hi guys I’ve been having a bit of a struggle with the math session. Can someone please teach me how to solve q27, 49, 52, 55 and 57? Thanks 
- The entire graph of the relation R of the ordered pairs (x,y) is shown in the standard (x,y) coordinate plane below. One of the following sets is the domain of the relation R. Which set is it? A. {1, 2, 4} B. {1, 2, 3, 4} C. {1, 2, 3, 6} D. {1, 2, 4, 6} E. {1, 2, 3, 4, 5, 6}
C.
Answer explanation:
Definition: Function, domain, range
A function is a set of ordered pairs in which no two ordered pairs have the same first coordinates and different second coordinates.
The domain of a relation is the set of all first coordinates of the ordered pairs.
The range of a relation is the set of all second coordinates of the ordered pairs.
According to the graph, the ordered pairs are (1,2), (1,4), (2,1), (3,4) and (6,2).
Therefore, the domain of the relation R is the set of the first coordinates of the above ordered pairs, i.e. the set of {1, 2, 3, 6}.
- In the standard (x,y) coordinate plane, for what value(s) of x, if any, is there NO value of y such that (x,y) is on the graph of
A. -3, -2, and 2 only
B. -2, 2, and 3 only
C. -3 only
D. 3 only
E. There are no such values of x.
A.
Answer explanation:
The denominator of any fraction cannot have the value zero. If the denominator of a fraction is zero, the expression is not a legal fraction because it’s overall value is undefined.
Therefore for the denominator (x+3)(x+2)(x-2) NOT to be zero, x cannot have the value of -3, -2, or 2.
- From point A outside a circle and in the same plane as the circle, 2 rays are drawn tangent to the circle with the points of tangency labeled B and C, respectively. Segment BC is then drawn to form ∆ABC. If∠A measures 70°, what is the measure of ∠ABC? A. 70° B. 55° C. 40° D. 35° E. Cannot be determined from the given information
B.
Answer explanation:
Since the two lines are tangent with the circle at points B and C, respectively, ∆ABO can be proved to be congruent to ∆ACO (proof omitted). Therefore, segments AB and AC are the same in length. It follows that ABC = ACB = (180° - 70°) / 2 = 55°
- Carrie and Manuel are side by side when they begin to run at the same time in the same direction around a track. Carrie runs at a constant rate of 30 seconds per lap, while Manuel runs at a constant rate of 50 seconds per lap. How many seconds after beginning to run will Carrie have run exactly 1 more lap than Manuel? A. 20 B. 40 C. 75 D. 80 E. 125
C.
Answer explanation:
Let the number of seconds after beginning to run be X;
let the number of laps run by Carrie be C;
let the number of laps run by Manuel be M.
Then, we have the following equations
(1) C = X / 30
(2) M = X / 50
(3) C = M + 1
Solving for the equations (1), (2) and (3), we have:
X / 30 = X / 50 + 1
X = 75
- Consider the fractions l/a, l/b , and l/c, where a and b are distinct prime numbers greater than 3 and c = 3a. Suppose that a • b • c is used as the common denominator when finding the sum of these fractions. In order for the sum to be in lowest terms, its numerator and denominator must be reduced by a factor of which of the following? A. 3 B. a C. b D. c E. ab
B.
Answer explanation:
The sum of the fractions:
And because c=3a, with c replaced by 3a, the sum can be re-written as follows, where the numerator and denominator can be both reduced by a.
The complete answer explanations for the math section of Form 74E can be read here:
http://acthelper.com/act-form-73e-math-answer-explanations/