MATHEMATICS HIGH SCHOOL

Given that x=1.5 is the only solution to the equation 4x^2 - ax + b = 0, find the values of a and b. Show all workings. Answer: a = 12, b = 9

Answers

Answer 1
Answer: If x = 1.5 is the only solution to the equation 4x² - ax + b =0 then

4x² - ax + b = 4(x - 1.5)²      |use p² - 2pq + q² = (p - q)²

4x² - ax + b = 4(x² - 2x · 1.5 + 1.5²)

4x² - ax + b = 4(x² - 3x + 2.25)

4x² - ax + b = 4x² - 12x + 9  |subtract 4x² from both sides

-ax + b = -12x + 9

therefore

-a = -12 ⇒ a = 12 and b = 9



Related Questions

MIDDLE SCHOOL

Help me solve this equation:
5X+7X+6-26=29
Thanks! I'll give 20 pts.

Answers

Answer: x = 49/12

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

5x+7x+6−26=29

5x+7x+6+−26=29

(5x+7x)+(6+−26)=29(Combine Like Terms)

12x+−20=29

12x−20=29

Step 2: Add 20 to both sides.

12x−20+20=29+20

12x=49

Step 3: Divide both sides by 12.

12x/12 = 49/12

Answer:

1.3

Step-by-step explanation:

5x+7x+6-26=29

12x-20=29

12x=29-20

12x=9

x=1.3

HIGH SCHOOL

A triangle’s first angle measure is 72∘. A triangle’s second angle measure is 44∘.
A triangle’s third angle measure is 64∘.

What triangle would this make?

Answers

An Acute triangle because none of the angels are above 90

MIDDLE SCHOOL

RATIOS (please help me please! I need the question in 5 hours) A food company that produces peanut butter decides to try out a new version of its peanut butter that is extra crunchy, using twice the number of peanut chuncks as normal. The company host a sampling of its new product at grocery stores and finds that 5 out of every 9 customers prefer that new extra crunchy version.


If the company normally sells a total of 90,000 containers of regular crunchy peanut butter, how many containers of new extra crunchy peanut butter should it produce, and how many containers of regular crunchy peanut butter should it produce? What would be helpful in solving this problem? Does one if our comparison statements above help us? (also know as the last question)

Answers

For every 9 customers that perfer extra crunchy there is 5 customers who like orignal, so that means...

9 can go into 9000 1, 000 times.
So It should be...
5 x 1, 000 = 5, 000.
They would probably need to make 5, 000.
Answer:REGULAR IS 40,000

EXTRA IS 50,000

(I HAD TO DO THIS IN SCHOOL TODAY)

Step-by-step explanation:

MIDDLE SCHOOL

Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boys survey it was determined that for every three boys who enjoyed soccer five boys enjoyed basketball. The girl's survey had a ratio of the number of girls who enjoy soccer to the number of girls who enjoy basketball of 7:1. If the same number of boys and girls were surveyed in 90 boys enjoy soccer how many girls enjoying each sport?

Answers

Using proportions, it is found that:

  • 210 girls enjoy soccer.
  • 30 girls enjoy basketball.

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

  • For every 3 boys that enjoyed soccer, 5 enjoyed basketball. Thus, of the boys enjoyed soccer, and enjoyed basketball.
  • 90 boys enjoy soccer, which is 3/8 of the total number of boys. Thus:

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

  • There are 240 boys.
  • The number of girls is also the same, 240.
  • The soccer:basketball ratio for girls means that of them enjoy soccer and basketball, thus:

  • 210 girls enjoy soccer.
  • 30 girls enjoy basketball.

A similar problem is given at brainly.com/question/17245640

Answer:

210 soccer and 30 enjoying basketball

Step-by-step explanation:

Given:  for every three boys who enjoyed soccer five boys enjoyed basketball. The girl's survey had a ratio of the number of girls who enjoy soccer to the number of girls who enjoy basketball of 7:1

To Find: If the same number of boys and girls were surveyed, 90 boys enjoy soccer how many girls enjoying each sport

Solution: For every 3 boys enjoying soccer = 5 boys enjoying basketball

    ratio  of boys enjoying soccer and basketball =  

    ratio  of girls enjoying soccer and basketball =  

    Now,

    let total number of boys enjoying sports =

    let total number of girls enjoying sports =

    Number of boys enjoying soccer =

    it is given that,

                            =

    total number of boys =

                                           =

  total number of girls enjoying sports = total number of boys enjoying                                                                 sports

    total number of girls enjoying sports =

    number of girls enjoying soccer  =  

                                                           =  

                                                           =  

    number of girls enjoying basketball  =  

                                                           =  

                                                           =  

number of girls enjoying soccer is and number of girls enjoying basketball is

HIGH SCHOOL

True or False?

Set A = { X | X is an even whole number between 0 and 2} = ∅

Answers

Here are examples of "even whole numbers:"  2, 4, 8, 12, 16, ...

X must be a whole number.  The only whole number between 0 and 2 is 1.  Unfortunately, that's not an even number.  Thus, Set A is "empty."  The given statement is FALSE.
It is false because 0and 2 and the middle number will be 1

MIDDLE SCHOOL

Approximately how many ounces are equivalent to 1 kilogram?

Answers

Answer: 35.27 oz

The answer is: The change of 1 kg ( kilogram ) unit for a weight and mass measure equals = into 35.27 oz ( ounce ) as per its equivalent weight and mass unit type measure often used.

MIDDLE SCHOOL

A map has a scale of 1/2 inch to 4 miles. The shortest distance between two cities on the map measures 8 inches. If d represents the shortest distance between the two cities, what is d? A. 16 mi.

B. 32 mi.

C. 64 mi.

D. 72 mi.

Answers

The answer would be C because for every 1 inch, would be 8 miles, so we then multiply the inches by 8 to get to 8 inches, so we then multiply the miles by 8 and we get 64 miles.

D = 64 mi.

Answer:

C

TOOK SAME TEST ON EDGE 2021

MIDDLE SCHOOL

How many 2s are 120

Answers

Answer: 2 can go into 120 60 times.

Step-by-step explanation:

120/2 = 60

Answer:

60

Step-by-step explanation:

s = 60

2s → 2*60=120

MIDDLE SCHOOL

Use mental math to find the value of 15/124*230/30divided by 230/124

Answers

If we are not allowed to use calculator, lets make some mental gymnastics!
take into account that dividing by a fraction is the same as multiplying by its inverse, that is changing numerator and denominator from one place another:
(15/124)(230/30)/(230/124)
= (15/124)(230/30)(124/230)
here we can see that 124 is in the denominator but in the numerator as well, so we can get rid of it altogether, the same reasoning for 230, so we simplify:
= (15/1)(1/30)(1/1)
= 15/30
= 1/2
that is the final result
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