1. In a class of 32 students, 18 offer Chemistry, 16 offer Physics and 22 offer Mathematics, 6 offer all three subjects, 3 offer Chemistry and Physics only and 5 offer Physics only. Each student offers at least
one subject. Find the number of students who offer
(a) Chemistry only
(b) only one subject
(c)
only two subjects

Step-by-What do we call the cloud of gas and dust from which a star forms?

a.

a quasar

b.

a pulsar

c.

a nebula

d.

a neutrino

step explanation:

i believe the answer is d.

hope it you! : d

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3