Mathematics High School

Solve this quadratic equation using the quadratic formula.

x2 - 6x + 6 = 0

Answers

Answer 1
x=3+√3 or x=3−√3 would be the answer. Hope this helps!
Answer 2

The solutions of the quadratic equation are 3 ± √3.

What are Quadratic Equations?

Quadratic equations are defined as the polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given quadratic equation is x² - 6x + 6 = 0.

The solutions of a quadratic equation ax² + bx + c = 0 can be found using the quadratic formula,

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

From the given equation,

a = 1, b = -6 and c = 6

Substituting in the quadratic formula,

x = [-(-6) ± [tex]\sqrt{(-6)^2-(4*1*6)}[/tex] ] / [2 × 1]

  = [6 ± [tex]\sqrt{36-24}[/tex]] / 2

  = [6 ± [tex]\sqrt{12}[/tex]] / 2

  = [6 ± 2√3] / 2

  = 3 ± √3

Hence the solutions of the given quadratic equation are 3 + √3 and 3 - √3.

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Related Questions

BRAINLIESTTTT!!!

1. Which of the following statements best describes the graph of x + y = 4?

It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.

Answers

Problem 1

A is false because any point on the x axis will have y = 0
B is false because any point on the y axis will have x = 0
C is false; the coordinates add up to 4
D is the only thing left. It's true since x+y = 4 indicating that the coordinates add up to 4

Answer: choice D

==============================================================

Problem 2

You're close but the answer is actually choice C. The shaded region is below the slanted line so we'll have a "less than or equal to" sign instead of a "greater than or equal to" sign for the first inequality.

=================================================================

Problem 3

Using geogebra (see attached image) I'm getting the graph that matches with choice A

So it looks like you have the correct answer. Nice job.

Write the equation for the vertical line that contains point E (10,-3)

Answers

A vertical line is known as undefined and goes straight up and down.

This means it eventually crosses the x axis.

Undefined equations are represented by x= (wherever it crosses the x axis)

So since this point is (10 , -3), it crosses the x axis at 10 and goes up and down forever.

The equation of the line is x = 10.

Hope this helped C:

write an expression for the quotient of a number and 5 decreased by 4

Answers

q=x/5-4

let me know if you have any questions

Are the graphs of the lines in the pair parallel? Explain. y = 3/7 x + 11 and –3x + 7y = 13

Answers

yes; both have a slope of 3/7
Yes. They have the same slope.

How do you solve this equation

Answers

Answer:

  -4

Step-by-step explanation:

Use your knowledge of multiplication facts.

  [tex]\sqrt[3]{-64}=\sqrt[3]{(-4)^3}=-4[/tex]

__

Your calculator may be able to do this for you.

0.74 as a fraction in simplest form

Answers

0.74.....the last digit (4) is in the hundredths place...so put it over 100

74/100 reduces to 37/50 <==

is 3.774447444744474447444 a rational number

Answers

No it is an irrational number because it is a decimal with repeating numbers.

Sadie's ice cream shop sold 11 sundaes with nuts and 1 sundae without nuts. what is the ratio of the number of sundaes without nuts to the number of sundaes with nuts?

Answers

the ration of the number of sundaes without nuts to the number of sundaes with nuts is:
1:11

the ration of the number of sundaes without nuts to the number of sundaes with nuts is:
1:11

Seth is reading a long novel. if he reads 45 pages per hour, how many hours will it take him to read 585 pages?

Answers

It will take Seth 13 hours to read the novel.
This is true because:
You need to divide 585 by 45, and you get the answer, 13.

If a sports car is traveling at 95 miles per hour, how long would it take the sports car to overtake a family car traveling at 35 miles per hour that left the same starting point 4.5 hours earlier?

Answers

distance = speed * time
d = st

The sports car travels d distance for t time at speed, s, 95 mph until it overtakes the family
car.
The equation for the sports car is
d = 95t

The family car travels the same distance, d, but since it left 4.5 hours earlier  than the sports car, it travels for t + 4.5 time until it is overtaken. It travels at speed, 35 mph.
The equation for the family car is
d = 35(t + 4.5)

We solve the two equations as a system of equations.

d = 95t
d = 35(t + 4.5)

Since d = d, set the right sides of the equations above equal to each other.

95t = 35(t + 4.5)

95t = 35t + 157.5

60t = 157.5

t = 2.625

The answer is 2.625 hours, or 2 hours, 37 minutes, and 30 seconds.

Check:
In 2.625 hours, the sports car travels: 95 mph * 2.625 h = 249.375 miles
The family car traveled 2.625 hours plus the extra 4.5 hours, or 7.125 hours.
In 7.125 hours, the family car travels 35 mph * 7.125 h = 249.375 miles.
The cars have traveled the same distance 2.625 hours after the sports car left, so our answer is correct.

Find the missing measures for the rectangle.

l = _?_
w = 2 cm
A = _?_
P = 25 cm

A) 12.5 cm; 25 cm2

B) 10.5 cm; 21 cm2

C) 12.5 cm; 21 cm2

D) 10.5 cm; 25 cm2

Answers

P = 2(L + W)
P = 25
W = 2

25 = 2(L + 2)
25 = 2L + 4
25 - 4 = 2L
21 = 2L
21/2 = L
10.5 = L.......so ur length is 10.5 cm

A = L * W
A = 10.5 * 2
A = 21 cm^2

so ur answer is B. 10.5 cm, and 21 cm^2

Divide. Write your answer in simplest form.
4 ÷ 5/6

Answers

4 / (5/6)

4 x (6/5)                    - flip the fraction and flip the second number

4 x (6/5) =  4.8

4.8 is your answer

hope this helps

If number is added to its square, the result is 56. find the number.

Answers

Answer:

  -8 or +7

Step-by-step explanation:

Let x represent the number. The the problem statement tells us ...

  x² + x = 56

  x² +x -56 = 0 . . . . . subtract 56 to put into standard form

  (x +8)(x -7) = 0 . . . . factor

Solutions to the equation are values of x that make the factors zero:

  x = -8 . . . or . . . x = +7

The number could be -8 or +7.

_____

Check

For x = -8, the square is (-8)² = 64. Adding -8 to that gives 64-8 = 56.

For x = 7, the square is 7² = 49. Adding 7 to that gives 49+7 = 56.

5.Thomas walked 1 1/4 miles from his home to his school. Jackson walks 1 2/3 miles from his home to work. How much farther does Jackson walk to school than Thomas?

Answers

Jackson walks 5/12 miles farther than Thomas to work. So, Jackson walks approximately [tex]\( \frac{5}{12} \)[/tex] miles farther than Thomas.

To find out how much farther Jackson walks to work than Thomas, we need to subtract the distance Thomas walks from the distance Jackson walks.

Thomas walks 1 1/4 miles, which is equivalent to 5/4 miles. Jackson walks 1 2/3 miles, which is equivalent to 5/3 miles.

To subtract fractions, we need a common denominator, which in this case is 12. So, 5/3 is equivalent to 20/12, and 5/4 is equivalent to 15/12.

Now, subtracting, we get 20/12 - 15/12 = 5/12 miles.

Therefore, Jackson walks 5/12 miles farther than Thomas.

Which function is negative for the interval [–1, 1]?



The answer is the second graph

Answers

Answer:

the answer is the 2nd graph your welcome:)

Step-by-step explanation:

A function is the relationship between two variables such that each input has exactly one output

The function which is negative for the interval [-1, 1] is the function represented by the second graph

The reason the second graph is the correct option is as follows:

The output values of a function are the y-values of the function. A function is negative over an interval if its y-values are negative in the interval

The given interval is [-1, 1], which is the interval from x = -1, to x = 1

From the given graphs, the graph of the function that is negative over the interval [-1, 1] which is the second graph

a·x² + b·x + c = 0

At x = 0, y = -2

At x = 1, y = 0

At x = -1, y = 0

At x = 2, y = 2

Solving the above gives; The equation of the function is f(x) = x² - 2

The graph of the function is attached

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Jill is 7 kilometers away from joe. both begin to walk toward each other at the same time. jull walks at 1.5 kilometers per hour. they meet in 2 hours. how fast is joe walking?

Answers

it would be 21 kilometers

PLEASE HELP QUICK I'M OFFERING 12PTS AND BRAINLIEST ANSWER
what is the solution set for the open sentence with the given replacement set w^2 + 9 = 6w, (0,3,6,9)

Answers

do you mean solve it 

The inverse of x y is: x y x y y x x y y x

Answers

Answer:

The inverse of xy is yx.

Step-by-step explanation:

Given:  xy

We need to find the inverse of xy.

To find inverse of an expression, we need to replace the variable x by y and y  by x.

Given xy.

Now replace x by y and y by x, we get

yx

Therefore, the inverse of xy is yx.

Let me show you an example.

y = x - 2

To find the inverse function, replace x by y and y by x, we get

x = y - 2

It is an equation, to write the equation in terms of y, add 2 from both sides, we get

x + 2 = y -2 + 2

x + 2 = y

Therefore, y = x + 2

Guys please help! 15 points and brainliest! In triangle CDE, the measure of angle C is 90 degrees, side CD is 15 and DE is 3 more than CE. Find the length of the longest side of CDE.

Answers

You can calculate it using the law of cosines: c^2=a^2+b^2-2*a*b*cos(C)

your triangle is
CD=15=a
CE=?=b
DE=CE+3=b+3=c
and C=90°

-> insert those values, with c substituted with b+3 to remove c

c^2=a^2+b^2-2*a*b*cos(C)
(b+3)^2=15^2+b^2-2*15*b*cos(90)
cos(90)=0->
(b+3)^2=15^2+b^2
b^2+2*3*b+3^2=225+b^2
6b+9=225
6b=216
b=36=CE

DE=CE+3=36+3=39

Find equations in standard form of the lines through point P that are A.) parallel to, and B.) perpendicular to, line L. P(0,-4); L: 2y=x. I've tried solving it and looking at examples, but no examples in my book are like this problem.

Answers

2y = x
y = 1/2x....the slope of this line is 1/2.

A parallel line will have the same slope.
y = mx + b
slope(m) = 1/2
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 1/2(0) + b
-4 = b
so ur equation is : y = 1/2x - 4...but we need it in standard form Ax + By = C

y = 1/2x - 4....subtract 1/2x from both sides
-1/2x + y = -4...multiply both sides by -2
x - 2y = 8 <== standard form of parallel line
==========================
the slope of the line was 1/2. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular line will have a slope of -2...see how I flipped 1/2 making it 2/1...and changed the sign, making it -2.

y = mx + b
slope(m) = -2
(0,-4)...x = 0 and y = -4
sub and find b
-4 = -2(0) + b
-4 = b
so this equation is : y = -2x - 4....but we need standard form

y = -2x - 4....add 2x to both sides
2x + y = -4 <== standard form of perpendicular line

Lima is constructing a square in which two of its vertices are points A and B. He has already used his straightedge and compass to construct the lines and arcs shown.

Answers

The location above point b, label as point C. That distance is the span at which the compass should stay. I am presuming that is is the same distance from A to B in which two sides of the square are consructed. Keeping the span the same, place the point of the compass on point C and create an arc in the vacinity of the third vertex of the square. Repeat this process with the point of the compass on point A without changing the span of the compass. Where the arcs intersect, label point D. Use the straight edge to draw in AD and CD. The square is completed. 

How to find the perimeter of a polygon with vertices

Answers

Step 1 Draw the triangle in a coordinate plane by plotting the vertices and connecting them. Step 2 Find the lengths of the base and height.
Final answer:

To find the perimeter of a polygon with vertices, calculate the sum of the lengths of all the sides of the polygon by taking the distance between each pair of consecutive vertices and adding them together.

Explanation:

To find the perimeter of a polygon with vertices, you need to calculate the sum of the lengths of all the sides of the polygon. The perimeter is the distance around the polygon. You can do this by taking the distance between each pair of consecutive vertices and adding them together. For example, if you have a triangle with vertices A, B, and C, you would calculate the length of AB, BC, and AC, and then add these lengths together to find the perimeter of the triangle.

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The length of a rectangle is 4 in longer than its width. if the perimeter of the rectangle is 28 in , find its area.

Answers

The area is 45 inches squared

PLEASE HELP! 15 POINTS

Answers

she earns 550 per week

 so that is one one side of the equation 550w

 the other side would be the 4500 she spent plus the 200 per week' so 4500 +200w

 equation is 550W> 4500+200W

It would take her 13 weeks to make a profit

What is the value of x?

Answers

the answer would be 35 because you take 120 and add 25 and get 145. then because it can make a straight line you do 180-145 and that equals 35.

Please help!! Rewrite the expression as the product of two binomials. What are the two binomials for the expression? x(x-8)-9(x-8)

Answers

that would be (x-9) (x-8)

At Chelsea's workplace, 30 people drink 2 cups of coffee a day on average. A pot of coffee has 10 cups of coffee. How many pots of coffee are needed each day?

Answers

6 pots would be the answer. 
30*2=60
1 pot=10
60 divided by 10 = 6

6 pots

6 pots

6 pots

6 pots


Which of the following is more than 0.35 but less than 0.41
A.
8/25
B.
3/10
C.
2/5
D.
9/26

Answers

its B because 3/10ths is a little bit more than 0.35, but way less than 0.41

Answer:

C. [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Let x be the number which is more than 0.35 but less than 0.41,

⇒ 0.35 < x < 0.41

[tex]\implies \frac{35}{100}< x < \frac{41}{100}[/tex]

[tex]\implies \frac{7}{20} < x < \frac{41}{100}[/tex]

∵ Only [tex]\frac{2}{5}[/tex] is between [tex]\frac{7}{20}[/tex] and [tex]\frac{41}{100}[/tex],

Hence, option C is correct.

Which of the following characteristics of a parallelogram leads to the conclusion that every square can always be classified as a parallelogram? Select all that apply.

four equal sides
two pair of opposite equal angles
bisecting diagonals
two pair of opposite parallel sides

Answers

The properties of a parallelogram that lead to the conclusion that a square is a type of parallelogram are 2nd, 3rd and 4th options.

Answer:

two pair of opposite equal angles

bisecting diagonals

two pair of opposite parallel sides

math help easy will give brainliest

Answers

the equation will be of the form 
y = 8x + b  because the slope is same  = 8.
using point slope form

y - -3 = 8(x - - 2)
y + 3 = 8x + 16

y = 8x + 13  Answer

Answer: the equation will be of the form  

y = 8x + b  because the slope is same  = 8.

using point slope form

y - -3 = 8(x - - 2)

y + 3 = 8x + 16

y = 8x + 13  Answer

I hope that this helps! :3

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