1. how did astronomers confirm the existence of dark energy?
a. by calculating it using kepler’s third law
b. by measuring the mass of galaxies
c. by detecting it with telescopes
d. by the ages of globular clusters

2. how did astronomers confirm the existence of dark matter?
a. by measuring how fast the universe is expanding
b. by detecting very hot gas in galaxy clusters that emits x-rays
c. by measuring the amount of compressed gas in the universe
d. by detecting electromagnetic radiation reflecting from the dark matter

1. d

2. b

Explanation:

Dark energy is defined as the unknown energy that has an immense impact on the universe. It was first observed from a supernovae measurements, which showed evidence that the universe's expansion was accelerating.

Dark matter makes up approximately 85% of the universe's matter, it is defined as a invisible component that interacts with visible matter through gravity.

answer-

the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

solution-

it solely depends on b, whether the function will have one or two or zero x intercept.

this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.

1-   if b is zero, the graph will have exactly one x-intercept, at x= -a

2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ the statement is sometimes true.