Answer : ) 1. which number is not the sum of three consecutive integers? a. 65 b. 150 c. 42 d. 572. train a leaves a station traveling at 48 kilometers per hour. four hours later, train b leaves the same station traveling in the same direction at 68 kilometers per hour. what equation can you use to find the time t in hours that it took train b to catch up with train a, and what is the value of t? a. 68(t – 4) = 48t; t = 13.6 hoursb. 48(t + 4) = 68t; t = 10.6 hoursc. 68(t + 4) = 48t; t = –9.6 hoursd. 48(t + 4) = 68t; t = 9.6 hours3. the sum of two consecutive integers is –27. if n represents one of the integers, what equation can you write to find the value of the two integers and what are the integers? a. n + (n – 1) = –27; –14 and –15b. n + (n + 1) = –27; –14 and –12c. n + (n + 1) = –27; –14 and –13d. n + (n + 1) = –27; –14 and –154. the length of a rectangle is one fourth its width. the perimeter of the rectangle is 60 centimeters. if w represents the width of this rectangle, which expression represents its length? a. l = 1 over 4wb. l = 4wc. l = 60 – wd. l = 60 – 2w

1. A

2. A

3. C

4. A

Step-by-step explanation:

1. Three consecutive integers are represented as n, n+1, and n+2. The sum

n+(n+1)+(n+2) = # must be only true using integers (no fractions/decimals).

So try the first answer 65.

n+(n+1)+(n+2) =65

3n+3=65

3n=62

n=62/3

n=20.6666666666666

This is not an integer so A is the solution.

2. The first train arrives at 48t since it travels 48 km per hour for t hours.

The second train is 68(t-4) since it travels 68 km per hour for the same t hours minus 4 (it left 4 hours later). The time they reach each other is when they are equal. So 68(t-4)=48t or answer A.

3. Two consecutive integers are represented as n and n+1. Notice when added they must equal -27. The only answer option that works is -14 + -13 = -27. Answer C is the solution.

4. The length is one fourth of its width is multiplication by 1/4. So l = 1/4 w or answer A is the solution.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.