MMBL Sudden Quiz
03-31-19
Questions with answers:
1.) If the cube of x is 125^69, and the product of x and the square of 125^69 is 5^y, what is y?
ANSWER: 483
Solution:
Given: x³ = 125^69, 5^y = x(125^69)
x = 5^69
5^y = (5^69)(5^3*69)²
5^y = 5^(69+414)
y = 483
2.) In a linear function, f(96) – f(69) = 378 , what is f(69) – f(34)?
ANSWER: 4901.
S
olution:
In a linear function, f(96) – f(69) = 378 , what is f(69) – f(34)?
Solution:
f(x)=ax+b
f(96)=96a+b
f(69)=69a+b
Solve for a:
f(96)-f(69)=378
96a+b-(69a+b)=378
96a+b-69a-b=378
27a=378
a=14
Now,
f(69)-f(34)
69a+b-(34a+b)
69a-34a+b-b
35a
35(14)
490
3.) What is the reciprocal of cbrt(25) – 3 in simplest form?
ANSWER: - (5 cbrt(5) + 3 cbrt(25) + 9) / 2
4.) If f(x) = (3x + 5) / (1 – 7x), what is f^-1(3)?
ANSWER: -1/12
Solution:
4
. -1/12
X= 3y+5/1-7y
(1-7y)(x)=3y+5(equate to y)
(-7xy-3)=(5-x)
Y=(5-x)/(-7x-3)
F(3)=x
X=3
Substitution: (5-3)(-7)(3)-(3)
F(x)=2/-24(lowest term -1/12)
5.) The sides of an isosceles triangle measure 5x + 3, 3x + 7 and 2x + 15, where x is some number. What is the smallest possible perimeter of the triangle?
ANSWER: 45 units
Equate first 2 equations
x=2
6.) In a dining area, there are two tables, Table A and Table B. If x number of plates are transferred from A to B, the number of plates will be equal, moreover, if x number of plates are transferred from B to A, the ratio of the plates of A to B will be 5:3. If the total number of plates of A and B is between 40 to 50, find the plates in Table A, Table B, and find x.
ANSWER: Table A = 27, Table B = 21, x = 3
Solution:
First is just use logic
There will be 5:3 so 5z and 3z, a total of 8z. Between 40 and 50, there is just one multiple of 8, which is 48. So, the sum of plates is 48
a + b = 48
9a + 9b = 432
a - x = b + x
a - b = 2x
4a - 4b = 8x
3(a + x) = 5(b - x)
3a + 3x = 5b - 5x
5b - 3a = 8x
4a - 4b = 5b - 3a
7a = 9b
9a + 7a = 432
16a = 432
a = 27
b = 21
x = 3
7.) A triangle whose sides are in the ratio 3:4:5 is circumscribing a circle with area 4,761 pi sq.cm. What is the area of the triangle?
ANSWER: 28,566 sq.cm.
8.) The sides of a triangle are 7cm, 8cm, and 9cm. Find the altitude of the triangle from the side 8 cm
Answer: 3 sqrt(5) cm
Solution:
8. 3√5
Side: 7,8,9
s=7,8,9/2
s=12
a=√12(12-7)(12-8)(12-9)
a=√12(5)(4)(3)
a=√720 or 12√5
Area=bh/2
12√5=4(from 8 cm)h
12√5/4=h
3√5=h(h is altitude)
9.) How many integers from 1 to 1000, inclusive, is divisible by 6 or 9 but not both?
Answer: 167
Solution:
1000÷6=166
1000÷9=111
1000÷18=55(2)
166+111=277-110
167
10.) What is the 6900th term of the sequence if its first six terms are 69, 90, 112, 135, 159, and 184?
Answer: 23,939,599
Solutions:
SOLUTION 1:
Notice that the difference is 21, 22, 23, 24, 25, and so on. The 6900th term is the 6899th term plus 6919
Summation from 21 to 6919
(21+6919)(6899/2) = 23,939,530
Then add the first term which is 69
23,939,599
SOLUTION 2:
Notice that it is quadratic because the second differences are equal
first term = 69
second term = 90
third term = 112
ax² + bx + c = y
a(1)² + b(1) + c = 69
a + b + c = 69
a(2)² + b(2) + c = 90
4a + 2b + c = 90
a(3)² + b(3) + c = 112
9a + 3b + c = 112
Solve for a, b, and c
a = 1/2
b = 39/2
c = 49
So our quadratic equation is
x²/2 + 39x/2 + 49 = y
We will now get the 6900th term..Just substitute 6900
(6900)²/2 + 39(6900)/2 + 49
= 23,939,599
