$c equals fraction numerator x over denominator y end fraction$ The given equation relates the variables c, x, and y, where c > 0, x > 0, and y > 0. Which equation correctly expresses y in terms of c and x ?

In right triangle ABC, the length of side $stack A C with minus on top$ is 12 , the measure of $angle A$ is $40 to the power of ring operator end exponent$ , and $angle B$ is a right angle. Which of the following can be determined using the information given?
I) The measure of $angle C$
II) The length of side $stack A B with minus on top$

Any triangle that has one 90-degree angle is said to have a right angle. Right triangles are those with an angle of 90 degrees, or "right angles," hence those with this angle. First, determine the third angle's measurement. You already know that C = 90 degrees because it is a right angle, and you are also aware of the size of A or B. Since a triangle's internal degree measurement must always equal 180 degrees, the third angle's measurement can be determined by applying the following formula: 180 – (90 + A) = B. The formula can also be turned around so that 180 - (90 + B) = A.
As an illustration, if you know that A is 40 degrees, then B is 180 – (90 – 40). It is easy to work out that B = 50 degrees if you simplify this to B = 180 - 130. Triangles can be resolved using the Law of Sines. Knowing the length of one side and the measurement of one other angle in addition to the right angle will especially assist you in finding the hypotenuse of a right triangle. The Law of Sines asserts that for any triangle with sides a, b, and c and angles a, b, and c, a / sin A = b / sin B = c / sin C.
Any triangle can be resolved using the Law of Sines, but only a right triangle will have a hypotenuse.

In right triangle ABC, the length of side $stack A C with minus on top$ is 12 , the measure of $angle A$ is $40 to the power of ring operator end exponent$ , and $angle B$ is a right angle. Which of the following can be determined using the information given?
I) The measure of $angle C$
II) The length of side $stack A B with minus on top$

Quadrilateral ABCD is shown. Which equation shows how the measures of the angles of the quadrilateral are related?

If 2n + 12 = 26n, what is the value of 6n ?

Which of the following is equivalent to $4 x to the power of 3 end exponent plus 8 x to the power of 2 end exponent$ ?

$vertical line 2 x minus 4 vertical line equals 8$ What is the positive solution to the given equation?

Two lines intersect as shown. What is the value of x ?

Albedos of Various Earth Surfaces

An albedo is the amount of light reflected from a surface divided by the amount of light falling on the surface. The amount is typically measured in watts per square meter. The table shows the minimum and maximum albedos for different types of surfaces on Earth.
For which of the following surfaces is the range of albedos the greatest?

The ratio of trumpets to violins in a particular music classroom is 1 to 3 . If there are 9 trumpets in the classroom, how many violins are there?

$2 n equals negative 22$
What value of n satisfies the given equation?

The line graph above shows the population, in thousands, of people living in Alaska every 10 years from 1900 to 2000.
What was the population of Alaska, in thousands, in 1990?

$straight K space equals space fraction numerator 200 straight v squared over denominator 2 end fraction$
In the equation above, the kinetic energy, K , of a 200-gram object is given in terms of its speed, v. If the equation is rewritten in the form $straight v space equals space straight a space square root of straight K$ , where a is a positive constant, what is the value of a ?

For the exponential function f, the table shows some values of x and the corresponding values of f (x). The function can be written in the form $f left parenthesis x right parenthesis equals p r to the power of x$ , where p and r are constants. What is the value of r ?

Number of Contestants by Score and Day

The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above.
No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?

A system of two linear equations has no solutions. The graph of one of the equations in the system is shown in the xy - plane.

The second equation in the system is $a x minus y equals 1$ , where a is a constant. What is the value of a ?