The junior class is selling caramel apple lollipops and gourmet lollipops to raise money for prom. They profit 50 cents and 75 c

Answer:

The height of the triangular pyramid base is represented by s√3/2 units.

Step-by-step explanation:

This question focuses on calculating the height of the equilateral triangle at the base of the oblique pyramid.

According to the question, the equilateral triangle side has a length of a units.

Let’s review some properties of equilateral triangles:

a. All sides are identical in length, in this case, side s represents all sides.

b. All angles measure the same, at 60 degrees each.

c. Drawing a perpendicular line from the top vertex to the base divides the triangle into two right triangles, which have angles of 60 and 30 degrees, respectively.

To find the height of this triangular base, we can utilize either of the two right-angled triangles.

Recall the angles of 30, 60 and the side length s.

For height h calculation, trigonometric functions will assist us.

The relevant trigonometric relationship involves the sine of the angle (where side length s is the hypotenuse and height h is the opposite side relative to the 60-degree angle).

Thus, we can express this as:

Sine of an angle = opposite side length/hypotenuse length

sin 60 = h/s

Consequently, h = s sin 60.

In surd form, this yields:

sin 60 = √3/2.

Therefore, we find:

h = s * √3/2 = s√3/2 units.

Response:

D. The sidelines are parallel because they are perpendicular to a common line.

Justification:

According to the perpendicular transversal theorem, when a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line. Furthermore, the converse of the theorem states that if two lines are perpendicular to the same line, they must be parallel. Therefore, the sidelines are indeed parallel and also perpendicular to this single line.

Greetings!

The conclusion is:

The return trip will take 18 hours.

Reasoning:

To determine the duration of the return journey, we must calculate the distance from the destination back to the starting point.

The ship travels at 15 miles per hour (mph) over 6 hours, yielding a distance of:

The distance from the starting point to the destination is 90 miles, and for the return trip, the motor operates at a speed of 5 mph. Thus, computing the time taken gives us:

Consequently, the return trip will take 18 hours to complete.

Have a nice day!

Answer:

0.03

Step-by-step explanation:

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