculator.

To do it without a calculator, use prime factorization.

I'll only do the second one which is the answer.

27 x 8

= 3^3 x 2^3 = 6^3

Which is a perfect cube.

5 0

4 years ago

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George and Carmen went on a bicycle trip. they took a bus to their starting point, and then biked the rest. They traveled 3oo ki

jeka94

Answer:

George and Carmen traveled 185 kilometers by bike and 115 kilometers by bus

Step-by-step explanation:

The question is

Find how many kilometers they traveled by bike

Let

x ----> kilometers traveled by bike

y ----> kilometers traveled by bus

we know that

They traveled 300 kilometers in total

so

$x+y=300$ ----> equation A

They biked 70 kilometers more than they were bus

so

$x=y+70$ ----> equation B

substitute equation B in equation A

$(y+70)+y=300$

solve for y

$2y+70=300\\2y=300-70\\2y=230\\y=115$

Find the value of x

$x=115+70=185$

therefore

George and Carmen traveled 185 kilometers by bike and 115 kilometers by bus

8 0

3 years ago

A mouse is trapped in a maze. To

Svetradugi [14.3K]

Answer: Approximately 9.43 meters

The more accurate version is 9.4339811320566 but that's not exact.

This is exact magnitude is sqrt(89)

=======================================================

Explanation:

Let's draw an xy grid for this. Place the starting point at (0,0) which I'll call point A. Now let's say the mouse goes east 15 meters. That would move it to (15,0) which is marked as point B. Refer to the diagram below.

From point B, we move to C which is at (15,8). So the mouse has gone 8 meters north. It might help to turn the page so that the east direction is facing completely north, and then look to the left and you'll see "north". In other words, each 90 degree left turn is a 90 degree counterclockwise turn.

After doing another 90 degree counterclockwise turn, the mouse will move 10 meters westward. It moves from C(15,8) to D(5,8). Point D is the final position of the mouse.

-----------------------

A(0,0) was the initial position and D(5,8) is the final position

The vector v is

v = <5,8>

This is because we basically are saying "the mouse ultimately moved 5 meters east and 8 meters north" when going from start to finish. We're ignoring the intermediate stops along the way.

------------------------

Recall that for any vector of the form

v = <a,b>

the magnitude of that vector is

|v| = sqrt(a^2+b^2)

this is the length of the vector based on the pythagorean theorem.

Applying this formula gets us

|v| = sqrt(5^2+8^2)

|v| = sqrt(89)

|v| = 9.43398 approximate

This represents the straight line distance from start to finish, where we ignore any intermediate stops. So this isn't the distance the mouse travels (since it goes from A to B, to C to D). Instead, it's the distance it would travel if it wanted to take the shortest path from A to D.