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3 years ago

In a 30-60-90 triangle, the length of the long leg is 8. Find the length of the hypotenuse.

Mathematics

1 answer:

fiasKO [112]3 years ago

5 0

Answer:

Step-by-step explanation:

In a 30-60-90 triangle, the ratio of the lengths of the angles' opposite sides are 1-√3-2.

If the long leg is 8, then the short one is 8/√3, or 8√3/3.

Therefore, the hypotenuse, which is double the short leg, is 16√3/3.

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Robin has a collection of dimes, nickels and quarters. He has 4 times as many dimes as nickels. He has 20 more quarters than nic

Margarita [4]

Answer: Robin has 50 nickels, 60 dimes, and 120 quarters.

Step-by-step explanation:

7 0

3 years ago

Write an explicit formula for an the nth term of the sequence 75,15,3,...

Usimov [2.4K]

Step-by-step explanation:

it is geometric

so we will use this equation:

a(n)=a1*(r)^(n-1)

and we have a(1)=75 , r=15/75=3/15=1/3

explicit formula: a(n)=75*(1/3)^(n-1)

hope this helps

3 0

3 years ago

Read 2 more answers

15 / √31 - 4

NeX [460]

Answer:

$\frac{15}{ \sqrt{31} - 4}} = \sqrt{31} + 4$

Step-by-step explanation:

$\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4$

6 0

2 years ago

The function y=x²-4x+8 approximates the height, y, of a bird, and its horizontal distance, x, as it flies from one

trapecia [35]

When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet , Minimum at (2,4)

Therefore Option C and D is the correct answer.

<h3>What is a Quadratic Function?</h3>

The equation for a quadratic function is given by

y = a(x-h)² +k²

where (h,k) is the extreme value(vertex).

Here the equation given is

y = x²-4x +8

y = x²-4x+4+4

y = (x-2)² +4

Here the value of a = 1 , h = 2 and k = 4

The extreme value is at (2,4)

Therefore When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet , Minimum at (2,4)

Therefore Option C and D is the correct answer.

To know more about Quadratic Function

brainly.com/question/5975436

#SPJ1

7 0

2 years ago

12 less than the quotient of a number and seven is -2 find the number

kiruha [24]

A quotient is the result of a division.
Let the unknown number be x.

We translate the problem into an equation, piece by piece.

"quotient of a number and seven" ----> x/7

"12 less than the quotient of a number and seven" ----> x/7 - 12

The word "is" means "="
x/7 - 12 =

All the above is -2, so it equals -2.

x/7 - 12 = -2

$\dfrac{x}{7} - 12 = -2$

First, add 12 to both sides and simplify.

 $\dfrac{x}{7} - 12 + 12 = -2 + 12$


 $\dfrac{x}{7} = 10$ 

Next, multiply both sides by 7.

$\dfrac{x}{7} \times 7 = 10 \times 7$

$x = 70$

Answer: The number is 70.

5 0

3 years ago

Read 2 more answers