A carnival charges $1.50 per ride after an entrance fee. You paid a total of $30

Write an expression that can be used to check the quotient of 646 ÷ 3

Ipatiy [6.2K]

646/3=x
To check it: x*3 should =646

5 0

3 years ago

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

as required

4 0

3 years ago

When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, should the signs in the binom

gtnhenbr [62]

When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, the signs in the binomials should be both positive

<h3>What are quadratic equations?</h3>

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

<h3>How to determine the true statement?</h3>

The form of the polynomial is given as:

ax2 + bx + c

Where a, b, and c are positive real numbers.

Since a, b, and c are positive real numbers. then the form of the expansion would be:

ax2 + bx + c = (dx + e)(fx + g)

<h3>Example to verify the claim</h3>

Take for instance, we have the following quadratic equation

x^2 + 6x + 8

Expand the equation

x^2 + 6x + 8 = x^2 + 4x + 2x + 8

Factorize the equation

x^2 + 6x + 8 = (x + 2)(x + 4)

Hence, the signs in the binomials should be both positive

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

5 0

1 year ago

Solve the equation <br><br> 3x-5< 8x-1/2<br><br> x+7≤ 4x+1

vladimir1956 [14]

This is all I got. Hope this helps:

6 0

2 years ago

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So, I need to find the Mean Median Mode and Range with this frequency table, and I have no idea how to do that. Can somebody ple

olya-2409 [2.1K]

Mean: average of the numbers. Add them up, divide by how many numbers/entries there are.
-2 + -1 + 0 + 0 + 0 + 0 + 2 + 4 = 3
3 divided by 8 = 0.375
Your mean is 0.375

Median: write the data in numerical order, find the middle number.

-2, -1, 0, 0, 0, 0, 2, 4
In this data set, there are an even number of entries, so we average the middle two numbers. Thankfully, here, the middle two are the same, so your median is 0.

Mode: the number that appears the most often in the data set

Your mode is also 0, because there are more zeroes than any other number in the data set.

Range: the distance on a number line between the highest and lowest number.

The distance between -2 and 4 is 6.4 - (-2) = 6

Please LMK if you have questions

8 0

3 years ago