Editorial - Matwa - Soal TKA 3

Problem 1

[[2*a+4,3*c],[5,30]]+[[4,2],[3*b+1,-6]]=[[4,14],[9,24]]

2*a+4+4=4

∴a=-2

5+3*b+1=9

∴b=1

3*c+2=14

∴c=4

∴a+b+c=3

Problem 2

Subproblem 2.1

Statement:64of people got a grade ≤79

(5+12+15+8)/(5+12+15+8+6+4)=4/5=80

False.

Subproblem 2.2

Statement: The mean and the mode are in the same class.

True, just by observation.

Subproblem 2.3

Statement: The mode of the data is 71.5

69.5+4⋅((15-12)/(2⋅15-8-12))=69.5+5⋅3/10=71

False, as the dataset is discontinuous.

Subproblem 2.4

Statement: The difference between the median and the mode is 1.17

69.5+(25-17)/15⋅5=72.167=72.17

The difference is 72.17-71=1.17, correct.

Problem 3

What possible solutions are there to this?

3(2*x)-8⋅3x-9=0

3(2*x)-8⋅3x-32=0

3x=p

p2-8*p-9=0

(p-9)*(p+1)=0

∴p=9,-1

p=9, only real solution.

Problem 4

3*x+y=5

x-y=-1

2*a*x+b*y=4

a+b=what

4*x=4

x=1

-y=-1-1

y=2

2*a⋅1+b⋅2=4

∴a+b=2

Problem 5

Find the boundary of m where we have real roots.

x2+(2*m-1)*x+(m2-3*m+5)=0

(2*m-1)2-4⋅(m2-3*m+5)≥0

4*m2-4*m+1-4*m2+12*m-20≥0

8*m-19≥0

m≥19/8

Problem 6

Incomplete problem.

Problem 7

The answer is B.

x+2*y≤8

3*x+2*y≤12

x≥0

y≥0

Problem 8

ƒ(x)=x2+2*x+4

g(x)=2/(x+3)

ƒ(-2)/g(-2)=(4-4+4)/2/1=2

Problem 9

y=a*(x-(x_p))2+(y_p)

4=a+2

a=2

y=2*(x-1)2+2=2*x2-4*x+4

Problem 10

x2+2*x-8=0

1/(x_1)+1/(x_2)=(x_2)/((x_1)*(x_2))+(x_1)/((x_1)*(x_2))=-2/(-8)=1/4