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3 years ago

12. The sum of three consecutive integers is 12 more than twice the largest integer. Which of the following

Mathematics

1 answer:

baherus [9]3 years ago

5 0

Answer:

OPTION 4

Step-by-step explanation:

Let the three consecutive numbers be n, (n + 1) and (n + 2).

Note that the largest number of the three is (n + 2) and the smallest is n.

So, according to the given data, the sum of all the three integers is equal to 1 more than twice more than the largest number.

Writing it mathematically, we have:

n + (n + 1) + (n + 2) = 12 + 2(n + 2)

This is OPTION (4) and is the answer,

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Determine if graph is a function

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No it is not a function.

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3 years ago

If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

======================================================

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

----------------

Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

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4 years ago

Write 0.4 as a fraction

scoundrel [369]

0.4 / 2 = 0.2

1/0.2 = 5

2/5 is the answer

4 0

3 years ago

Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need

Archy [21]

Method 1:

$\begin{array}{ccc}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}\\\\1\dfrac{1}{2}=\dfrac{3}{2}\ \text{cup of corn}&-&x\ \text{cup of water}\end{array}\qquad\text{cross multiply}\\\\\\\dfrac{1}{4}\cdot x=\dfrac{3}{2}\cdot\dfrac{1}{2}\\\\\dfrac{1}{4}x=\dfrac{3}{4}\qquad\text{multiply both sides by 4}\\\\\boxed{x=3}$

<h3>Answer: Henry will need 3 cups of water.</h3>

Method 2:

$\begin{matrix}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}&|\text{multiply both sides by 2}\\\\\dfrac{1}{2}\ \text{cup of corn}&-&1\ \text{cup of water}&|\text{multiply both sides by 2}\\\\1\ \text{cup of corn}&-&2\ \text{cup of water}&|\end{matrix}$

$\begin{matrix}\left(\dfrac{1}{2}+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1\dfrac{1}{2}\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}$

<h3>Answer: Henry will need 3 cups of water.</h3>

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