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3 years ago

There are 3 consecutive integers that add up to 9 which integers are they?

Mathematics

1 answer:

matrenka [14]3 years ago

7 0

Answer:

The integers are 2,3,4

Step-by-step explanation:

Let one integer be = $x$

Since, the integers are consecutive, so they will increase by one.

So, 2nd integer will be = $x+1$

3rd integer will be = $x+1+1=x+2$

It is given that the 3 integers add up to 9.

So, we have the sum equation as:

$x+x+1+x+2=9$

Solving for $x$

Combining like terms.

$3x+3=9$

Subtracting both sides by 3.

$3x+3-3=9-3$

$3x=6$

Dividing both sides by 3.

$\frac{3x}{3}=\frac{6}{3}$

$x=2$

∴ 1st integer = $2$

2nd integer = $2+1 = 3$

3rd integer = $2+2 = 4$

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LeRon draws an orange counter from one bag and a red counter from another bag. Which statement is true?

Gelneren [198K]

Hello there!

The question asks if the events are independent or dependent.
Well, let's establish what an independent and dependent event is.

An independent event is an occurrence in which two or more events do not have effect on each other, regardless what happens during each scenario.

An independent event would be (for example) "I flipped a coin and rolled a dice." Both of these are independent events, as they do not have any effect on eachother.

A dependent event is an occurrence in which two or more events have effects on eachother. For example "I pull a red card out of a deck of cards. I then pull a black card out of the same deck."

The question you have is:
LeRon draws an orange counter from one bag and a red counter from another bag. Are the events dependent or independent?

Since that LeRon draws two different counters from two separate bags, the events do not effect each other, thus making the events independent.

I hope this helps!

5 0

3 years ago

n is a positive integer with exactly two different divisors greater than 1, how many positive factors does n^2 have? A. 4 B. 5 C

Evgesh-ka [11]

Answer:

C. 5

Step-by-step explanation:

Remember that for any integer $n$ , the integers $1 \text{and} n$ are both divisors (or factors) of $n$ . First, we will prove that n is a square, and then we will compute the factors of the n².

In this case, the integer n has exactly two different divisors greater than 1. It's impossible that $n=1$ , since 1 doesn't have positive factors greater than 1. Then $n>1$ , therefore $n$ itself is one of the required divisors. Denote by $a$ the other divisor greater than 1, and note that to satisfy the condition on the divisors, $a$ .

Because a divides n, there exists some integer $k$ such that $n=ak$ . We must have that $k>1$ , if not, then $k\leq 1$ , which implies that $ak=n\leq a$ , which contradicts the part above.

Now, $k>1$ and, by definition of divisibility, k divides n. Then k must be equal either to n or a, since we can't have three different divisors of this kind. If $k=n$ then $n=an$ and by cancellation, $1=a$ which is a contradiction. Therefore $k=a$ and $n=a^2$ .

We have that $n=(a^2)^2=a^4$ . We can write n as $n=a^3a=a^2a^2=a^4 \cdot 1$ . From the first equation, a divides n and a³ divides n. From the second equation, a² divides, and from the last one, 1 divides n and a⁴=n divides n. Thus n has exactly 5 positive factors.

4 0

4 years ago

write the equation of the line that passes through the vertex of the parabola y=-2x^2+12x-11 and the point (-2,47)

pshichka [43]

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$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-8}(x-\stackrel{x_1}{3}) \\\\\\ y-7=-8x+24\implies y=-8x+31$