Thomas decides on a destination for his vacation. If he takes the train there, it will take him 1/8 hours to get there. If he takes the plane, it will take him 2/3 hours. How many hours does the plane save?

The plane takes hours shorter.

Step-by-step explanation:

To calculate the number of hours that the plane saves, you must make the difference between the number of hours that must travel by train and the hours that must travel by plane. This is:

A mixed fraction is the combination of a whole number and a fraction, as in this case. To subtract mixed numbers, one way to do it is, firstly, to convert both fractions into improper fractions, remembering that the procedure for this consists of multiplying the whole number by the denominator of the fraction, to which the numbered one must be added. of the fraction. This number will be the numerator of the new fraction.

In this case:

Then:

Fractions have different denominators, so you need to find a common denominator in order to do the subtraction. A common denominator can be found by multiplying both denominators.  Then you rewrite each fraction as an equivalent fraction with a denominator that is the common denominator. Finally you subtract the numerators and simplify the answer if necessary.

In this case:

Now you write the answer as a mixed number. For that you divide 59 by 24 to obtain 2 with a remainder of 11, being able to express the number as:

So:

The plane takes hours shorter.

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true