Yesterday, Grace drove 43 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?

Mathematics

1 answer:

iren [92.7K]3 years ago

4 0

Answer: 34.8 or 34 4/5

Step-by-step explanation:

1.25 divided by 1.25 = 1

43.5 divided by 1.25 = 34.8

= 34 4/5

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George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, and arrive

alex41 [277]

Answer:

George must run the last half mile at a speed of 6 miles per hour in order to arrive at school just as school begins today

Step-by-step explanation:

Here, we are interested in calculating the number of hours George must walk to arrive at school the normal time he arrives given that his speed is different from what it used to be.

Let’s first start at looking at how many hours he take per day on a normal day, all things being equal.

Mathematically;

time = distance/speed

He walks 1 mile at 3 miles per hour.

Thus, the total amount of time he spend each normal day would be;

time = 1/3 hour or 20 minutes

Now, let’s look at his split journey today. What we know is that by adding the times taken for each side of the journey, he would arrive at the school the normal time he arrives given that he left home at the time he used to.

Let the unknown speed be x miles/hour

Mathematically;

We shall be using the formula for time by dividing the distance by the speed

1/3 = 1/2/(2) + 1/2/x

1/3 = 1/4 + 1/2x

1/2x = 1/3 - 1/4

1/2x = (4-3)/12

1/2x = 1/12

2x = 12

x = 12/2

x = 6 miles per hour

4 0

3 years ago

What are the coordinates of the hole in the graph of the function f(x) ?

Vinvika [58]

ANSWER

$(3, \infty )$

EXPLANATION

The given function is

$f(x) = \frac{ {x}^{2} - 9}{x - 3}$

When we plug in x=3 into this function, we obtain,

$f(3) = \frac{0}{0}$

This means that the function is discontinuous at x=3.

We need to simplify the function to obtain,

$f(x) = \frac{(x - 3)(x + 3)}{(x - 3)}$

This implies that,

$f(x) = x + 3$

The graph this function is a straight line that is continuous everywhere.

To graph

$f(x) = \frac{ {x}^{2} - 9}{x - 3}$
we draw the graph of

$f(x) = x + 3$
and leave a hole at x=3.

See diagram in attachment.

Hence the coordinates of hole is

$(3, \infty )$