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3 years ago

How many integers n leave remainder 4 when divided by 7, if n satisfies the given inequality?

Mathematics

1 answer:

bekas [8.4K]3 years ago

4 0

Consider inequality $|-n|$ This inequality is equivalent to inequality $|n|$

This means that $-46$

The greatest integer number n, such that $-46$ when dividing by 7 gives the remainder 4 is 39. Then subtract 7, you get 32, then 25 and so on.

When n=-39, -32, -25, -18, -11, -4, 4, 11, 18, 25, 32, 39 then dividing by 7 the remainder is 4.

Answer: 12 integers.

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Please help!! What is the solution to the quadratic inequality? 6x2≥10+11x

fredd [130]

Answer:

The solution of the inequation $6\cdot x^{2} \geq 10 + 11\cdot x$ is $\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)$ .

Step-by-step explanation:

First of all, let simplify and factorize the resulting polynomial:

$6\cdot x^{2} \geq 10 + 11\cdot x$

$6\cdot x^{2}-11\cdot x -10 \geq 0$

$6\cdot \left(x^{2}-\frac{11}{6}\cdot x -\frac{10}{6} \right)\geq 0$

Roots are found by Quadratic Formula:

$r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}$

$r_{1} = \frac{5}{2}$ and $r_{2} = -\frac{2}{3}$

Then, the factorized form of the inequation is:

$6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0$

By Real Algebra, there are two condition that fulfill the inequation:

a) $x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0$

$x \geq \frac{5}{2}\,\wedge\,x \geq-\frac{2}{3}$

$x \geq \frac{5}{2}$

b) $x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0$

$x \leq \frac{5}{2}\,\wedge\,x\leq-\frac{2}{3}$

$x\leq -\frac{2}{3}$

The solution of the inequation $6\cdot x^{2} \geq 10 + 11\cdot x$ is $\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)$ .

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1- AT OAKNOLL SCHOOL, 90 OUT OF 270 STUDENTS OWN COMPUTERS. WHAT PERCENT OF STUDENTS OF OAKNOLL SCHOOL DO NOT OWN COMPUTERS? ROU

V125BC [204]

1. 270÷90=3=30% have and 70% don't have a computer.

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Which number is irrational √81 √169 √156 √144

kupik [55]

Answer:

(under root 81 is equals to 9

under root 144 is equals to 12

under root 169 is equals to 13) these are rational numbers

therefore irrational number is under root 156

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Write a unit rate for the situation: 2520 kilobytes in 18 seconds

elixir [45]

140 kilobytes per second

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Please help mee! <33<br><br> y+4=-4(x+2)<br> in standard form! <3

Pachacha [2.7K]

Answer:

y = -4x - 12

Step-by-step explanation:

y + 4 = -4(x + 2)

y = -4x -8 - 4

y = -4x - 12

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