You start driving north for 63 miles, turn right, and drive east for another 16 miles.
how many miles must you travel to return directly back to your starting point?

You must travel 65 miles to return directly back to your starting point

Given that you start driving north for 63 miles, turn right, and drive east for another 16 miles.

Hence we can say that, you have traveled in form of right angled triangle where the vertical leg is 63 miles and horizontal leg is 16 miles

The route you travel to get back to starting point is the hypotenuse

The reference figure for right angled triangle is attached below

BC = length of hypotenuse

AB = length of vertical leg of right angled triangle

AC = length of horizontal leg of right angled triangle

Let from the figure AB = 63 miles,  

Then I turned right and drive east for another 16 miles

So, let AC = 16 miles

Now, To reach directly back to the starting point,  

The amount of distanced to be traveled back to starting point is BC

Which can be calculated using Pythagoras theorem

The Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, we get

BC = 65 miles

Hence , the distanced to be traveled back to your starting point is 65 miles

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is