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2 years ago

Find the length of the side of an equilateral triangle that has an altitude length of 24 feet.

1 answer:

7 0

$\bf \textit{height of an equilateral triangle}\\\\
h=\cfrac{\sqrt{3}\ s}{2}\qquad 
\begin{cases}
h=height\\
s=\textit{one side's length}
\end{cases}
\\\\\\
\cfrac{2h}{\sqrt{3}}=s$

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A telephone company charges its customers per minute to make long-distance calls. The cost, c, can be represented by c = .12m wh

Ksivusya [100]

Answer:

m ≥ 0

Step-by-step explanation:

Since the cost is represented by c = 0.12m, the domain should be a positive number, this is because number of minutes can't be written in negative. Therefore, the most reasonable number for the domain would be the set of positive whole numbers which means, m≥0.

7 0

2 years ago

What is the sum of the first 70 consecutive odd numbers? Explain.

expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1$

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

$\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)$

The second sum is simply the sum of N ones:

$\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N$

So, the final result is

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2$

which ends the proof.

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2 years ago

Will mark brainliest and 10 points

KengaRu [80]

Answer:

Student 3

Step-by-step explanation:

Part of the 3-4-5 Pythagorean triples.

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3 years ago

The cost of sending an overnight package from Kansas City to Miami is $23.50 for a package weighing up to but not including 1

Dimas [21]

Answer:

For every pound that the package weight increases, the price of sending it increases by $3.80.

Step-by-step explanation:

The coefficient 3.80 multiplies the variable x (package weight), so if x is 1 pound the cost increase $3.80, if x is 2 pound the cost increase 2*3.80 = $7.6, and so on. Generally speaking, for every pound that the package weight increases the cost increases by $3.80.

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3 years ago

Read 2 more answers

In the following questions, look at different ways to represent the relation given by the equation y = x2 - 1. The table below s

Nady [450]

Answer:

a= 3

b= 0

Step-by-step explanation:

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2 years ago