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Solve the equation for x∈Z <br><br>-x² +8x -14 ≥ 0

kenny6666 [7]

$ax^2+bx+c=0\\\Delta=b^2-4ac\\if\ \Delta < 0\ then\ no\ solutions\\if\ \Delta=0\ then\ one\ solution:x=\frac{-b}{2a}\\if\ \Delta > 0\ then\ two\ solutions:x=\frac{-b\pm\sqrt\Delta}{2a}\\================================\\\\-x^2+8x-14\geq0\ \ \ \ |multiply\ both\ sides\ by\ (-1)\ \{change\ \geq\ on\ \leq\}\\\\x^2-8x+14\leq0\\\\a=1;\ b=-8;\ c=14\\\\\Delta=(-8)^2-4\cdot1\cdot14=64-56=8 > 0\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2$

$x_1=\frac{-(-8)-2\sqrt2}{2\cdot1}=\frac{8-2\sqrt2}{2}=\frac{8}{2}-\frac{2\sqrt2}{2}=\boxed{4-\sqrt2}\\\\x_2=\frac{-(-8)+2\sqrt2}{2\cdot1}=\frac{8+2\sqrt2}{2}=\frac{8}{2}+\frac{2\sqrt2}{2}=\boxed{4+\sqrt2}\\\\============================$

$ax^2+bx+c=0\\\\if\ a > 0\ then\ the\ parabola\ o pen\ up\\if\ a < 0\ then\ the\ parabola\ o pen\ down\\========================\\\\a=1 > 0-therefore\ o pen\ up\ (look\ at\ the\ picture)\\\\===============================\\\\Answer:x\in\left$

$Solutions\ in\ \mathbb{Z}:\\\\\sqrt2\approx1.4\\\\threfore:4-\sqrt2\approx4-1.4=2.6\ and\ 4+\sqrt2\approx4+1.4=5.4\\\\look\ at\ the\ second\ picture:x=3\ or\ x=4\ or\ x=5\ (x\in\{3;\ 4;\ 5\})$

6 0

2 years ago

Read 2 more answers

30*x=204. What is x?

IgorC [24]

Answer: x = 6.8

or x = 102/15

Step-by-step explanation:

30x=204

204/30

simplify!

3 0

2 years ago

Read 2 more answers

Find an equation of the line with the slope m=6 that passes through the point (4,4). Write the equation in the form Ax + By = C

Ainat [17]

Answer:

Y - 6x = - 20

Step-by-step explanation:

Y = 6x + c

Substituting the value of x and y

4 = 24 + c

Subtracting 24 from both sides

C = - 20

Y = 6x - 20

Subtracting 6x from both sides

Y - 6x =- 20

7 0

3 years ago

What is the coefficient in the mathematical expression?

barxatty [35]

Using it's concept, it is found that the coefficient of the mathematical expression 7m² + 2(19) is of 7.

<h3>What is the leading coefficient of a polynomial?</h3>

The leading coefficient of a polynomial is the <u>term that multiplies the highest exponent</u>.

In this problem, the expression is given by:

7m² + 19.

The highest exponent is of 2, in m², hence the leading coefficient is of 7.

More can be learned about the coefficient of a mathematical expression at brainly.com/question/24380382

#SPJ1

4 0

1 year ago

A class of 33 students elected a class treasurer. there were 111votes for candidate a and 15 votes for candidate

Advocard [28]

Since 111 is greater than 33, I will assume that you meant 11 votes for a candidate. Also, assuming that each student can vote only once, the answer would be

11/33 x 100=33.333333...

About 33.333 of the voters voted for candidate a.

3 0

2 years ago