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melamori03 [73]

3 years ago

6

Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, u

p, or down. After $10$ steps, how many different points could Franklin end up at?

1 answer:

Anastaziya [24]3 years ago

8 0

Answer:

80 different points.

Step-by-step explanation:

right, left, up, or down = 4 possibilities x 2 since there is a coordinate with 2 numbers so,

8 possibilities.

8 x 10 = 80 possibilities.

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A car passes through a tollbooth at 8:00 A.M. and begins traveling east at an average speed of the same tollbooth an hour later

Alexandra [31]

The distance traveled by both cars is an illustration of a linear function.

The equations of both cars are $\mathbf{y=60x - 540}$ and $\mathbf{y=45x - 360}$ <u />
Both cars meet at 12:00pm

<u />

<u>Car A</u>

Speed = 45 miles per hour

So, the coordinates of car A are:

$\mathbf{(x,y) = (8,0) (9, 45) (10, 90) ....}$

<u>Car B</u>

Speed = 60 miles per hour

So, the coordinates of car B are:

$\mathbf{(x,y) = (9, 0) (10, 60) (11, 120) ....}$

<u>(a) The equation of both cars</u>

<u>Car A</u>

This is calculated as:

$\mathbf{y = mx+ b}$

Where m represents slope/speed.

So, m = 45

This gives

$\mathbf{y = 45x + b}$

y = 0, when x = 8.

So, we have:

$\mathbf{0= 45\times 8 + b}$

$\mathbf{0= 360 + b}$

Solve for b

$\mathbf{b=- 360}$

So, the equation of car A is:

$\mathbf{y=45x - 360}$

<u>Car B</u>

This is calculated as:

$\mathbf{y = mx+ b}$

Where m represents slope/speed.

So, m = 60

This gives

$\mathbf{y = 60x + b}$

y = 0, when x = 9.

So, we have:

$\mathbf{0= 60\times 9 + b}$

$\mathbf{0= 540 + b}$

Solve for b

$\mathbf{b=- 540}$

So, the equation of car B is:

$\mathbf{y=60x - 540}$

<u>(b) The graphs</u>

See attachment

<u>(c) The time which both cars meet</u>

We have:

$\mathbf{y=60x - 540}$ and $\mathbf{y=45x - 360}$

Equate both

$\mathbf{60x - 540=45x - 360}$

Collect like terms

$\mathbf{60x - 45x = 540- 360}$

$\mathbf{15x = 180}$

Divide both sides by 15

$\mathbf{x = 12}$

This means that both cars meet at 12:00pm

Read more about linear functions at:

brainly.com/question/20286983

8 0

3 years ago

In the human arm, the forearm and hand pivot about the elbow joint. Consider a simplified model in which the biceps muscle is at

qaws [65]

To answer this problem, we use moment balance, balancing the forces that tip the arm clockwise and those that tip the arm counterclockwise. In the balance, we multiply force by the perpendicular distance from the center.
If F is the force created by the bicep and the loads are in Newtons if the loads are in kg, then multiply kg by g (9.8) to get N
F(3.8) - 15(15) = 80(33)
solving for for F, F is equal to 753.98 Newtons

4 0

3 years ago

Read 2 more answers

Help i need an answer !

inna [77]

The answer to #1 is 0.

In order to find the answer to this one (or any of these problems, simply follow the order of operations. In the case of #1, we first want to stick the 0 in for a and then continue.

$\frac{a}{b} +\frac{a + 1}{b} +\frac{a - 1}{b}$

$\frac{0}{b} +\frac{0 + 1}{b} +\frac{0 - 1}{b}$

$\frac{1}{b} +\frac{-1}{b}$

Since these two numbers cancel, you will get the answer as 0. For the rest of these, follow the basic steps provided by your teacher in PEMDAS.

8 0

4 years ago

Equation of a line parallel y=1/5-6 that goes through the points -5,3

solong [7]

Point slope form would be y - 4 = 8 (x-5)

5 0

3 years ago

PLEASE HELP I DON'T UNDERSTAND! A florist is making regular bouquets and mini bouquets. The florist has 118 roses and 226 peonie

Anna [14]

Answer:

The florist can make 11 regular bouquets and 21 mini bouquets

Step-by-step explanation:

The number of roses the florist has = 118 roses

The number of peonies the florist has = 226 peonies

The number of roses in each regular bouquet = 5 roses

The number of peonies in each regular bouquet = 11 peonies

The number of roses in each mini bouquet = 3 roses

The number of peonies in each mini bouquet = 5 peonies

1. The equation that gives the total number of roses to be used in both kinds of bouquet is given as follows;

Let r represent the number of regular bouquet the florist can make and let m represent the number of mini bouquet the florist can make, we have;

5·r + 3·m = 118...(1)

2. Similarly, we have;

11·r + 5·m = 226...(2)

Making m the subject of the formula of both equations, and equating both values of m to find a common solution, we have;

m = (118 - 5·r)/3

m = (226 - 11·r)/5

(118 - 5·r)/3 = (226 - 11·r)/5

5 × (118 - 5·r) = 3 × (226 - 11·r)

590 - 25·r = 678 - 33·r

33·r - 25·r = 678 - 590 = 88

8·r = 88

r = 88/8 = 11

r = 11

The number of regular bouquet the florist can make = r = 11

m = (118 - 5·r)/3 = (118 - 5×11)/3 = 21

m = 21

The number of mini bouquet the florist can make = m = 21

The number of regular bouquet the florist can make = 11 bouquets

The number of mini bouquet the florist can make = 21 bouquets.

3 0

3 years ago