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faltersainse [42]
3 years ago
12

Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram ?

Mathematics
1 answer:
Kipish [7]3 years ago
8 0

Answer:

Square

Step-by-step explanation:

Given

\angle 1 = x + 60

\angle 2 = 2x + 30

1 and 2 are consecutive

Required

Determine a special name to the parallelogram

For consecutive angles 1 and 2 of a parallelogram, we have:

\angle 1 + \angle 2 = 180

x + 60 + 2x + 30 = 180

3x +90 = 180

Collect like terms

3x = 180 - 90

3x = 90

x = 30

Next, is to calculate angles 1 and 2

\angle 1 = x + 60

\angle = 30 + 60 = 90

\angle 2 = 2x + 30

\angle 2= 2*30 + 30 = 90

Both angles are 90.

This implies that each angle in the parallelogram is 90.

<em>Such a parallelogram is either a rectangle or a square</em>

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Which graph shows that Cindy reads about 3/4 of the time while riding in the car?
wolverine [178]

The graph that shows a unit rate of 3/4, which is the time Cindy reads while riding in the car is the graph attached below.

<h3>What is Unit Rate?</h3>

Unit rate can be described as a constant or exactly how much of one quantity is per 1 unit of another quantity.

Unite rate (k) = x/y.

In the graph attached below, when x (hours driving) = 3, y (hours reading) = 4.

Therefore, unit rate = 3/4. We can then conclude that the graph that shows that Cindy reads 3/4 of the time she rides in a car is the graph attached below.

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Please answer question
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The value of the expression 2\cos(t) + \tan^2(t) is 4 and the exact value of \sin^{-1}(\sin(\frac{5\pi}{3})) is \frac{5\pi}{3}

<h3>How to determine the trigonometry expression?</h3>

The point on the unit circle is given as:

P = (\frac 12, \frac{\sqrt{3}}2)

A point on a unit circle is represented as: (x,y), such that:

cos(t) = x and sin(t) = y.

This means that:

\cos(t) = \frac 12

\sin(t) = \frac{\sqrt 3}{2}

Calculate tan(t) using:

\tan(t) = \frac{\sin(t)}{\cos(t)}

So, we have:

\tan(t) = \frac{\frac{\sqrt 3}{2}}{1/2}

Evaluate

\tan(t) = \sqrt 3

The expression is then calculated as:

2\cos(t) + \tan^2(t) = 2 * \frac12 + (\sqrt 3)^2

Evaluate each term

2\cos(t) + \tan^2(t) = 1 + 3

Evaluate the sum

2\cos(t) + \tan^2(t) = 4

Hence, the value of the expression 2\cos(t) + \tan^2(t) is 4

<h3>How to solve the arcsin expression?</h3>

The expression is given as:

\sin^{-1}(\sin(\frac{5\pi}{3}))

As a general rule, the arc sine of sine x is x.

This means that:

\sin^{-1}(\sin(\frac{5\pi}{3})) = \frac{5\pi}{3}

Hence, the exact value of \sin^{-1}(\sin(\frac{5\pi}{3})) is \frac{5\pi}{3}

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