Solve for x . x^2+6x+6=0

Answers

Answer 1

Answer:

[tex]\boxed {x = \sqrt{3} - 3}[/tex]

[tex]\boxed {x = -\sqrt{3} - 3}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]x^2 + 6x + 6 = 0[/tex]

-When you use the quadratic formula ( [tex]\frac{-b\pm \sqrt{b^{2} - 4ac}}{2a}[/tex] ), it would give you two solutions. So, use the quadratic formula:

[tex]x = \frac{-6\pm \sqrt{6^{2} - 4 \times 6}}{2}[/tex]

-Simplify [tex]6[/tex] by the exponent [tex]2[/tex]:

[tex]x = \frac{-6\pm \sqrt{6^{2} - 4 \times 6}}{2}[/tex]

[tex]x = \frac{-6\pm \sqrt{36 - 4 \times 6}}{2}[/tex]

-Multiply both [tex]-4[/tex] and [tex]6[/tex]:

[tex]x = \frac{-6\pm \sqrt{36 - 4 \times 6}}{2}[/tex]

[tex]x = \frac{-6\pm \sqrt{36 - 24}}{2}[/tex]

-Add [tex]34[/tex] and [tex]-24[/tex]:

[tex]x = \frac{-6\pm \sqrt{36 - 24}}{2}[/tex]

[tex]x = \frac{-6\pm \sqrt{12}}{2}[/tex]

-Take the square root of [tex]12[/tex]:

[tex]x = \frac{-6\pm \sqrt{12}}{2}[/tex]

[tex]x = \frac{-6\pm 2\sqrt{3}}{2}[/tex]

-Now solve the equation when [tex]\pm[/tex] is plus, So, add [tex]-6[/tex] to [tex]2\sqrt{3}[/tex]:

[tex]x = \frac{-6\pm 2\sqrt{3}}{2}[/tex]

[tex]x = \frac{2\sqrt{3} - 6}{2}[/tex]

-Divide  [tex]-6 + 2\sqrt{3}[/tex] both sides by [tex]2[/tex]:

[tex]x = \frac{2\sqrt{3} - 6}{2}[/tex]

[tex]\boxed {x = \sqrt{3} - 3}[/tex] (Answer 1)

-Now solve the equation when [tex]\pm[/tex] is minus. So, Subtract [tex]2\sqrt{3}[/tex] from [tex]-6[/tex]:

[tex]x = \frac{-2\sqrt{3} - 6}{2}[/tex]

-Divide [tex]-2\sqrt{3} - 6[/tex] by [tex]2[/tex]:

[tex]x = \frac{-2\sqrt{3} - 6}{2}[/tex]

[tex]\boxed {x = -\sqrt{3} - 3}[/tex] (Answer 2)


Related Questions

The sum of three consecutive even numbers is 66. Find the numbers​

Answers

Answer:

20, 22, and 24

Step-by-step explanation:

hope this helps. can I also have brainliest please :)

Answer:

BRAINLIEST PLZZ

Step-by-step explanation:

The other 2 numbers are (x + 2) and (x + 4)

Their sum is 66:

x + (x + 2) + (x + 4) = 66

x + x + 2 + x + 4 = 66

3x + 6 = 66

3x = 60

x = 20

2nd number = x + 2 = 20 + 2 = 22

3rd number = x + 4 = 20 + 4 = 24

Answer: The numbers are 20, 22 and 24

Help! look at the image of the table of values below. Over which interval of x is the average rate of change the largest?

Answers

Answer:

A

Step-by-step explanation:

There is no way to tell a pattern.

y=2x-3 in standard form. I’ll give brainliest if you answer it right. But hurry. It’s for my missing assignment.

Answers

Answer:

It would be 2x-y=3.

Determine the slope of the line that passes through the points M(-3, 5) and N(1, 8). Represent the slope in decimal form.

Answers

Answer:

The slope of the line that passes through the points M(-3, 5) and N(1, 8) in decimal form is 0.75

Step-by-step explanation:

The given points are M(-3, 5) and N(1, 8)

The formula for finding the slope, m, given the coordinates of two points on the line is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where, (x₁, y₁) = (-3, 5), and (x₂, y₂) = (1, 8), we have;

[tex]Slope, \, m =\dfrac{8-5}{1-(-3)} = \dfrac{3}{4} = 0.75[/tex]

The slope, m = 0.75

The slope of the line that passes through the points M(-3, 5) and N(1, 8) in decimal form = 0.75.

10 Brynlee's monthly cell phone bill
is $60 a month plus $2.50 per
gigabyte used. Raylin's cell phone bill is $450
per month plus $3.25 per gigabyte used.
Determine after how many gigabytes used
would the cell phone plans cost the same
for the month what is the answer??

Answers

Answer:

20 gigabytes

Step-by-step explanation:

Let n represent the amount of gigabytes used.

First make an equation for each senario, Brynlee's would be 60+2.50n and Raylin's would be 45+3.25n.

Set them to equal each other, 60+2.50n=45+3.25n.

Then isolate for n.

60-45=3.25n-2.50n

15=0.75n

Divide both sides by 0.75 to get 20

aleena bought 15 kg of fruits she brought 3kg 750 g of apples 4kg 250g of mangoes and rest were oranges find the weight of oranges
pls urgent will surely mark u the brainliast​

Answers

Answer:

8.950 kg

Step-by-step explanation:

Lemme know if incorrect

What is the value of n in the equation -1/2 (2n + 4) + 6 = -9 + 4(2n + 1)?
n =

Answers

Answer:

n=1

Step-by-step explanation:

Answer:

n=1

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = lwh. Which is the equivalent equation solved for h?​

Answers

Answer:

V /(lw) = h

Step-by-step explanation:

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

V /(lw) = h

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

solve for t. 79t=14 write your answer here

Answers

Answer: im pretty sure its 14 divided by 79 soo 0.17?

if not im sorry

use your brain tho:)

hope this helps you

Plz help !!!! Failing class plz help!!

Answers

Answer:

that is alot  I  would help you but I don't know how to do it

Step-by-step explanation:

The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is
18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 11 feet from a wall to its left.
Samuel throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor.
Does Samuel's dart land on the dartboard?

Answers

Answer:

Yes, Samuel dart does land on the dart board

Step-by-step explanation:

The given parameters are;

The height from the floor to the bulls eye = 5 feet 8 inches

The size of the standard board = 18 inches diameter

The distance of the bulls eye from the wall to the left = 11 feet

The distance the dart Samuel throws land from the left wall = 11.5 feet

The distance above the ground, the dart Samuel throws land = 5.5 feet

Whereby Samuel throws the dart directly at the dartboard, we have;

The location of the bulls eye = (11, 5.67)

The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625

The unit of the radius is in feet

The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)

Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;

(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²

Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;

Yes, Samuel dart does land on the dart board.

From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;

Samuel's dart does not land on the dartboard.

We are given;

Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft

Diameter of the standard dartboard = 18 in = 1.5 ft

Thus, radius; r = 1.5/2 = 0.75 ft

Distance of the bulls eye from the wall to the left = 11 ft

Distance of dart thrown by Samuel from the left wall = 11.5 ft

Height of dart thrown by Samuel above the ground = 5.5 ft

We know that general equation of a circle is;

(x - a)² + (y - b)² = r²

Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft

And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft

Thus;

(x - 11)² + (y - 5.67)² = 0.75²

(x - 11)² + (y - 5.67)² = 0.5625

Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;

r² = (11.5 - 11)² + (5.5 - 5.67)²

r² = 0.2789

r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.

Read more at; https://brainly.com/question/18430680

Mrs. Greene wants to plant a vegetable garden in her yard. She purchased a package containing 30 sections of fencing, each 1-foot long If she uses all 30 sections to create rectangular space, how many different arrangements are possible? What is the largest area she can enclose for her garden with this fencing?

Answers

Answer:

The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]

Step-by-step explanation:

Suppose the rectangular space Mrs. Greene wants to plant has dimensions x feet and y feet.

Since each section of fencing is 1-foot long, both x and y must be integer numbers.

The perimeter of the rectangular space is calculated as:

P = 2x + 2y

And we know she uses all 30 sections of fencing, thus:

2x + 2y = 30, where x, y are integers and positive.

Simplifying by 2:

x + y = 15

Solve for x:

x = 15 - y

This equation doesn't have infinitely many solutions, since both numbers must be integers and positive. Suppose we start by setting y=1, then x=14. That is a possible arrangement for the garden.

Another valid option is for y=2, x=13

Continuing with these patterns, we find the maximum value for y is 7, x=8, because if we set y=8, x=7, this is the same condition as y=7, x=8.

Thus, from y=1 to y=7, there are 8 possible combinations for the arrangement of the garden.

The area of a rectangle is

[tex]A=x\cdot y[/tex]

Testing some possible arrangements:

y=1, x=14

[tex]A=1\cdot 14= 14 ft^2[/tex]

y=2, x=13

[tex]A=2\cdot 13= 26 ft^2[/tex]

y=3, x=12

[tex]A=3\cdot 12= 36 ft^2[/tex]

We can notice the combination y=7, x=8 has an area of:

[tex]A=7\cdot 8= 56 ft^2[/tex]

This is the largest possible area of all combinations, thus:

The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]

If f(x)=4x-3 and the domain of f is {0,5,10}, what is the range of f?

Answers

{-3, 17, 37}
As well I know this is the answer try checking it again in your book or whatever thing you learnt from.

can someone answer this and explain? and the one below, will mark brainlest

Answers

Step-by-step explanation:

there were 50 boxes of gum

each box had 36 packs of gum

in each pack were 15 pieces of gum

so total pieces of gum:

for one box of gum total pieces= 15*36= 540 pieces

for 50 boxes= 540*50= 27000 pieces of gum in total

number sentence:

15*36=540

540*50= 27000

bonus question:

27 gums in 1 day

27000 gums in x days

27000/27= 1000 days

Answer:

540 pieces x 50

27000/27=1000 days

Given: ΔABC, where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ΔABC be an isosceles triangle with AB = BC. given 2. Create point D on side so bisects ∠ABC. constructing an angle bisector 3. M∠ABD = m∠CBD definition of angle bisector 4. BD = BD Reflexive Property of Equality 5. ΔABD ≅ ΔCBD 6. M∠BAC = m∠BCA Corresponding angles of congruent triangles have equal measures. What is the reason for statement 5 in this proof? A. ASA B. SSS C. AAS D. SAS

Answers

Answer:

D. SAS

Step-by-step explanation:

Given: ΔABC

Bisecting <ABC to create point D implies that BD is a common side to  ΔABD and ΔCBD.

Also,

m<ABD = m<CBD (angle bisector)

BA = BC (given property of the isosceles triangle)

Therefore,

ΔABD ≅ ΔCBD (Side Angle Side)

The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.

Answer:

Option D is correct trust me

Step-by-step explanation:

If B = 3x^2-x+3and A=x-6, find an expression that equals 2B+3A in standard form?

Answers

Answer:

[tex]6x^{2} +x-12[/tex]

Step-by-step explanation:

All you need to do is multiply equation B by 2 and multiply equation A by 3, then put an addition sign between them and combine like terms after you've distributed what you needed for each one.

Which sequences of transformations confirm the congruence of shape II and shape I?

a reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 180° rotation about the origin

Answers

A,B,C

Step-by-step explanation:

Answer:

A, B and C

Step-by-step explanation:

please help me solve this​

Answers

Answer:

-1

Step-by-step explanation:

Eight rolls of paper towels cost $4.80. At the same unit rate, how much will six rolls of paper towels cost? Describe the steps that you took to determine your answer.Eight rolls of paper towels cost $4.80. At the same unit rate, how much will six rolls of paper towels cost? Describe the steps that you took to determine your answer.

Answers

Answer:

$3.6

Step-by-step explanation:

Given that 8 rolls cost $4.80

let us compute how much 1 roll will cost (that is the unit cost of a roll)

so  8 rolls cost $4.80

     1 roll will cost x

x= 4.8/8

x=$0.6

so the paper tower cost $0.6 per roll (this is the rate)

therefore 6 rolls will cost

=6*0.6

=$3.6

Holden wants to earn money teaching kids how to skate. It costs him $250 to advertise his new skate school. He charges students $16 and hour to learn how to skate. How many hours does he have to teach in order to make $768, the amount needed to
buy a new gaming system?

Create an equation where r represents the
number of hours Holden needs to work.

Answers

Answer:

16r - 250 = 768

Step-by-step explanation:

First, create a term that represents his revenue:

Since he charges students $16 per hour, the amount of money he makes from this can be represented by 16r.

Then, subtract the advertising cost of $250 from this.

Set it equal to 768, because that is how much the gaming system costs.

16r - 250 = 768 will be the equation

Jenny works mowing lawns and babysitting. She earns $8.80 an hour for mowing and $7.70 an hour for babysitting. How
much will she earn for 1 hour of mowing and 3 hours of babysitting?

Answers

Answer:

$31.90

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

i need help on this

Answers

Answer:

2

Step-by-step explanation:

63/9 = 7 and -5 + 7 is the same thing as 7-5 so it's 2

Answer:

2

Step-by-step explanation:

[tex]\frac{63}{9} = 7[/tex]  Plug 7 in: -5 + 7-5 + 7 = 2

I hope this helps!

Multiply. Use the greatest common factor to write each answer in simplest form. 8/21 x 7/10

Answers

Answer:

56/210---> 8/30---> 4/15

Step-by-step explanation:

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper how many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper

Answers

Given :

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper.

To Find :

How many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper.

Solution :

Mass of copper in 50 gm alloy = [tex]50\times 0.12 = 6\ gram[/tex].

Mass of copper in 78 gm alloy = [tex]78\times 0.98 = 76.44\ gram[/tex].

Total mass of copper, ( 6 + 76.44 ) gm = 82.44 gram.

Percentage of copper in resulting mixture :

[tex]\%=\dfrac{82.44}{50+78}\\\\\%=64.4\ \%[/tex]

Hence, this is the required solution.

PLEASE HELP ANYONE:))

Answers

Answer:

3 million dollars

Step-by-step explanation:

i just did this and got it right

The shampoo Eva likes to use costs $6 for a 24-ounce bottle. The conditioner she likes to use costs $12 for a 30-ounce bottle. How much more per ounce does her conditioner cost than her shampoo? $ per ounce

Answers

Answer:

0.15

Step-by-step explanation:

6 divided by 24 equals 0.25

12 divided by 30 equals 0.4

0.4 minus 0.25 is 0.15

$0.15 more per ounce does her conditioner cost than her shampoo.

Given that, the shampoo Eva likes to use costs $6 for a 24-ounce bottle.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The conditioner she likes to use costs $12 for a 30-ounce bottle.

Cost of shampoo per ounce =Total cost/Number of ounce

= 6/24

= $0.25 per ounce

Cost of conditioner per ounce =Total cost/Number of ounce

= 12/30

= $0.4 per ounce

Difference =0.4-0.25

= $0.15

Therefore, $0.15 more per ounce does her conditioner cost than her shampoo.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

If 15 is subtracted from three times a certain number,
the result is 27. Find the number

Answers

Answer:

x=14

Step-by-step explanation:

3x-15=27 (add 15 to both sides)

3x=42 (divide both sides by three)

x=14

The required number is -4.

What are linear equation?

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now it is given that, 15 is subtracted from three times a certain number,

the result is 27.

Now let x be the number.

Three times the number = 3x

Therefore, 15 is subtracted from three times a certain number = 15 - 3x

Therefore, the equation for 15 is subtracted from three times a certain number, the result is 27 is,

15 - 3x = 27

Subtracting 15 both the side we get,

15 - 3x - 15 = 27 - 15

⇒ -3x = 12

or, x = -12/3

⇒ x = -4

which is the required number.

Thus, the required number is -4.

More about linear equation :

brainly.com/question/16584198

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x - 17 = 32 * linear equations

Answers

x= 49 hope this is what you needed!

Answer: x=49

x-17=32

Subtract 17 from both sides.

x=32+17

x=49

Simplify the following expression.
(5^3)^5

Answers

Answer:

5 ^15

Step-by-step explanation:

(5 ^3)^5 =5 ^(3×5)=5 ^15

Answer:  5^15

The rule used is (a^b)^c = a^(b*c)

If you raise some exponential expression to another exponent, then you multiply the exponents. You keep the base the same.

In this case, a = 5, b = 3, c = 5.

Using a calculator,

5^15 = 30,517,578,125

But it's likely your teacher will want you to keep the answer in exponential form since it's easier to work with.

Someone please help! Asap

Answers

4x + 3 + 9x + 5 = 47
13x + 8 = 47
13x = 39
X = 3

9(3) + 5

Answer: 32
Answer :
X=3

Steps :

4x+3 + 9x+5
= 13x+8

Then
13x+8 = 47

X=3
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