Find the values of x and y. <br><br> x=

Ethan sold 2 3 gallon of lemonade. Kayla sold some lemonade too. Together, they sold 1 1 4 gallons. Who sold more lemonade, Etha

dezoksy [38]

Answer:

Kayla sold more lemonade.

Step-by-step explanation

All you do to solve this problem is subtract 23 from 114.

6 0

3 years ago

During the first part of a trip, a canoeist travels 96 miles at a certain speed. the canoeist travels 15 miles on the second pa

blondinia [14]

This problem is a problem using
d = r * t
First part of the trip
d = 96 miles
r = ??
t = ??

Second part of the trip
d = 15 miles
r = r - 5
t = 4 - t

Solve for r first.
96/r + 15/(r - 5) = 4 hours multiply through by r and r - 5
96(r - 5) + 15r = 4*(r - 5)(r) Remove the brackets on the left
96r - 480 + 15r = 4*r*(r - 5) Collect like terms on the left.
111r - 480 = 4r(r - 5) Remove the brackets on the right.
111r - 480 = 4r^2 - 20r Bring the left side over to the right side.
0 = 4r^2 - 20r - 111r + 480 Collect like terms.
0 = 4r^2 - 131r + 480

The only way I could do this was to use the quadratic equation.

$\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}$

a = 4

b = - 131

c = 480

$\text{x = }\dfrac{ -(-131) \pm \sqrt{(-131)^{2} - 4*4*480 } }{2*4}$
$\text{x = }\dfrac{ 131 \pm \sqrt{(17161) - 7680 } }{8}$
$\text{x = }\dfrac{ 131 \pm \sqrt{9481 } }{8}$
$\text{x = }\dfrac{ 131 \pm 97.37 }{8}$

x = (131 + 97.38)/8
x = 28.55
x = (131 - 97.37)/8
x = 4.20

4.2 isn't going to work because the slower speed has to be larger than 5, otherwise you will get a negative speed (as this solution will give), so 4.20 is an extraneous solution.

r = 28.55 for the first part of the trip and
r = 23.55 for the second part of the trip.

Check.
Let's see if the times add up to 4
d/r = t
96/28.55 = 3.36
15/22.75 = 0.64

The times do = 4, so the rates are correct.

Answers
r1 = 28.55 for the 96 mile trip.
r2 = 23.55 for the 15 mile trip.

8 0

3 years ago

Evaluate the expression 4y - 11 when y = 14

vampirchik [111]

Answer:

The answer is 45 because 4 times 14 is 56 if you subtract 11 you get 45

8 0

2 years ago

Read 2 more answers

What is the slope of the following graph? (write your answer as a fraction unless divided by 1. Do not use spaces in your answer

alexira [117]

The slope of the graph is 4/5