The temperatures at several times of the day are shown in the coordinate plane below. The xxx-axis represents the number of hours before or after noon. For example, -1−1minus, 1 would represent 11 \text{ a. m.}11 a. m.11, start text, space, a, point, m, point, end text The yyy-axis represents the temperature in degrees Celsius. At 5 \text{ p. m.}5 p. m.5, start text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p. m.}2 p. m.2, start text, space, p, point, m, point, end text and the temperature at 8 \text{ p. m.}8 p. m.8, start text, space, p, point, m, point, end text What coordinates represent the temperature at 5 \text{ p. m.}5 p. m.5, start text, space, p, point, m, point, end text ?

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.

your answer is

a.

5

step-by-step explanation:

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.