Mathematics High School

Solve the following equations by using the Quadratic formula and answer the subsequent questions:

x^2 - 6x + 9 = 0

a. Are the roots equal or unequal?
b. Are the roots rational or irrational?
c. Are the roots real or non-real?

(Please explain how you got the answers)​

Answers

Answer 1

Answer:

Step-by-step explanation:

Note that x^2 - 6x + 9 = 0 can be rewritten as the square of a binomial:

(x - 3)^2

and the roots are found by setting this equal to zero and solving for x:

(x - 3)^2 = 0, or x - 3 = ±0, or x = 3 and x = 3

a) there are two equal roots:  {3, 3}

b) the roots {3, 3} are rational

c) the roots {3, 3) are real

If you want to use the quadratic formula, proceed as follows:

1.  Identify the coefficients of the quadratic:  {1, -6, 9}

2. Find the discriminant b^2 - 4ac:  It is (-6)^2 - 4(1)(9) = 36 = 36 = 0

   As a general rule, if the discriminant is zero, the quadratic has two equal, real roots.  These roots are rational:  3 can be rewritten as 3/1, which is a ratio.

Related Questions

5 b.) Bill swims 2/3 of a lap in 7 minute.
What is his speed in laps per minute?

Answers

Answer:

.095 laps per minute (if you need this answer as well 10.5 minutes per lap)

Step-by-step explanation:

(2/3)/7 =.095238 this is laps per min

7/(2/3)= 10.5 this is minutes per lap

I hope this is what you were looking for.

A set of 25 cards are shown.
what is the probability of choosing a card with a sheep on it?

Answers

Answer:

probability of choosing a card with a sheep on it will be 12.5 out of 25

Hope it helps

Please mark me as brainliest

Thank you

The probability would be 12.5 out of 25

Susan read 130 pages of a book in 2.5 days. If she read the same amount each day, how many pages did she read each day ?

A 5.2
B 5.6
C 52
D 56

Answers

Answer:

c.52

Step-by-step explanation:

if susan reads 130 pages in 2.5 days then we have to divide 130 and 2.5 which gives us 52 which kinda means she reads 52 pages per day i hope that clear

The first three terms of an arithmetic sequence are as follows.
37, 29,21
Find the next two terms of this sequence.

Answers

Answer:

13, 5

Step-by-step explanation:

First, we find the common difference.

d = 29 - 37 = -8

Now we add -8 to the last term to find the next term.

21 + (-8) = 13

13 + (-8) = 5

Answer: 13, 5


[tex]3 \sqrt{ - 125 - ( - {5)3}^{?} } [/tex]
​

Answers

Wait I can’t solve it because of the “3^?” Can you fix that?
I think the answer to your question is 75

1. Which of the following moving at the same speed, wouldbe hardest to stop?*
(12 points)
car
bus
Frisbee
stroller

Answers

Answer:

Bus

Step-by-step explanation:

If the bus has the most weight than the force it would edmit would be greater than any other

A dog ran along a fence 10 times. The fence is 5 feet 3 inches long. How far did the dog travel? (12 inches = 1 foot)

Answers

52 feet and 2 inches

I converted the 5 ft and 3 inches to inches (63) I then multiplied that by 10 (630) and then divided it by 12. I believe this is correct tell me if I’m wrong!

The whole distance travelled by the dog is 630 inches.

We shall now approach the question in the following steps;

First, we  shall convert the length of the fence to inches using the conversion factor as shown in the question.

12 inches = 1 foot

x inches =  5 feet

x = 12 inches × 5 feet /1 foot

x = 60 inches

The total length of the fence is 60 inches + 3 inches = 63 inches

The dog ran round it ten times hence the total distance travelled = 10 * 63 inches = 630 inches

Learn more about distance travelled: https://brainly.com/question/1214027

hi i have problems with some of my mathematic question if you are super good in maths pls kindly send a message or comment so we can work it out together ...thanks in advance​

Answers

Answer:

yeah okay sure!

Step-by-step explanation:

In slope-intercept form, what is the equation of the line containing the points (−1, 2) and (2, −1)?

Answers

Answer:

y=-x+1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-2)/(2-(-1))

m=-3/(2+1)

m=-3/3

m=-1

y-y1=m(x-x1)

y-2=-1(x-(-1))

y-2=-(x+1)

y=-x-1+2

y=-x+1

Factor the following...
[tex]9n^2-34n-8[/tex]
Please show work

Answers

Step-by-step explanation:

9x8= 72

therefore 36 x 2 are the products

9 n^2 - 36n + 2 n -8

9 n( n-4) + 2( n- 4)

therefore the two factors are

( 9 n +2) ( n-4)

There is supposed to be a 5 at the end PLEASE HELPPPPPPPPPPP ​

Answers

Answer:

D

Step-by-step explanation:

You basically just add the numbers where x is. I tried it with 5 and both equalled 28. Using 5 as x makes the equation equal which is what we are looking for. So the answer is x=5.

If 3+3 is 6 and 6 + 6 is 12... whats 500x - y

Answers

500x-y?
Well what x or y, you need that do this problem. But if not then it could be just 500- xy
The answer to this question could
Honestly be 500- xy. Just putting the two variables together.

Select All the correct answers. Select all the statements that are true for the following systems of equations. System A 2x - 3y = 4 4xy18 System B 3x - 4y = 5 y = 5x + 3 System C 2x-3y и 4 12x-3y 54 System C simplifies to 2x-3y 4 and 4x y 18 by dividing the second equation by three. O Systems A and C have the same solution D Systems A and B have different solutions. Systems B and C have the same solution All three systems have different solutions.​

Answers

Answer:

hi

Step-by-step explanation:

Answer:

The true statements are:

the first statement: Systems A and C have the same solution

the fourth statement: System C simplifies to 2x - 3y = 4 and 4x - y = 18

the fifth statement: Systems A and B have different soltuoins.

Explanation:

1) The first statement: systems A and C have the same solutiotn: TRUE

The fourth statement proves that that the two systems are equivalent which means that both have the same solution.

2) The second statement: All three systems have different solutions: FALSE

The fourth statement proves that the systems A and C have same solution, so this second statement is false.

3) The third statement: Systems B and C have the same solution: FALSE

You can solve the two systems and will find the solutions are different

Solution of system B.

3x - 4y = 5

y = 5x + 3

replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5

=> 3x - 20x - 12 = 5

=> - 17x = 5 + 12

=> -17x = 17

=> x = - 17 / 17

=> x = - 1

y = 5x + 3 = 5(-1) + 3 = - 5 + 3 = - 2

=> solution x = -1 and y = -2

Solution of system C.

2x - 3y = 4

12x - 3y = 54

subtract

4) fourth statement: System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three: TRUE

Look:

Second equation of system C = 12x - 3y = 54

Divide by 3:

12x - 3y     54

----------- = -----

    3           3

Distributive property:

12x      3y      

------ - ----- = 18

  3        3

4x - y = 18, which is the same second equation of system A, so the system C simplifies to the same system A, which is 2x - 3y = 4 and 4x - y = 18.

5) The fifth statement: systems A and B have different solutions: TRUE

You can solve the two systems and will find the solutions are different

Solution of system A:

 2x - 3y =  4      

12x - 3y = 54           since it is equivalent to 4x - y =  18

-------------------

12x - 2x = 54 - 4      subtracting the first equation from the secon

10x = 50                  adding like terms

x = 5                        dividing by 10

From 2x - 3y = 4 => 3y = 2x - 4 = 2(5) - 4 = 10 - 4 = 6

=> y = 6 / 3 = 2

=> x = 5, y = 2

Solution of system B.

3x - 4y = 5

y = 5x + 3

replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5

=> 3x - 20x - 12 = 5

=> - 17x = 5 + 12

=> -17x = 17

=> x = - 17 / 17

=> x = - 1

Which is enough to prove that the two systems have different solutions.

For the graph shown, the slope is changed to 1/5, but the y-intercept remains the same. What is the resulting equation for the new graph?
A)y = x + 15
B)y = x - 15
C)y = 15x + 1
D)y = 15x - 1

Answers

Answer: C. y=1/5x+1

Step-by-step explanation:

Need help answer it in the bottom

Answers

Answer:

it depend

Step-by-step explanation:

i can edit this answer but-

do they mean that both objects together costs that much or does that mean that pens and pencils cost the same?

can somebody help.................

Answers

Answer:

y=2x+2

Step-by-step explanation:

Answer:

y=2x+2 is the answer

Step-by-step explanation:

hope this helped!! :D

5,574 mg= how many grams?

Answers

Answer:

5.574 grams

Step-by-step explanation:

Answer:

The answer is 5.574 grams

Step-by-step explanation:

19. If 4 + 2(3x - 4) = 8, then 4x -4 =
4
8
6
2

Answers

Answer:

4

Step-by-step explanation:

First, solve for x:

4 + 2(3x - 4) = 8

4 + 6x - 8 = 8

6x = 12

x = 2

Now, plug x into 4x - 4:

4(2) - 4 => 8 - 4 = 4

it's has to be 4 my friend did it and she said she got it right hope this helps

I might just post the whole packet cuz I’m not smart enough to understand what the hecc is going on ;-;

Answers

Answer:

It would be the fourth choice.

Evan makes cards numbered 1-18 and places them in a bag. What is the probability that he will pull out an even number, replace the card, then choose another even number?​

Answers

Answer:

1-8

Step-by-step explanation:

A factory produces 80,000 candies each day.They produce equal quantity of four flavors:cherry,lemon,orange and strawberry. The candies are mix together during packaging. What is the probability of selecting orange.

Answers

Answer:

1 /4

Step-by-step explanation:

Total number of candies produced per day = 80,000

Number of flavors made = 4

Since the number of each flavor produced are equal ;

Number of each flavor produced :

80000 /4 = 20000

Probability of selecting orange flavor :

Number of orange flavor / total candies produced

= 20000 / 80000

= 1/4

Please help ASAP! Will mark brainliest if correct!

Answers

Answer:

x equals 2 cm

In the triangle CDE, point Y is the midpoint of segment CD and point X is the midpoint of segment DE,
Solve for x

A, 8
B. 6
C. 10
D-10

Answers

Answer:

Option A. 8 will be your answer

Step-by-step explanation:

hope it helps you

have a great day!!!

Any idea. I have no clue. Thanks

Answers

Answer:

your answer should be B :)

Direction: Name at least 2 examples of each of the following terms below from figure 2.

1.angle
2.line segment
3.ray​

Answers

Answer:

1.acute angle

right angle

2.pencil

the edge of a table

3.a Ray from light

a Ray from sun

Answer:

Angle = LABC and LACD

Line segment = AB and DC

Ray = AB and CD

pls help! will mark brainliest if correct

Answers

I dont know what is it sorry but I try the love yaaysya

Use the net to find the surface area of the pyramid

Answers

Answer:

56

Step-by-step explanation:

5ft x 4ft = 20ft / 2 = area =10     10 x 4 triangles = 10 x 4 = 40 + square= area, so 4 x 4 = 16 + 40 = 56ft

Hope this helps!

mr. jaw needs 1 bag of sand for every 5 square feet of the sandpit. of bags of sand cost $8 each, about how much will mr. jaw spends on sand use ~ 3.14

Answers

Answer:

$125.60

Step-by-step explanation:

3.14*5 = 15.7

15.7*$8 = $125.60

HOPE THIS HELPS!!!! <3333

-Silver

Maths homework volumes anyone can help?

Answers

Answer:

1) Volume of cuboid =l * b*h9.7*1.8*2.5=43.65 2a =......

Step-by-step explanation:

look at the diagram .the third is complete and the Instruction says they all have same volume so :2.5 *8*9 = 180.definitely the volume for each of the cuboid is 180. Volume of cubiod = l*b*ha)180 = 4*5*a 180 = 20a180/20 = 20a/20a= 9

b) 180 = 6*6 *b 180 = 36b b= 180/36 b= 5

c) 180= 2.5 *9*c 180 = 22.5 *cc=180/22.5c=8 I don't know 3and 4pls mark me brainlest I need it dearly

A manager records the number of projects employees complete in one month. If the manager wants to summarize the data, which two statements are true?

The manager should use a measure of center to summarize how many projects the employees that complete the least projects complete.
The manager should use a measure of center to summarize how the number of projects employees complete differs.
The manager should use a measure of center to summarize the typical number of projects an employee completes.
The manager should use a measure of variability to summarize how the number of projects employees complete differs.
The manager should use a measure of variability to summarize the typical number of projects an employee completes.

Answers

Answer:

The manager should use a measure of center to summarize how many projects the employees that complete the least projects complete.

Step-by-step explanation:

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