Ben's Responses in WyzAnt Answers

The way to solve this is to solve one of the equations for x or y.

The bottom one looks easier.

x=32-5y

Substitute that value into the top equation.

-3(32-5y)+5y=44

-96+15y+5y=44

20y=140

y=7

Now substitute y into the bottom equation

x+5(7)=32

x+35=32

x=-3

Now double check the answer by plugging in the answers to both equations.

-3(-3)+5(7)=44

-3+5(7)=32

The answer is x=-3 and y=7

Because any number multiplied by 1 is itself...1 X n = n, you could restate this function as f(n)=2^(n-1).

Therefore

f(0)=2^-1=1/2=.5.

f(1)=2⁰=1

f(2)=2¹=2

etc.

The first thing to notice about this problem is that you have a mixture of Metric and English units.  The first thing that I would recommend is to convert 410 miles into Kilometers

1 mile = 1.61 km

410 miles = (410*1.61) = 660 km (rounded to the nearest km)

Now you need to know the time.  The formula for travel is d=rt.  You know the distance, and you know the rate, solve the formula for time.

t=d/r.

t=660km/120km/k

t=5.5 hours.  Plus add the 2 15 minutes breaks.  2*15=30 minutes.  60 minutes in an hour means that you add 30/60 hours to the trip, or another .5 hours.

Therefore the answer is 5.5+.5 hours.

The answer is: time=6 hours.

We need a line that is parallel to y=3/4x+1 that goes through (8,-10).  The formula for a line is y=mx+b  Since it is parallel to the given line we already know the slope or m is 3/4, we know the x is 8 and y is -10, we just need to find the y-intercept or b.  We can also use b=y-mx to find the y-intercept. 

b=(-10)-(3/4(8))

b=-10-6

b=-16

The equation is

y=3/4x - 16

Let's plug this back into the y=mx+b formula to make sure

-10=(3/4(8)) - 16

-10=6-16

And that works.

This is telling you that a line that cross the coordinates (5,y) and (7,-9) has a slope of -4.

To compute the slope, we use the formula rise over run.  The rise is (y -(-9)) and the run is (5-7).  Therefore, the slope formula is (y-(-9))/(5-7)=-4.  Now we solve for y.

1.  (y-(-9))/(5-7)=-4

2.  Simplify...(y+9)/-2=-4

3.  Multiply both sides by -2...y+9=8

4.  Subtract 9 from both sides...and we get the answer -1.

5.  Check the work by substituting -1 in the formula.

(-1+9)/(5-7)=-4

This verifies that the answer is y=-1.