Three more than the quotient of a number and 6 is 8.

Mathematics

1 answer:

meriva3 years ago

6 0

Answer:

x/6 + 3 = 8

x/6 = 5

x = 30

Step-by-step explanation:

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Kimmi and her mom count 254 guests coming to the wedding. There are 9 tables at the wedding. How many guests sit at each table?

valkas [14]

Answer:

28 guests with 2 guests remaining

Step-by-step explanation:

254/9 = 28.2222222

so 28 remainder 2

hope this helps :) mark brainliest?

6 0

2 years ago

Evaluate the integral ∫2−1|x−1|dx

defon

I think you might be referring to the definite integral,

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx$

Recall the definition of absolute value:

$|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x$

Then $|x-1|=x-1$ if $x\ge1$ , and $|x-1|=1-x$ is $x$ . So spliting up the integral at <em>x</em> = 1, we have

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx$

The rest is simple:

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}$