Exercise 40

When plotting the following system of equations: [ begin{cases} 0.5 x + y = 2 \[.5em] 0.4 x + 2y = 2 end{cases} ] we obtain two straight lines that are: perpendicular to each other orthogonal to each other parallel and coincident parallel and distinct secant Try to solve it before checking the answer. Answer […]

Exercise 39

A retailer increases the price of its merchandise by 20% before promoting a 20% discount. The new selling price, relative to the original ((x)), is: ( x ) ( cfrac{x}{20} ) ( cfrac{24x}{25} ) ( cfrac{19x}{25} ) ( cfrac{14x}{25} ) Try to solve it before checking the answer. Answer ( cfrac{24x}{25} ) Step by Step […]

Exercise 38

In a two-digit number, the ones digit is twice the tens digit, and if we add the number with the result of inverting its digits, we obtain 66. If (U) represents the ones digit and (D) represents the tens digit in the original number, then: ( D = 2U; ; U + D = 6 […]

Exercise 37

The following table shows the relationship between the variables (x) and (y). (boldsymbol{x}) 1 2 3 (boldsymbol{y}) 1 3 5 This relationship can be defined as: ( y = 2x ) ( x = y – 1 ) ( y = 2x – 1 ) ( y = x^2 – 1 ) ( x = […]

Exercise 36

Half the area of a square is ( u^4 ). Then, the length of side is: ( 2 u^2 ) ( u^2 sqrt{2} ) ( u^2 ) ( u sqrt{2} ) ( 4 u^2 ) Try to solve it before checking the answer. Answer ( u^2 sqrt{2} ) Step by Step Solution If ( L […]

Exercise 35

The numbers (x), (y) and (z) are located on the real line as shown in the figure: We can state that: ( xy < xz ) ( xy > z ) ( y^2 < x^2 ) ( x^2 < z^2 ) ( xy < z ) Try to solve it before checking the answer. Answer […]

Exercise 34

What value of ( y ) satisfies the following system of equations? [ begin{cases} x^2 – y^2 = 4 \[.5em] x + y = 4 end{cases} ] ( cfrac{5}{2} ) ( cfrac{-5}{2} ) ( cfrac{3}{2} ) ( cfrac{-3}{2} ) ( 4 ) Try to solve it before checking the answer. Answer ( cfrac{3}{2} ) Step […]

Exercise 33

There is a pair of numbers and one is twice as large as the other. If you subtract 10 from both numbers, their sum is equal to the lowest of the original pair. Thus, the smallest of the original numbers is: 10 8 4 20 40 Try to solve it before checking the answer. Answer […]

Exercise 32

One value of the constant ( k ) for the function ( f(x) = kx^2 + 2x + k ) (the equation ( kx^2 + 2x + k = 0 ) ) to have only one root, is: One value of the constant ( k ) for the function [ begin{aligned} &f(x) = kx^2 + […]

Exercise 31

The triangle ( triangle ABC ) is equilateral and it has two of its heights drawn. Then the angle ( omega ) measures: ( 30^{circ} ) ( 45^{circ} ) ( 60^{circ} ) ( 90^{circ} ) ( 120^{circ} ) Try to solve it before checking the answer. Answer ( 120^{circ} ) Step by Step Solution Recall […]