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3 years ago

Right triangle abc has one leg of length 6 cm, one leg of length 8 cm and a right angle at

Mathematics

1 answer:

Sauron [17]3 years ago

6 0

Answer:
side length of the square = 10 cm

Explanation:
The attached image shows a diagram representing the scenario described in the problem.
Taking a look at this diagram, we can note that the side length of the square is equal to the hypotenuse of the right-angled triangle
Therefore, we can get the side of the square by calculating the length of the hypotenuse using Pythagorean theorem as follows:
(hypotenuse)² = (length of first leg)² + (length of second leg)²
(hypotenuse)² = (8)² + (6)²
(hypotenuse)² = 64 + 36
(hypotenuse)² = 100
hypotenuse = √100
hypotenuse = 10 cm

This means that the length of the side of the square is also 10 cm

Hope this helps :)

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the first term of an arithmetic sequence is 2 and the sum of the first 15 terms is 292.5. Find the common difference

adelina 88 [10]

Given:

First term of an arithmetic sequence is 2.

Sum of first 15 terms = 292.5

To find:

The common difference.

Solution:

We have,

First term: $a=2$

Sum of first 15 terms: $S_{15}=292.5$

The formula of sum of first n terms of an AP is

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

Where, a is first term and d is common difference.

Putting $S_{15}=292.5$ , n=15 and a=2 in the above formula, we get

$292.5=\dfrac{15}{2}[2(2)+(15-1)d]$

$292.5=\dfrac{15}{2}[4+14d]$

$292.5=15[2+7d]$

Divide both sides by 15.

$\dfrac{292.5}{15}=2+7d$

$19.5=2+7d$

$19.5-2=7d$

$17.5=7d$

Dividing both sides by 7, we get

$\dfrac{17.5}{7}=d$

$2.5=d$

Therefore, the common difference is 2.5.

8 0

3 years ago

WHICH IS LONGER 2 MILES OR ````3 KILOM`ETERS

kompoz [17]

I think 2 miles hoped this helped

8 0

3 years ago

Read 2 more answers

A company manager for a tire manufacturer is in charge of making sure there is the least amount of defective tires. If the tire

Anestetic [448]

Answer:

0.347% of the total tires will be rejected as underweight.

Step-by-step explanation:

For a standard normal distribution, (with mean 0 and standard deviation 1), the lower and upper quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.

And the manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires.

1.5 of the Interquartile range = 1.5 × 1.34896 = 2.02344

1.5 of the interquartile range below the lower quartile = (lower quartile) - (1.5 of Interquartile range) = -0.67448 - 2.02344 = -2.69792

The proportion of tires that will fall 1.5 of the interquartile range below the lower quartile = P(x < -2.69792) ≈ P(x < -2.70)

Using data from the normal distribution table

P(x < -2.70) = 0.00347 = 0.347% of the total tires will be rejected as underweight

Hope this Helps!!!

6 0

3 years ago

AveGali [126]

Answer:

Total time taken by walking, running and cycling = 22 minutes.

Step-by-step explanation: