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3 years ago

Identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0

1 answer:

4 0

Solve for x over the real numbers:
4 x^4 + 31 x^3 - 4 x^2 - 89 x + 22 = 0

The left hand side factors into a product with three terms:
(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0

Split into three equations:
x + 2 = 0 or 4 x - 1 = 0 or x^2 + 6 x - 11 = 0

Subtract 2 from both sides:
x = -2 or 4 x - 1 = 0 or x^2 + 6 x - 11 = 0

Add 1 to both sides:
x = -2 or 4 x = 1 or x^2 + 6 x - 11 = 0

Divide both sides by 4:
x = -2 or x = 1/4 or x^2 + 6 x - 11 = 0

Add 11 to both sides:
x = -2 or x = 1/4 or x^2 + 6 x = 11

Add 9 to both sides:
x = -2 or x = 1/4 or x^2 + 6 x + 9 = 20

Write the left hand side as a square:
x = -2 or x = 1/4 or (x + 3)^2 = 20

Take the square root of both sides:
x = -2 or x = 1/4 or x + 3 = 2 sqrt(5) or x + 3 = -2 sqrt(5)

Subtract 3 from both sides:
x = -2 or x = 1/4 or x = 2 sqrt(5) - 3 or x + 3 = -2 sqrt(5)

Subtract 3 from both sides:
Answer: x = -2 or x = 1/4 or x = 2 sqrt(5) - 3 or x = -3 - 2 sqrt(5)

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Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x

meriva

✨ SAMPLE ANSWER ✨

The entire expression should be subtracted from 30. To subtract the quantity, distribute the negative sign, which changes the signs on the terms. So, the –2 changes to positive and gets added to 30 instead of subtracted from it.

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3 years ago

What is the sum of 3/10s and 5/100s (Fractions)

vampirchik [111]

Answer:

80/100

Step-by-step explanation:

this is simplified ones

8/10

4/5

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3 years ago

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ? sin Θ = square root 2 ov

densk [106]

Answer:

$\huge\boxed{\sin\theta=-\dfrac{\sqrt2}{2};\ \tan\theta=-1}$

Step-by-step explanation:

We have:

$\\cos\theta=\dfrac{\sqrt2}{2},\ \dfrac{3\pi}{2}$

For sine use:

$\sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x$

Substitute:

$\sin^2\theta=1-\left(\dfrac{\sqrt2}{2}\right)^2\\\\\sin^2\theta=1-\dfrac{(\sqrt2)^2}{2^2}\\\\\sin^2\theta=1-\dfrac{2}{4}\\\\\sin^2\theta=\dfrac{4}{4}-\dfrac{2}{4}\\\\\sin^2\theta=\dfrac{4-2}{4}\\\\\sin^2\theta=\dfrac{2}{4}\to\sin\theta=\pm\sqrt{\dfrac{2}{4}}\\\\\sin\theta=\pm\dfrac{\sqrt2}{\sqrt4}\\\\\sin\theta=\pm\dfrac{\sqrt2}{2}$

θ in IV quadrant, therefore sine is negative.

$\sin\theta=-\dfrac{\sqrt2}{2}$

For tangent use:

$\tan x=\dfrac{\sin x}{\cos x}$

Substitute:

$\tan\theta=\dfrac{-\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}=-\dfrac{\sqrt2}{2}\cdot\dfrac{2}{\sqrt2}=-1$

8 0

3 years ago

find the volume of A trapezoid prism of height 4Km.The parallel sides of the base have length 8km and 5km. The other sides of th

igor_vitrenko [27]

Answer:

Volume of prism = 39 km cubed

Step-by-step explanation:

IMPORTANT FORMULA: Volume of any prism = Area of base * Height

In this case, the area of the base means the area of the trapezoid.

Area of trapezoid = base1+base2/2 * height

Area of trapezoid = 8+5/2 * 1.5

Area of trapezoid = 13/2 * 1.5 = 9.75

We already know that the height of the trapezoidal prism is 4 kilometers.

So, we have all of the values that are needed to correctly fill in the formula.

Volume of the prism = 9.75 * 4 = 39

7 0

3 years ago

On a coordinate plane, square p q r s is shown. point p is at (4, 2), point q is at (8, 5), point r is at (5, 9), and point s is

Masteriza [31]

A statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is: option D.

<h3>How to calculate the slope of a line?</h3>

Mathematically, the slope of a line is given by the following formula;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

For line RP, we have:

$Slope = \frac{9\;-\;2}{5\;-\;4}\\\\Slope = \frac{7}{1}$

Slope RP = 7.

For line SQ, we have:

$Slope = \frac{6\;-\;5}{1\;-\;8}\\\\Slope = \frac{1}{-7}$

Slope SQ = negative one-sevenths.

For the midpoint, we have:

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate = (8 + 1)/2 = 9/2 = 4.5.

Midpoint on y-coordinate = (9 + 2)/2 = 11/2 = 5.5.

In conclusion, a statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is that the midpoint of both diagonals is (4.5, 5.5), the slope of RP is 7, and the slope of SQ is negative one-sevenths.

Read more on squares here: brainly.com/question/2882032

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3 0

2 years ago

Read 2 more answers