gwenspooner85

From A to B, the distance is 200. The time taken is 200/40=5 hours. From B to A, the distance is also 200. The time taken is 200/60=10/3 hours. The average speed is total distance/total time.

200+200/(5+10/3)

=400/(25/3)

=1200/25

=48 kph

All numbers that fall under this category can be described as 5n+3, where n is a number. 

The smallest 3 digit number that fits in the expression 5n+3 is 103. The greatest is 998. The list of these numbers is 103, 108, 111, ...998. The number of numbers in this list is (998-103)/5+1=895/5+1=179+1=180.

We find the prime factorization of 36 and 104 first. 

36: 2^2*3^2

104: 2^3*13.

Then the gcd must be 2^2*3^2, which is 36.

1-kx=-3y

3y-kx=-1

From here we plug in the given point.

3y-kx=-1

3(-3)-k(4)=-1

-9-4k=-1

-4k=8

k=-2

i don't see the question.

Let x be the cost of a kilogram of jelly beans and y the cost of a kilogram of gummy worms. We form two equations:

2x+2y=32 

2x+y=25

We have a system of equations now and we solve for x and y.

Subtracting 2x+y=25 from 2x+2y=32, we get y=7. Then we plug the y value into 2x+y=25 to get the value of x.

2x+y=25

2x+7=25

2x=18

x=9.

Therefore jelly beans cost $9 per kilogram and gummy worms $7 per kilogram.

We write this equation in slope intercept form using the two given points. With the slope formula, we find that the slope, m is 4/3. We currently have y=4/3x+b. We can plug either given point into this equation to find b. We plug in (6, 10) to get

y=4/3x+b

10=4/3(6)+b

10=8+b

b=2.

We write Line 1 in slope intercept form. 

3x+4y=-14

4y=-3y-14

y=-3/4x-14/4

The slope of line 2 must be 4/3. So we currently have y=4/3x+b. We plug in the given point (-5, 7) to find b.

y=4/3x+b

7=4/3(-5)+b

7=-20/3+b

b=41/3.

The equation of line 2 is y=4/3x+41/3. m is 4/3 and b is 41/3. Therefore m+b=4/3+41/3=45/3=15.

We write 4x+5y=1 in slope intercept form.

4x+5y=1

5y=-4x+1

y=-4/5x+1/5

The slope of perpendicular line must be 5/4. We know it is y=5/4x+b. We plug in the given point to find b.

y=5/4x+b

-2=5/4(2)+b

=-2=10/4+b

=b=-9/2.

Therefore the equation is y=5/4x-9/2.

I reworked it but nothing was wrong...?