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3 years ago

Solve for x x^2+3x<28

Mathematics

1 answer:

Klio2033 [76]3 years ago

6 0

X² + 3x < 28
x² + 3x - 28 < 0
(x+7)(x-4) < 0

the zeros will be at x = -7 and x =4

∴ the solution of inequality
x ∈ (-7,4)

See the attached figure

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Can please someone help me? The question is in the picture. Thank you

maxonik [38]

Answer:

C. $9\pi$

Step-by-step explanation:

We proceed to solve for $x$ by the Pythagorean Theorem:

$(x+1)^{2} = (x-1)^{2} + (2\cdot x - 4)^{2}$ (1)

$x^{2} + 2\cdot x + 1 = (x^{2}-2\cdot x + 1) + (4\cdot x^{2}-16\cdot x + 16)$

$x^{2} + 2\cdot x + 1 = 5\cdot x^{2}-18\cdot x + 17$

$4\cdot x^{2} -20\cdot x + 16 = 0$

$(2\cdot x)^{2} -10\cdot (2\cdot x) + 16 = 0$

$(2\cdot x -8)\cdot (2\cdot x -2) = 0$

There are two different solutions:

$x_{1} = 4$ , $x_{2} = 1$

A solution of $x$ is considered realistic when the length of every side of the triangle is a not negative number.

$x_{1} = 4$

$UV = 2\cdot (4) - 4$

$UV = 4$

$WU = 4 - 1$

$WU = 3$

$WV = 4 + 1$

$WV = 5$

$x_{2} = 1$

$UV = 2\cdot (1) - 4$

$UV = -2$

$WU = 1 - 1$

$WU = 0$

$WV = 1 + 1$

$WV = 2$

The only realistic set of solutions is for $x = 4$ , and the radius of the circle is represented by the line segment $WU$ : $r = 3$

And the area of the circle ( $A$ ) is calculated from the following formula:

$A = \pi\cdot r^{2}$

$A = \pi\cdot (9)$

$A = 9\pi$

The correct answer is C.

6 0

3 years ago

Rationalize the denominator: Please give step by step solution

MrMuchimi

Answer:

1 + i

Step-by-step explanation:

To rationalize multiply numerator and denominator by (2 + i )

$\frac{3+i}{2-i}= \frac{3+i}{2-i} \times \frac{2+i}{2+i} = \frac{(3+i)(2+i)}{(2-i)(2+i)} = \frac{6+3i+2i-1}{4-(-1)} = \frac{5+5i}{5} = 1 + i$

5 0

3 years ago

Pls answerfor 10 points

Gnesinka [82]

Answer:your welcome

Step-by-step explanation:

Mhhh

4 0

3 years ago

Which polynomial is in standard form.

garik1379 [7]

Answer:

4- $7x^{7} y^{2} + 5x^{11} y^{5} - 3xy^{2} + 2$

Step-by-step explanation:

In a standard polynomial degree drops from left to right

so , option 4 is correct.

$7x^{7} y^{2} + 5x^{11} y^{5} - 3xy^{2} + 2$

8 0

3 years ago

Find the equation of the line.

mario62 [17]

Answer:

y = 2/3x - 7

Explanation:

First we must turn 3x + 2y = 6 to slope intercept form. In order to do this first subtract 3x on both sides of the equal sign, so we can get 2y by its self. Now we're left with 2y = -3x + 6 .

Next divide 2 from both sides to get y by its self. Now you got y = -3/2x + 3 (since 6 can be divided by 2 it's a 3 now) Look above to see y= -3/2x +3 graphed. ⤴⤴⤴

To find out the other equation we first need to know what its y-intercept is, and luckily for us we've already been given -3.

Look above to see (6,-3) graphed. ⤴⤴⤴

Look above to see both y = -3/2x + 3 and

y = 2/3x -7 graphed. ⤴⤴⤴

This is a bit lengthy, but I hope you get it :)

5 0

3 years ago