The area of a right triangle is 270 m². The height of the right triangle is 15 m. What is the length of the hypotenuse of the right triangle?

Answers

Answer 1

Answer: The area of a triangle is calculated by the expression given as:

Area = bh/2

where b is the base and h is the height.

We calculate as follows:

270 = b (15) / 2
b = 36

hypotenuse = sqrt ( 15^2 + 36^2 ) = 39

Answer 2

Answer:

Answer:

hypotenuse = 39m

Step-by-step explanation:

Area of a triangle= 1/2 * base * height

where base = ?

height = 15

Plugin values into the formula:

270 = 1/2 base (15)

base = 270 (2)

base = 36

hypotenuse = √(base² + height²)

= √( 36² + 15² )

= 39

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A company wants to installan underground storage tank that is in the shape of acylinder with both ends being in the shape of a hemisphere. The tank will have anoutside diameter of 20 feet and a total length of 50 feet (that is from the tip of one end ofthe hemisphere shape to the tip of the other hemisphere shape)lf the walls of the tankare 3 inches thick, what is the volume of the tank in cubic feet and how many gallons ofliquid can be contained in the tank (1 cubic foot 7.48 gallons)?

Answers

wallsare 3 inches thick
diameter is 20 feet, find real diametter
legnth is 50 feet, find real legnth

minus 6 inches from each measurement since that is not included

20ft-6in=19.5ft
50ft-6n=49.5ft

we have a cylinder and a 2 hemispheres
2 hemispheres=1 sphere

Vcylinder=hpir^2
Vsphere=(4/3)pir^3

r=d/2
r=19.5/2=9.75
h=49.5

Vcylinder=49.5*pi*9.75^2=14783.058738886 ft^3
Vspere=(4/3)pi9.75^3=388419466778 ft^3
add them
Vcylinder+Vspher=14783.058738886+388419466778 ft^3=18665,478205664ft^3

V=18665,478205664 ft^3
times 7.48 to find gallons
Vingallons=139617.77697837 gallons

How do you find the largest 6-digit multiple of 11 such that the sum of all its digits equals 40. What is the answer?

Answers

There is a certain way to find the answer for your question. First, you must be familiar with the divisibility rule for 11: the difference between the sums of even digits and odd digits should either be 0 or 11 only. For example, 1430, here the odd digits are 4 and 0 (which are the 3rd and 1st digits); the even digits on the other hand are 1 and 3, placed as the 4th and 2nd digits respectively.

Adding the sums of odd and even digits will give 4 (4+0) and 4 (3+1). Now, the difference of these sums is obviously equal to 0. Therefore, 1430 is divisible by 11. Same case will hold for numbers whose sums of odd and even digits is 11.

Moving on, now let us try to find the biggest 6-digit number divisible by 11. Intuitively, the last digit should be "9" - the hundred thousands digit - for it is the biggest number among numbers from 0-9. Furthermore, since there is no restriction as to whether the same number could or could not repeat, we can still use "9" all throughout the remaining 5 digits (ten thousands down to ones digit), giving the greatest possible 6-digit number, 999,999.

To check if the number we have obtained, 999,999, is divisible by 11, we need to use the divisibility rule for 11. Sum of even digits is 18 (9+9+9); sum of odd digits is 18 (9+9+9) as well. The difference of the sums is 0. Therefore, 999,999 is divisible by 11, hence the greatest 6-digit number multiple of 11.

As for the 6-digit number whose digits' sum is 40 and multiple of 11, we can assume its first 4 digits to be as 999,9** - four 9s is already equal to 36 - we only need to find two numbers whose sum is 4 to make the sum's total be 40. These remaining numbers should also be divisible by 11 since 9999 is already divisible by 11. The remaining numbers should only be 2 and 2 since the sum of its digit is 4, and that if we put them together, 22, a multiple of 11. This is the only combination of numbers that will give a sum of 4 while maintaining its structure a multiple of 11.

At last, the greatest 6-digit number whose digits' sum equal to 40 and is a multiple of 11 is 999,922. True, for 999,922 / 11 is equal to 90,902.

What is the solution to the equation fraction 4 over 5 n minus fraction 3 over 5 equals fraction 1 over 5 n?n = 1

n = −3

n = fraction 3 over 4

n = fraction 1 over 4

Answers

If you would like to know the solution to the equation, you can calculate this using the following steps:

4/5n - 3/5 = 1/5n /*5n
4 - 3/5 * 5n = 1
4 - 3n = 1
4 - 1 = 3n
3 = 3n
n = 1

The correct result would be n = 1.

Answer:

n = 1

Step-by-step explanation:

How has the Pythagorean Theorem helped us through life?