A rectangle with 8 cm width and 3 cm length What is the perimeter and area of the rectangle?

The Hypotenuse-Leg theorem states that two right triangles are congruent if and only if their hypotenuses and any of their corresponding legs are congruent. That is to say:

$\overline {AC} \cong \overline {DF}$ , $\overline{BC} \cong \overline {EF}$

$AC = DF, BC = EF$

$\sqrt{AB^{2}+BC^{2}} = \sqrt{DE^{2}+EF^{2}}$ , $BC = EF$

If we know that $AB = 10$ , $BC = 4$ , $DE = 10$ and $EF = 4$ , then we have the following outcomes:

$\sqrt{10^{2}+4^{2}} = \sqrt{10^{2}+4^{2}}$

$4 = 4$

Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

We kindly invite to check this question on triangles: brainly.com/question/21972776

3 0

3 years ago

On Monday, students at a summer camp spent 4 hours 25 minutes at the pool learning to swim. In the morning, they spent 2 hours 4

Lilit [14]

4 hours and 25 minutes simplifies to 265 minutes
2 hours and 48 minutes simplifies to 168 minutes

Subtract the numbers: 265-168 = 97 minutes left

Convert back to hours and you have 1 Hour 37 minutes at the pool in the afternoon.

5 0

3 years ago

The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approxi

VikaD [51]

Answer:

$512.90 should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Normally distributed with mean $480 and standard deviation $20.

This means that $\mu = 480, \sigma = 20$

How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05?

This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95, so X when Z = 1.645.

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

$1.645 = \frac{X - 480}{20}$

$X - 480 = 1.645*20$

$X = 512.9$

$512.90 should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05

5 0

3 years ago

A rectangle with 8 cm width and 3 cm length What is the perimeter and area of the rectangle?​

A rectangle with 8 cm width and 3 cm length What is the perimeter and area of the rectangle?