1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna [14]
3 years ago
14

A) Show that 4x² -6x+9 is positive for all values real numbers x.

Mathematics
1 answer:
wolverine [178]3 years ago
7 0

Answer:

(4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

Step-by-step explanation:

a) Use the formula a²-2ab+b²= (a-b)² (You need to make squared expression because it is always positive)

Consider 4x² as a² and -6x=-2ab

4x²=a² a=2x  ab=3x 2x*b=3x

b=1.5

Express 4x² -6x+9= (4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

You might be interested in
PLEEEEEEEEEEEASE HELP
Artemon [7]

Step-by-step explanation:

5f

5 + n times of a number

3 0
3 years ago
Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, fin
BabaBlast [244]

Complete question is;

Multiple-choice questions each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.

Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.

P(WWWWC) =

Answer:

P(WWWWC) = 0.0819

Step-by-step explanation:

We are told that each question has 5 possible answers and only 1 is correct. Thus, the probability of getting the right answer in any question is =

(number of correct choices)/(total number of choices) = 1/5

Meanwhile,since only 1 of the possible answers is correct, then there will be 4 incorrect answers. Thus, the probability of choosing the wrong answer would be;

(number of incorrect choices)/(total number of choices) = 4/5

Now, we want to find the probability of getting the 1st 4 guesses wrong and the 5th one correct. To do this we will simply multiply the probabilities of each individual event by each other.

Thus;

P(WWWWC) = (4/5) × (4/5) × (4/5) × (4/5) × (1/5) = 256/3125 ≈ 0.0819

P(WWWWC) = 0.0819

4 0
3 years ago
[2 x 2(2 + 1)^2= please help
aleksandrvk [35]

Answer:

36x

Step-by-step explanation:

PEMDAS RULE

3 0
3 years ago
Rewrite 2 7/9 as a improper fraction
Alborosie
The answer would be 25/9 as a improper fraction
6 0
3 years ago
What is the correct symbol?
Nadusha1986 [10]

Answer:

Since 10/9 is greater than 1, multiplying by 10/9 makes the value larger

Step-by-step explanation:

Step 1: Solve the fraction

10/9 = 1.1112

Therefore 10/9 > 1

Step 2: Multiple the fraction by itself

10/9 x 10/9 = 100/81

Convert fraction to decimals

100/81 = 1.2345678901.....

1.234567901 > 1.1112

Therefore 10/9 x 10/9 is bigger than 10/9

3 0
4 years ago
Other questions:
  • Judy pays $29 for 8 gallons of gas and 2 bottles of water.carmen pays $45 for 12 gallons of gas and 4 bottles of water. How much
    8·1 answer
  • Which point is located at (Negative 3.5, Negative 4.5)? On a coordinate plane, point A is 3.5 units to the left and 4.5 units do
    15·2 answers
  • Find a positive angle less than one rotation that is coterminal with –308°.
    9·2 answers
  • True or False: In a uniform probability distribution, any random variable is just as likely as any other random variable to occu
    10·1 answer
  • Evaluate (if possible) the six trigonometric functions of the real number t. (if an answer is underfunded, enter UNDEFINED)
    5·1 answer
  • During the past month, you withdrew $22 from your savings account and then deposited $24. If your balance at the end of the mont
    5·1 answer
  • 5x ^ 2 + 2x + 11 - 7 + 4x - 2x ^ 2
    15·1 answer
  • Yo can i get some help no links or pictures only say the truth or get reported
    11·2 answers
  • - ALGEBRA In the figure, line m is
    15·1 answer
  • Select all expressions that are equivalent to 5x - 15 - 20x + 10.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!