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
worty [1.4K]
3 years ago
5

The expression $x^2 15x 54$ can be written as $(x a)(x b),$ and the expression $x^2 - 17x 72$ written as $(x - b)(x - c)$, where

$a$, $b$, and $c$ are integers. What is the value of $a b c$?
Mathematics
2 answers:
Natalka [10]3 years ago
7 0

Answer: a=6 b=9 c=8

Step-by-step explanation:

The problem consists of finding the roots of the quadratic equations:

x^2+15x+54=0\\

x^2-17x+72=0\\

The roots can be found with the following equation for solving quadratic equations:

x_{12}=\frac{-B\pm\sqrt{B^2-4AC}}{2A}  for equation: Ax^2+Bx+C=0

After solving the equations you can write the result as:

x^2+15x+54=(x+6)(x+9)\\

x^2-17x+72=(x-9)(x-8)

Naya [18.7K]3 years ago
7 0

Answer:

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

Question:

The expression $x^2 - 15x - 54$ can be written as $(x-a)(x-b),$ and the expression $x^2 - 17x + 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?

Step-by-step explanation:

To determine the values of a,b and c.

We need factorize the two equations.

i) x^2 -15x +54

x^2 -6x -9x +54

x(x-6) -9(x-6)

=(x-6)(x-9)

ii) x^2 -17x +72

x^2 -9x -8x +72

x(x-9) -8(x-9)

=(x-9)(x-8)

From the question:

Comparing

(x-a)(x-b) to (x-6)(x-9)

And

(x-b)(x-c) to (x-9)(x-8)

We can see that b is common in the two cases and also 9 is common in the two factorised equations.

So,

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

You might be interested in
68 is 100% of what number?
sweet [91]

Answer: 68

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The solutions of x^2= 16x-28
STALIN [3.7K]

Answer:

Simplifying

x2 = 16x + -28

Reorder the terms:

x2 = -28 + 16x

Solving

x2 = -28 + 16x

Solving for variable 'x'.

Reorder the terms:

28 + -16x + x2 = -28 + 16x + 28 + -16x

Reorder the terms:

28 + -16x + x2 = -28 + 28 + 16x + -16x

Combine like terms: -28 + 28 = 0

28 + -16x + x2 = 0 + 16x + -16x

28 + -16x + x2 = 16x + -16x

Combine like terms: 16x + -16x = 0

28 + -16x + x2 = 0

Factor a trinomial.

(2 + -1x)(14 + -1x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying

2 + -1x = 0

Solving

2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.

2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0

0 + -1x = 0 + -2

-1x = 0 + -2

Combine like terms: 0 + -2 = -2

-1x = -2

Divide each side by '-1'.

x = 2

Simplifying

x = 2

Subproblem 2

Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying

14 + -1x = 0

Solving

14 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-14' to each side of the equation.

14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0

0 + -1x = 0 + -14

-1x = 0 + -14

Combine like terms: 0 + -14 = -14

-1x = -14

Divide each side by '-1'.

x = 14

Simplifying

x = 14

Solution

x = {2, 14}

Step-by-step explanation:

I type fast lol

5 0
3 years ago
Read 2 more answers
Which list of angle measures could be the angle measures of a triangle?
Dovator [93]
Hello there! So the answer would be D: 35 degrees, 60 degrees and 85 degrees. We know this because angles in a triangle sum to 180 degrees. By simply adding each angle up, we can confirm that 35 + 60 + 85 = 180. :)
8 0
2 years ago
Yeah so can u answer this​
Rzqust [24]

Answer:

give me the points its c c c c c c cc c cc c c. c cc cccc c cc c cc

4 0
2 years ago
Read 2 more answers
HELPPPP I DONT KNOW THE ANSWER PLEASE HELP ME
lidiya [134]

Answer:

IM PRETTY POSITIVE ITS B

PLS MARK BRAINLIEST

SORRY IF IM WRONG :P

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • You and your friend share a paper route you can deliver 4 papers in one minute
    12·1 answer
  • The sum of a set of values is 84 and the mean is 6. how many values are there?
    10·1 answer
  • What is the difference of r+2/r+4 and 3/r+1?
    8·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bs%2B24%7D%7B7%7D" id="TexFormula1" title="\frac{s+24}{7}" alt="\frac{s+24}{7}" align
    9·1 answer
  • The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it i
    6·1 answer
  • 2. Three numbers whose product is 64 are 2, 4,
    12·2 answers
  • A butterfly population is decreasing at a rate of 0.82% per year. There are currently about 100,000 butterflies in the populatio
    7·1 answer
  • Tina has a pet sitting business. She charges a flat service fee of $30, plus $15 per day for each animal. If one of her customer
    7·2 answers
  • Deondre's baseball team is selling raffle tickets for a fundraiser. It cost them $105 to print the tickets. They set a goal to m
    13·1 answer
  • 3.5x + 197=494.50<br><br> Please answer this!!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!