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3 years ago

Determine the number and nature of the roots. 2.2 + 12x = -4

Mathematics

1 answer:

Klio2033 [76]3 years ago

5 0

Answer:

−0.516667

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12x+2.2=−4

Step 2: Subtract 2.2 from both sides.

12x+2.2−2.2=−4−2.2

12x=−6.2

Step 3: Divide both sides by 12.

12x

−6.2

x=−0.516667

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What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

3 years ago

A model of a building is made using a scale of 1 inch = 20 feet. What is the height of the actual building, in feet, if the heig

dezoksy [38]

Answer:

210.

Step-by-step explanation:

10.5 x 20 = 210

i hope that helps!!!

4 0

2 years ago

Which algebraic expressions are polynomials? Check all that apply. PLEASE HELP

Reptile [31]

Answer: B and E

Step-by-step explanation:

A polynomial is an algebraic expression of degree one variable and above.

A polynomial does not have negative in it exponent and cannot be divided by a variable.

Polynomial operations are addition, subtraction and multiplication. It also involves non-negative integer exponents of variables.

From the options given to you, only B and E are polynomials

7 0

3 years ago

A bus has velocity 20 m/s towards east and another bus has velocity 15 m/s in west direction. If they start to move from a point

Mashutka [201]

Answer:

<em>The first bus has covered 2,400 m and the second bus has covered 1,800 m. They are separated by 4,200 m</em>

Step-by-step explanation:

<u>Constant Velocity Motion</u>

A bun has a velocity of 20 m/s towards the east. It means it travels 20 meters each second in that direction. Assuming the east direction is positive, the distance traveled by this bus can be calculated as follows:

X1=20*t

Where t is the time in seconds.

Similarly, the distance traveled by the second bus towards the west is:

X2=-15*t

Note the negative sign because the direction points at the negative reference.

After 2 minutes = 120 seconds have passed, the distance of each bus is

X1= 20*120=2,400 m

X2=-15*120 = 1,800 m

They are separated by 2,400-(-1,800) = 4,200 m

The first bus has covered 2,400 m and the second bus has covered 1,800 m. They are separated by 4,200 m

6 0

2 years ago

Plz help what is this 8h+(-7.9d)-16+5d-3.4h

Klio2033 [76]

Answer:4.6h-2.9d-16

Step-by-step explanation:

7 0

2 years ago

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