which are the solutions of the quadratic equation x^2=9x+6

Answers

Answer 1

You can use the quadratic equation to solve this once you have this set equal to zero. The answers would be roughly 9.6 and -0.6.

Answer 2

The solutions of the quadratic equation [tex]$x^2 = 9x + 6$[/tex]are:

[tex]\[x = \frac{9 + \sqrt{105}}{2}\][/tex] and [tex]\[x = \frac{9 - \sqrt{105}}{2}\][/tex]

To find the solutions of the quadratic equation [tex]$x^2 = 9x + 6$[/tex], we need to rewrite it in standard quadratic form [tex]$ax^2 + bx + c = 0$.[/tex]

Given:

[tex]\[x^2 = 9x + 6\][/tex]

Subtract [tex]$9x$ and $6$[/tex] from both sides to get it in standard form:

[tex]\[x^2 - 9x - 6 = 0\][/tex]

Now, to solve this quadratic equation, we can factor it or use the quadratic formula:

The quadratic formula is:

[tex]\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\][/tex]

For our equation:

[tex]\[a = 1, b = -9, \text{ and } c = -6\][/tex]

Substituting these values into the quadratic formula:

[tex]\[x = \frac{-(-9) \pm \sqrt{(-9)^2-4(1)(-6)}}{2(1)}\]\[x = \frac{9 \pm \sqrt{81+24}}{2}\]\[x = \frac{9 \pm \sqrt{105}}{2}\][/tex]

So, the solutions of the quadratic equation [tex]$x^2 = 9x + 6$[/tex]are:

[tex]\[x = \frac{9 + \sqrt{105}}{2}\][/tex] and [tex]\[x = \frac{9 - \sqrt{105}}{2}\][/tex]

Related Questions

what is the answer to f(2)=2-5(2)

Answers

The answer -8. This can be found by using "PEMDAS" and muliplying -5 and 2 to get -10. Then combine like term by subtracting 10 from 2 to get -8.

The amount of grass seed needed to cover a lawn is proportional to its area. The lawn is rectangular and has an area of 2c^2 + 2c square meters. Factor this polynomial to find possible expressions for the length and width of the lawn. (Assume the factors are polynomials.) HELP ASAP!!

Answers

2c is a factor of both terms.
.. area = 2c(c+1)

Possible expressions for length and width are
1, 2, c, 2c, c+1, 2(c+1), c(c+1), 2c(c+1).

What is the solution of the equation 5x – 1 = 45? Round your answer to the nearest ten-thousandth

Answers

Final answer:

The solution to the equation 5x – 1 = 45 is x = 9.2, rounded to the nearest ten-thousandth.

Explanation:

The solution of the equation 5x – 1 = 45 is x = 9.2.

To solve this equation, we can start by isolating the variable x. Add 1 to both sides of the equation to get 5x = 46. Then, divide both sides by 5 to solve for x, giving us x = 9.2.

Therefore, the solution to the equation 5x – 1 = 45 is x = 9.2, rounded to the nearest ten-thousandth.

Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.

Answers

3- The number of tickets each game requires.
18 - The number of tickets bought.
g - The number of games played.

The "3g" represents the number of games we can determine Zhi and Diego went to. Both equations have values and variables that mean the same thing, however Diego chose to use the distributive property in setting up his equation.

Yes, Zhi's expression multiplies the tickets per game by the number of games to get the number of tickets used and then subtracts this amount from the total tickets.

50 points! Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled, and the sum of their outcomes is found. Each player gets a chance to guess the correct sum, and the player that guesses the correct sum wins the game.

Dustin decides to guess a sum of six. Melanie decides to guess a sum of seven.

Which player made the better decision? ________

Answers

Answer:

Melanie is the right answer

Step-by-step explanation:

Melanie made the better decision if Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.

If the sum is 6:

The possible outcomes are = {(3,3), (2,4), (4,2), (1,5), and (5,1)}

Total outcomes = 5

If the sum is 7:

The possible outcomes are = {(1,6), (6,1), (5,2),( 2,5), (3, 4), (4,3)}

Total outcomes = 7

Thus, Melanie made the better decision if Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

plz help "geometry"

the intersection of roads M and N creat a 71.4 degrees what are the complumentry and suplumentry angels of this intersection
A 161.4' ; 18.6'
B 18.6'; 161.4'
C 108.6' ; 18.6'
D 18.6' ; 108.6',

Answers

Complementary angles sum up to 90 degrees and supplementary angles sum up to 180 (I remember that because they are alphabetical). 90 - 71.4 = 18.6 180 - 71.4 = 108.6 Therefore, D. is the answer.

Rewrite the radical exponent as a radical

Answers

[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------\\\\ \left( 5^{\frac{3}{4}} \right)^{\frac{2}{3}}\implies 5^{\frac{3}{4}\cdot \frac{2}{3}}\implies 5^{\frac{1}{2}}\implies \sqrt[2]{5^1}\implies \sqrt{5}[/tex]

Ashur solves the following system of linear equations.

Which statement about the solution to this system can he say is true?
The values of a and b are both equal to –4.
The values of a and b are both equal to 4.
The value of a is equal to 4, and b is equal to –4.
The value of a is equal to –4, and b is equal to 4.

Answers

a. first choice

The values of a and b are both equal to –4.

The given equations that make up the systems are:

-3a+7b=-16...................(Equation 1)

-9a+5b=16...................(Equation 2)

To find the values of a and b we will have to solve the two equations. To solve the equations let us employ the method of elimination.

Let us multiply (Equation 1) by -3. This will give us:

[tex] -3\times (-3a+7b=-16)=9a-21b=48 [/tex]...........(Equation 3)

Let us now add (Equation 2) to (Equation 3) to eliminate a. This will give us:

-16b=64

[tex] \therefore b=-4 [/tex]

Plugging this value of b in any of the equations we will get the value of a. Let us plug it in (Equation 1). This gives:

[tex] -3(-4)+7b=-16 [/tex]

[tex] 12+7b=-16 [/tex]

[tex] \therefore b=\frac{-28}{7}=-4 [/tex]

Thus, out of the given options, the first option is the correct one. The values of a and b are both equal to –4.

What happens when you square a cubed root or cube a square root and problems like these. Please tell me how to do it!

Answers

You would do the innermost operation first, so for your first example: squaring a cubed root- you would first take the cubed root, get your answer, and square that answer. For example what's the square of the cubed root of 8? Well, the cubed root of 8 is 2. (Because multiplying 2, three times will give me 8). Since the cubed root of 8 is 2, I need to square 2 and I'll get 4.

at 4:00 am,there were 800,000 gallons of water remaining at a reservoir.after 4 hours of irrigation,there were 100,000 gallons of water remaining.write an equation that describes the number of gallons of water as a function of the time the field has been irrigated

Answers

Let the[tex]x-axis[/tex] presents the time, and the [tex]y-axis [/tex] the gallons of water remaining, so our first point will be (4,800000). We know from the problem that after 4 hours, at 8:00 am, there were 100000 gallons, so our second point will be (8,100000).
To relate those two points we are going to use the point slope formula:
[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} } [/tex]
where
[tex]x_{2}[/tex] is 8
[tex]x_{1}[/tex] is 4
[tex]y_{1}[/tex] is 800000
[tex]y_{2}[/tex] is 100000

So, [tex]m= \frac{100000-800000}{8-4} [/tex]
[tex]m= \frac{-700000}{4} [/tex]
[tex]m=-175000[/tex]

Now that we have our slope, we are going to use the point-slope formula to find our equation:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-800000=-175000(x-4)[/tex]
[tex]y-800000=-175000x+700000[/tex]
[tex]y=-175000x+1500000[/tex]

The equation that describes the number of gallons of water as a function of the time the field has been irrigated is [tex]y=-175000x+1500000[/tex]
where
[tex]y[/tex] are the remaining gallons of water in the reservoir after [tex]x[/tex] hours
[tex]x[/tex] is the time the field has been irrigated in hours

How long would it take to travel 630 miles at the rate of 35 miles per hour? 18 h 35 h 220 h 350 h

Answers

you get it by taking the # of miles/the # of hours would be A. 18 h

Answer:

18h

Step-by-step explanation:

a/an ______ angle measures less than 90degrees°, a/an ______ angle measures 90degrees°, a/an ______ angle measures more than 90degrees° and less than 180degrees°, and a/an ______ angle measures 180degrees°.

Answers

Acute
Right
Obtuse
Straight

when does a rhombus have 4 congruent angles?

Answers

It sometimes. A rhombus could have 2 pairs of opposite congruent angles. That means that the 2 adjacent angles are also supplementary. Two angles could be 50 degree and other two angles could be 130.

Factor completely. x^2−3x−40

Answers

This expression is a generic quadratic expression, so the first thing we need to look at is the last term (-40). Is it negative or positive? What are the factors of it? If the last term is negative, we know that one binomial is a subtraction while the other binomial is an addition. You may be asking, "an addition or subtraction of WHAT?" A binomial factored out of a quadratic expression would look something like this: (x + ____). The blank would equal a factor of the last term. In this case, a pair of factors that would fit is 8 and 5.
8x5 = 40 and -8 + 5 = -3.

Plug it into the binomial example I provided above and....
(x - 8)(x+5)=40

Voila! You have your factored quadratic expression, hope this helps!

To factor the quadratic expression x² -3x -40, we find that the expression factors into (x - 8)(x + 5).

The question involves factoring the quadratic expression x² -3x -40 completely. To factor this expression, we look for two numbers that multiply to -40 and add to -3. The numbers that meet these conditions are -8 and 5, since

(-8) * 5 = -40 and

(-8) + 5 = -3.

Therefore, the expression can be factored into (x - 8)(x + 5).

which is the directrix of parabola with equation x^2=4y

Answers

Answer:

[tex]y=-1[/tex]

Step-by-step explanation:

We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.

First of all, we will divide both sides of our given equation by 4.

[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]

[tex]\frac{x^2}{4}=y[/tex]

[tex]y=\frac{x^2}{4}[/tex]

Now, we will compare our equation with vertex form of parabola:

[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.

We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].

Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].

Substituting the value of a in above formula, we will get:

[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]

[tex]p=\frac{1}{1}=1[/tex]

We know that directrix of parabola is [tex]y=k-p[/tex].

Substituting the value of k and p in above formula, we will get:

[tex]y=0-1[/tex]

[tex]y=-1[/tex]

Therefore, the directrix of our given parabola is [tex]y=-1[/tex].

if she can read 22 pages in 1 hour how many hours did she read in 114.5 hours

Answers

We already know that 22 = 1, but we need to find how many pages she'd read if it were 114.5 hours: 114.5 x 22 = 2519.

Hope this helps,
♥A.W.E.S.W.A.N.♥

If mAD=85 degrees and mBC=31 degrees find the value

Answers

Answer: x = 11

To start, we know that a whole circle equals 360 degrees. If we subtract the 2 arcs we know, 85 and 31, we have 244 degrees left for the 2 congruent arcs. Dividing that by 2 gives us 122 for each arc.

Now, write the equation: 122 = 13x - 21

Solve this, to find the x = 11.

By the properties of angles on a circle, the degree measure of x in the circle is 11 degrees

Calculating the degree measure of x

From the question, we have the following parameters that can be used in our computation:

The circle

The angle in a circle is 360 degrees.

So, we have

Unused arcs = 360 - 85 - 31

Unused arcs = 244

This means that

2(13x - 21) = 244

So, we have

13x - 21 = 122

This gives

13x = 143

Evaluate

x = 11

Hence, the degree measure of x is 11 degrees

Answers

yes it would. did you happen to get the rest of the answers for this?

The DIAMETER of a sphere is doubled. What is the new volume of the sphere?
A)
8/3πr3
B)
16/3πr3
C)
32/3πr3
D)
64/3πr3

Answers

we know that
[volume of a sphere]=(4/3)*pi*r³
if the diameter is doubled
then
the radius also is doubled

the new volume=(4/3)*pi*(2r)³------> 8*[(4/3)*pi*r³]-------> (32/3)*pi*r³

the answer is C)
32/3πr3

) the length of a rectangle is 5 cm less than twice the width. if the area of the rectangle is 88 , find the dimensions of the rectangle.

Answers

pretty sure its done like this, hope it helps!

two positive integers have a sum of 17 and a product of 66

Answers

Hey there :)

Sum | Product
33 and 2 35 66 X
22 and 3 25 66 X
11 and 6 17 66 ←

11 and 6 have a sum of 17 and a product of 66

Use the data to create a scatter plot.
Size (lb)
8
12
9.5
5
7
7.5

Time (h)
5
6.5
4
3.5
2
5

Answers

For this case, what you should do is plot each ordered pair as a scatter diagram.
The ordered pairs are:
(5, 8)
(6.5, 12)
(4, 9.5)
(3.5, 5)
(2, 7)
(5, 7.5)
Answer:
See attached image.
There seems to be an increase in weight as time passes.

The first term of a sequence is -12. The recursive formula for the sequence is an = an-1 + 9. What are the next 3 terms in the sequence?

Answers

The next three terms are: -3, 6, and 15

To get each new term, we simply add 9 to the last term. So we add 9 to -12 to get -3. Then we add 9 to -3 to get 6. Finally we add 9 to 6 to get 15

In other words,
first term = -12
second term = first term+9 = -12+9 = -3
third term = second term + 9 = -3+9 = 6
fourth term = third term + 9 = 6+9 = 15

This process repeats forever though we only need three terms in this case.

So that's why the answer is the three values -3, 6 and 15

Number 11 please....

Answers

This is pretty easy
(39 + x) / 2 = 44
39 + x = 88
x = 49

The other number would be 5
Here is how I solved it all you have to do is 44-39= and you get 5
pretty simple if you have any other questions feel free to ask.

I hope this helps! ❤️

How do you determine whether to draw the boundary line of the graph of a linear inequality dashed or solid?

Answers

Solid is if x is greater/less than or equal to (there isn’t a symbol for it) the line and the line would be dashed if x is < or > something

which of the following are polynomial functions?check all that apply
(answers in picture)

Answers

A, C, and E are all polynomial functions.

Polynomial functions must have terms that have non-negative integer exponents. We can rewrite function B, [tex]F(x)=-x^3+5x^2+7\sqrt{x}-1[/tex] as:

[tex]F(x)=-x^3+5x^2+7x^1^/^2-1[/tex]

The exponent 1/2 is not an integer exponent.

We can also rewrite the function D, [tex]F(x)=\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex], as:

[tex]F(x)=\frac{3}{5}x^4-18x^2+5-10x^-^2[/tex]

We have a negative exponent, so this is not a polynomial.

Answer:

Step-by-step explanation: It is only c and e i just did the test.

If the measurement of a central angle is 77 degrees find the length of its intercepted arc in a circle with a radius of 15 inches.

Answers

The answer is C. 20.2 inches

Answer:

20.2 inches ;)

Step-by-step explanation:

Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high.The formula for the area of a rectangle is A=bh. What is the area of the wall?

Answers

The formula for the area of the rectangle is actually A = LW. The length of the rectangular wall is 414 yards while its width is 223 yards. To compute for its area, you just have to follow the formula:

A = 414 (223)

A = 92,322 yards^2

Therefore, the area of the wall is 92,322 square yards.

Answer:

hey the answer is 11 1/3

Step-by-step explanation:

ive taken the quiz and this is the answer 100%

If there are 15 girls and 9 boys in an art class, the ____________ of girls to boys in the class is 5:3.

Answers

the ratio of girls to boys in the class is 5:3

Angle A is a right angle in △ABC.

Which side is opposite to angle A?

side BC

side AB

side AC

Answers

side BC is opposite to angle A

Option 1 is correct. The side opposite to angle A is side BC, which is the hypotenuse.

In a triangle, the side opposite the right angle is known as the hypotenuse. Since angle A is given as a right angle in △ABC, the side opposite this right angle will be the hypotenuse.

In △ABC:

Side AB is adjacent to angle A, forming one leg of the right triangle.

Side AC is also adjacent to angle A, forming the other leg of the right triangle.

Side BC is opposite angle A and is the longest side of the triangle, making it the hypotenuse.

Therefore, side BC is opposite to angle A in △ABC.

Complete question:

Angle A is a right angle in △ABC.

Which side is opposite to angle A?

1. side BC

2. side AB

3. side AC

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