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2 years ago

Explain why drawing both diagonals on any rectangle will always result in two pairs of nonoverlapping congruent triangles.

Mathematics

1 answer:

raketka [301]2 years ago

7 0

Answer:

It is because not all sides of a rectangle are equal in length; unlike a square.

Step-by-step explanation:

Let's start by drawing the first diagonal.

You know already how a rectangle looks. It has 4 sides and 2 sets of parallel sides. Each pair of parallel sides has the same length.

A diagonal is a line crossing from one edge of a four-sided shape to the opposite edge; such that it divides the shape into two equal halves.

Now place your rectangle horizontally. Let the two longer sides be on the horizon while the two shorter sides go vertical.

We draw the first diagonal from the edge on the top right to the opposite edge (down left). This will divide the shape into two equal halves and each half will be a triangle; a congruent one at that.

When you fold this rectangle along its diagonal, the two triangles will not overlap! The resulting shape will be like two triangular mountains lying side by side. You can use a paper (cut in the shape of a rectangle) for this experiment.

Why does this happen, instead of the two triangles covering each other (overlapping)?

This happens because a rectangle doesn't have 4 equal sides. Check out a square and you'll see that both triangles will overlap after a diagonal is drawn across the square.

Draw the second diagonal of the rectangle (from up-left to down-right) and the same thing is observed.

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A rectangle sandbox has a width of 5 feet. Tbe sandbox is 5 times as long as it is wide. What is the perimeter of the sandbox?

NikAS [45]

The perimeter of the sandbox is 60 ft.
5x5=25
Two sides = 25, so 25+25 = 50.
Two other sides = 5, so 5+5=10
50+10 = 60, and that is the correct answer.
If you would like any more assistance with this type of questions, let me know and I will be able to further assist you. Thank you!

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2 years ago

A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting ta

nikklg [1K]

Using the normal distribution and the central limit theorem, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean $\mu = p$ and standard error $s = \sqrt{\frac{p(1 - p)}{n}}$

In this problem:

1,190 adults were asked, hence $n = 1190$

In fact 62% of all adults favor balancing the budget over cutting taxes, hence $p = 0.62$ .

The mean and the standard error are given by:

$\mu = p = 0.62$

$s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141$

The probability of a sample proportion of 0.59 or less is the p-value of Z when X = 0.59, hence:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.59 - 0.62}{0.0141}$

$Z = -2.13$

$Z = -2.13$ has a p-value of 0.0166.

0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

You can learn more about the normal distribution and the central limit theorem at brainly.com/question/24663213

7 0

1 year ago

Tina is saving to buy a notebook computer. She has two options. The first option is to put S200 away initially and save $10 ever

BigorU [14]

The equation for the first option is Y=10x + 200
The equation for the second option is Y=30x + 100

X = one month
To find when they would be the same about you have to set the equations equal to each other

10x + 200 = 30x + 100
-10x -100 -10x -100

100= 20x

5 = x

After five months she would save the same amount. To find how much is saved you have to plug in 5 for x in one of the equations. You can always double-check 5 by plugging it in both equations and making sure you get the same answer

Y= 10(5) + 200 = 250

Y= 30(5) + 100 = 250

She would have saved $250 after five months by using either method

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2 years ago

Determine which functions have two real number zeros by calculating the discriminant, b2 - 4ac. Check all that

Nuetrik [128]

Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4.

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2 years ago

Read 2 more answers

In the equation 5x = 60, what is the next step in the equation solving sequence?

muminat

Answer:

Step-by-step explanation: