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2 years ago

Solve the inequality and express your answer in interval notation. X^2-6x+7<0

Mathematics

1 answer:

kakasveta [241]2 years ago

8 0

Answer:

Step-by-step explanation:

2×6=8

8+7 =15

2+7 =9

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P(x)= 3x^3-5x^2-14x-4

nexus9112 [7]

$\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\
$

$\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)$

$\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm \sqrt{4+16}}{2}=\frac{2\pm \sqrt{20}}{2}=\frac{2\pm 2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}$

7 0

2 years ago

An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles. Prove th

seraphim [82]

Answer:

The answer is below

Step-by-step explanation:

We must first define the concepts a little:

We have that when the sides are congruent that is to say that they have the same direction and the same size and also the two opposite sides are parallel, the angles will be the same.

Now, in an isosceles triangle, two angles are congruent, because their two sides are congruent.

3 0

2 years ago

Are the ratios 14:18 and 7:9 equivalent

Pepsi [2]

Answer:

Yes

Step-by-step explanation:

14/18 equals 7/9

Dividing by two on the first ratio makes:

7/9 equals 7/9

4 0

2 years ago

Read 2 more answers

A bumper sticker has an area of five 24 ft.² which model correct present the area of the bumper sticker

Elodia [21]

A picture types of the models would be helpful.. but they could be found in a rectangular shape or square such as width=2 and length =12 vise versa or w=4 and length = 6 , etc etc

6 0

2 years ago

If a drug has a concentration of 400 mg per 10 ml, how many mL are needed to give 1.5 grams of the drug?

liq [111]

40,

since

400 x 4 + 1.6 grams. which is the closest

4 x 10 = 40

4 0

2 years ago