Mathematics, 03.08.2019 00:30 jep88

You and a friend start hiking toward each other from opposite ends of a 17.5-mile hiking trail. you hike 2/3 mile every 1/4 hour. your friend hikes 2 1/3 miles per hour. a. who hikes faster? how much faster? b. after how many hours did you meet? c. when you meet, who hiked farther? how much farther? answer this asap! you!

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Since you hike $\frac{2}{3}$ miles every $\frac{1}{4}$ hour, you'll hike $\frac{2}{3}*4=\frac{8}{3}=2\frac{2}{3}$ every hour. Comparing this to your friend's rate, we can see that you hike more miles in one hour. You hike $\frac{\frac{8}{3}}{\frac{7}{3}}=\frac{8}{3}*\frac{3}{7}=\frac{8}{7}$ times faster.

a) You hike faster. You hike $\frac{8}{7}$ times faster.

The two of you will meet when the total distance you've traveled sum up to 17.5

miles. You can find the distance both you and your friends traveled by multiplying your rate with the time you've been hiking. Since you both need to arrive at the same time, we will assign the same variable, t, to determine after how many hours you will meet.

$\frac{8}{3}t+ \frac{7}{3}t=17.5$
$\frac{15}{3}t=17.5$
$t=17.5*\frac{3}{15}=3.5$

b. The two of you will meet after 3.5 hours.

As said earlier, we just multiply the rate with the number of hours you've traveled to find the distance you've hiked.

You traveled: $\frac{8}{3}* \frac{7}{2} = \frac{28}{3}=9.33$ miles
Your friend traveled: $\frac{7}{3}* \frac{7}{2} = \frac{49}{6}=8.17$ miles

You hiked $\frac{28}{3}-\frac{49}{6} = \frac{7}{6}=1.167$ miles farther.

c)You hiked farther. You hiked 1.167 miles farther.

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has vertices $p(1,2),q(2,1),r(3,2),s(3,3)$ recall that for counterclockwise rotation about the origin, $(x,y)\rightarrow (-x,-y)$ when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will become $p1( - 1, - 2),q1( - 2, - 1),r1( - 3, - 2),s1( - 3, - 3)$ next, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain, $p'(1, - 2),q'(2, - 1),r'(3, - 2),s'(3, - 3)$ therefore the correct answer is c