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3 years ago

In Exploration 4.1.1 problem 3 pre calc

Mathematics

1 answer:

IrinaVladis [17]3 years ago

6 0

The reference triangle is a right triangle and therefore, the properties of

the reference triangle are similar to right triangle properties.

The correct options are as follows;

The reference triangle always have a leg perpendicular to the x-axis, the hypotenuse is positive, and θ is the angle adjacent to the x-axis and hypotenuse.

<h3>Reasons</h3>

The reference triangle is formed by the construction of a perpendicular

to the x-axis from the terminal side of an angle, oriented in the standard

position.

Therefore;

The reference triangle is a right triangle that always has a leg perpendicular to the x-axis.

The hypotenuse is taken as positive, given that the magnitude of the hypotenuse is the square root of the sum of the squares of the legs.

In the first quadrant, the reference angle, θ, is the same as the standard position angle and it is given by the angle formed between the x-axis and the hypotenuse side.

The correct options are therefore;

In Trigonometry it is important that the right triangle (reference triangles)

have a consistent orientation. The reference triangles always have a leg

perpendicular to the x-axis, the hypotenuse positive and the θ is

adjacent to the x-axis and hypotenuse.

Learn more about reference angles and right triangles here:

brainly.com/question/10657736

brainly.com/question/1593685

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3^x= 3*2^x solve this equation

kompoz [17]

In the equation

$3^x = 3\cdot 2^x$

divide both sides by $2^x$ to get

$\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3$

Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

$\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13$

Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$

(Both answers are equivalent)

8 0

3 years ago

A school district wants to determine the most effective way to prepare seniors for the SAT. They randomly select senior level ma

My name is Ann [436]

Answer:

In the SAT; Pedagogical relationships are not traditional but those of a group of people working together towards a common goal. Students and tutor challenge specific problems together and face a style of encounter that opens the way to self-learning.

● Within the SAT group, which is at the same time a group of neighbors who share possibilities and problems, learning to dialogue is both an educational objective and a means of training.

Step-by-step explanation:

The purpose of the SAT is for graduates to be competent to perform in their own communities at different levels of activity. The Booster, for example, works at the level of improvement of productive projects within its own productive units or those of its neighbors. The Pilot, in addition to the previous capacity, can organize different types of activities for the common good (health projects, the environment, work with children, recreation, production in solidarity). These two levels are approved by law with the basic secondary. At the Bachelor level, graduates are trained to participate in more complex organizations and develop long-term initiatives in both productive and organizational aspects.

To achieve greater ease and adaptation to the SAT, I consider that the group that is being taught with the non-traditional method and where the students work in groups, can easily adapt to the SAT learning system.

4 0

3 years ago

Out of seniors at a local high school, 60% went on the senior trip. At the hotel , one room was reserved for every 4 students .

sweet [91]

Answer:

Number of rooms reserved for the students are - 90 .

Step-by-step explanation:

Firstly ,

As we know 60% of the 600 students went on the trip,

Then ,

Number of students went on the trip = 60% of 600

= $\frac{60}{100}\times600$