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3 years ago

When is a rectangle a square?

Mathematics

2 answers:

ololo11 [35]3 years ago

6 0

Answer:

I think option B i.e. when its angles are right angles.

tankabanditka [31]3 years ago

6 0

Answer:

A. When its sides are congruent

Step-by-step explanation:

By definition a square is a four sided polygon (shape) which has four right angles and four sides of equal length.

So, when a rectangle has all congruent sides, its a square because its a rectangle so it has four right angles, and congruent sides are sides of the same length.

B is incorrect because a rectangle can have four right angles but have differing side lengths

C is incorrect because again a rectangle can have parallel sides but have differing side lengths

D is incorrect because it can have convex angles but again have differing side lengths

You might be interested in

How to use trig to find missing side or angle of right triangles.

andrew11 [14]

Explanation

Right triangles are triangles with one right angle i.e. one angle with a measure of 90° so when we deal with this type of figures we know at least one of its internal angles. The opposite side to the right angle is known as the hypotenuse whereas the other two sides are called legs.

Trigonometric functions in right triangles give us the following identities:

$\begin{gathered} \tan x=\frac{\text{opposite side}}{\text{adjacent side}} \\ \cos x=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \sin x=\frac{\text{opposite side}}{\text{hypotenuse}} \end{gathered}$

We also have the Pythagorean theorem that states that the square of the hypotenuse is the sum of the squares of the legs.

Let's imagine that we have a right triangle like the following:

If we want to find the missing angles A and/or B we need to know at least two sides of the triangle.

For example, if we want to find B and we have b and a we can use the tangent of B and its inverse the arctangent (tan^(-1)):

$\tan B=\frac{b}{a}\rightarrow B=\tan^{-1}(\frac{b}{a})$

If we know a and c we can find B using its cosine:

$\cos B=\frac{a}{c}\rightarrow B=\cos^{-1}(\frac{a}{c})$

If we know b and c then we can use the sine:

$\sin B=\frac{b}{c}\rightarrow B=\sin^{-1}(\frac{b}{c})$

We can also do the same for angle A, we just need to use its corresponding opposite side and adjacent side. And that's how you find a missing angle using trigonometry in a right triangle.

If we are looking for a missing side we can also use trigonometry. In order to find a missing side we need two other sides or another side and an angle. For example, let's assume that we want to find side a.

If we have b and c then we just need to use the Pythagorean theorem:

$c^2=a^2+b^2\rightarrow a=\sqrt{c^2-b^2}$

If we have b and A then we can use the tangent of A to built an equation for a:

$\tan A=\frac{a}{b}\rightarrow a=b\cdot\tan A$

If we have b and B we can use the tangent of B:

$\tan B=\frac{b}{a}\rightarrow a=\frac{b}{\tan B}$

If we have A and c we can use the sine of A:

$\sin A=\frac{a}{c}\rightarrow a=c\cdot\sin A$

If we have B and c we can use the cosine of B:

$\cos B=\frac{a}{c}\rightarrow a=c\cdot\cos B$

And that's how you find a missing side using trigonometry.

8 0

10 months ago

A wheelchair ramp rises 1.5 feet for every 18 feet of horizontal distance it covers. Find the rate of change of the ramp

Ierofanga [76]

By definition the rate of change of a function is given by:
$AVR = \frac{Change In Y}{Change In X}$
Or equivalently:
$AVR = \frac{y2 - y1}{x2 - x1}$
Substituting the values given in the problem we have:
$AVR = \frac{1.5}{18}$
Rewriting we have:
$AVR = 0.08$
Answer:
the rate of change of the ramp is:
$AVR = 0.08$

7 0

3 years ago

Which of the following functions is graphed below?

sasho [114]

Answer:

2nd choice B.

Step-by-step explanation:

You can use the options A-D to help you eliminate pretty quickly without actually graphing

So first chose says you have the graph on the left when x<1 But you should see our visual actually says we want to include what happens at 1 (the filled dot) so this isn't the answer

Second choice Possible

Third choice... I'm just going to look at one of the parts... x^2+4 for x<=1 says we should have part of a parabola to the left of x=1 (inclusive) but there is not parabola in our visual

Fourth choice: same reason as third choice

Answer is the 2nd

5 0

3 years ago

In her piggy bank, caitlin has 5.24 dollars the sum is made up of an equal number of four coins from 1 cent, 5 cents, 10 cents,

Ludmilka [50]

Answer:

1c, 5c, 25c and 1 dollar

Step-by-step explanation:

With 4 coins of 1c : 4 cents

4 coins of 5c: 20 cents

4 coins of 25c: 1 dollar

4 coins of 1 dollar: 4 dollars

So, 4c + 20c + 1 dollar + 4 dollars = 5.24 dollars

3 0

3 years ago

An insurance company issues life insurance policies in three separate categories: standard,preferred,and ultra- preferred. Of th

slega [8]

Answer:

a) 0.0002

b) 0.0057

c) 0.0364

Step-by-step explanation:

Lets start by stating the probabilities of a person belonging to each policy:

Standard: 0.3

Preferred: 0.5

Ultra- Preferred: 0.2

The probability of person belonging to each policy AND dying in the next year:

Standard: 0.3 x 0.015 = 0.0045

Preferred: 0.5 x 0.002 = 0.001

Ultra- Preferred: 0.2 x 0.001 = 0.0002

a) The probability a ultra - preferred policy holder dies in the next year is 0.001. To find the probability of a person being both a ultra - preferred policy holder AND die in the next year is: 0.001 x 0.2= 0.0002

b) The probability is given by adding the probabilities calculated before :

0.0045 + 0.001 + 0.0002 = 0.0057

c) We use the results above again. This is 0.0002 / (0.001 + 0.0045). The answer comes out to be 0.0364

6 0

3 years ago