Graphing Equations

Los triángulos similares son triángulos que tienen (a)   .

• Triángulos que tienen la misma forma

• Triángulos que tienen el mismo tamaño

• Triángulos que tienen ángulos diferentes

• Triángulos que tienen el mismo perímetro

Answer explanation

Similar triangles, like △JOE and △TED, have the same shape but can differ in size. This means their corresponding angles are equal, and their sides are in proportion, but the triangles themselves are not necessarily identical in size.

Match the following descriptions with the relationship between lines PQ and EF.

• Perpendicular lines

• They are parallel to each other.

• Parallel lines

• They intersect at a 90-degree angle.

• Lines forming an acute angle

• They do not intersect at all.

• Non-intersecting lines

• They form an acute angle.

Answer explanation

For lines PQ and EF to be perpendicular, they must intersect at a 90-degree angle. This means they form a right angle where they meet, distinguishing them from parallel lines or those that do not intersect.

¿Qué es una fracción compleja? Simplifica la fracción compleja dada en la imagen.

• Una fracción donde el numerador, el denominador, o ambos, contienen una fracción.

• Una fracción que no se puede simplificar más.

• Una fracción con una variable en el denominador.

• Una fracción que es mayor que 1.

Answer explanation

A complex fraction is defined as a fraction where the numerator, the denominator, or both contain a fraction. This distinguishes it from simpler fractions, making the first answer choice the correct one.

¿Cuál es la fórmula para la probabilidad condicional?

• P(A|B) = P(A) + P(B)

• P(A|B) = P(A) * P(B)

• P(A|B) = P(A y B) / P(B)

• P(A|B) = P(B) / P(A y B)

Answer explanation

The formula for conditional probability is P(A|B) = P(A and B) / P(B). This means the probability of event A occurring given that B has occurred is the probability of both A and B occurring divided by the probability of B.

Match the following trigonometric identities with their corresponding equations.

• Equality of sine and cosine

• sin²θ + cos²θ = 1

• Pythagorean identity

• sinθ = cosθ

• Cosecant identity

• tan²θ + 1 = sec²θ

• Secant identity

• 1 + cot²θ = csc²θ

Answer explanation

The Pythagorean identity states that for any angle θ, the square of the sine plus the square of the cosine equals one: sin²θ + cos²θ = 1. This is fundamental in trigonometry and confirms the relationship between these functions.

¿Cuál es el límite de 1/x cuando x tiende a infinito?

• 0

• 1

• Infinito

• Indefinido

Answer explanation

As x approaches infinity, the value of 1/x gets closer to 0. Therefore, the limit of 1/x as x approaches infinity is 0, making it the correct choice.

What is the capital of France?

• Berlin

• Madrid

• Paris

• Rome

Answer explanation

Graph A correctly represents the intersection of the quadratic equation y = x^2 - 2x - 3 and the linear equation y = -1/2x + 1, showing their points of intersection and the overall shape of both functions.

¿Cuál de los siguientes gráficos representa las ecuaciones y = cos x y y = sec x?

• Gráfico A

• Gráfico B

• Gráfico C

• Gráfico D

Answer explanation

Graph A correctly represents the equations y = cos x and y = sec x. The cosine function oscillates between -1 and 1, while the secant function has vertical asymptotes where cos x = 0, which is accurately depicted in Graph A.