Correct answer is A.

e^2x - 2e^x -15=0 › let e^x=a then w can write the equation as, a²-2a-15=0 

› (a-5)(a+3)=0 › e^x=a=5, e^x=a=-3 then the solution is; ln5 and ln-3.

Example

600 men are interviewed about which sports they like. It is found that 190 like football, 140 like basketball, 120 like volleyball, 65 like football and basketball, 50 like football and volleyball, 40 like basketball and volleyball, 30 like all three sports.

1. How many of them like at least one of these sports?
2. How many of them like none of these sports?
3. How many of them like only football?
4. How many of them like football and basketball but not volleyball?
5. How many of them like basketball or volleyball but not football?

Solution

Define

F = The set of all men who like football,

B = The set of all men who like basketball,

V = The set of all men who like volleyball.

Then s(F) = 190,    s(B) = 140,   s(V) = 120, s(F ? B) = 65,   s(F ? V) = 50,   s(B ? V) = 40,

s(F ? B ? V) = 30 where, as defined above, the symbol s(.) is used for the number of elements. Below, we give the Venn diagram solution of this problem where the numbers on the regions they are sitting indicate the number of elements of the corresponding set. For  example, the number 30 indicates that he number of elements of the intersection F ? B ? V is 30.

We can easily count the required numbers in the questions a. – e.

1. 105 + 35 + 30 + 20 + 65 +10 + 60 = 325
2. 600 – 325 = 275,
3. 105,
4. 65 - 30 = 35,
5. 60 + 10 + 65 = 135.

As also undersood from the information given, all statements in the options are correct according to the case given, so the correct answer is E.

2x - 8 = 0

2x= 8

x = 4

The y-intercept of y=-3x² - 2x - 1 is -1 because if x=0, then y=-3.0 - 2.0 -1 = 0 - 0 - 1 = -1. 

f(3)=3-1=2 and g(3)=(3+2)/4=5/4

(f.g)(3)=f(3).g(3)›2.5/4=5/2

The degree of f(x)=2x^3 + 4 is 3. The answer is B.

Since 2^-1 is 1/2¹ which equals to 1/2; 3^-1 is 1/3¹ which equals to 1/3; and 3^-2 is 1/3² which equals to 1/9, what we have in hand is ( (1/2) + (1/3) ) / (1/9). (1/2) + (1/3) equals to 11/18, and if we divide it by 1/9, this equals to 11/2. 

From the equation 3x+6=y we find x = f ^-1(y) = . Thus f ^-1(x) = , so the correct answer is B.

55 + 45 + 26 – x = 87 ; x = 126 – 87 = 39. Correct answer is D.

45 + 15 + 17 – 22 = x ; x = 55 . pg. 5. Correct answer is C.

x = (A ∩ B) \ C. Correct answer is B.

x = ((16 . 5)^1/2 / (5 . 5)^1/2) . (4 . 5)^1/2 = 8 . pg. 12 . Correct answer is D.

27^-2 / 9^-2 equals to (27/9)^-2 = 3^-2. When we do the operation 3^-2 . 3² , we find 3^-2+2 which equals to 3⁰. 3⁰ equals to 1. 

A \ B = [-1, 0)

The slope of y=7x+5 is 7 because the slope of a linear function of the form y=mx+n is m. The answer is D.