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
Igoryamba
2 years ago
12

1. 3 (x + 1)2 - 3

Mathematics
1 answer:
Ipatiy [6.2K]2 years ago
4 0
A is 3
h is 1
k is -3
You might be interested in
How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

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

0 4x² - x

- 4x² - 4x

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

0 + 3x - 3

- 3x - 3

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

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
2 years ago
Help me...
katen-ka-za [31]
<h2>>> Answer </h2>

________

3y + 1 = 10

3y = 10 - 1

3y = 9

y = 9 ÷ 3

y = 3

6 0
2 years ago
Read 2 more answers
I am not sure of the answers​
astra-53 [7]

Answer: 2 3/4 as an improper fraction would be B. 11/4

7 0
3 years ago
Read 2 more answers
Y=2 Enter the solution (x, y) to the system of equations shown 7y+3x=5
AnnyKZ [126]

Answer:

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

Step-by-step explanation:

Put the given value of y into the equation and solve for x.

... 7·2 +3x = 5

... 3x = -9 . . . . . . subtract 14

... x = -3 . . . . . . . divide by the x-coefficient

The solution (x, y) is (-3, 2).

6 0
3 years ago
HELPP QUICK PLEAAE I NEED IT NOW NO LINKS NO BOTS I WILL REPORT !!Which of the following equations describes the line shown belo
exis [7]

Answer:

A. y - 6 = -7/4(x + 5) is the answer.

6 0
2 years ago
Other questions:
  • The sum of eight and a number is 100 what is the number?
    6·2 answers
  • How do you simplify 243 1/5
    6·1 answer
  • What is the range of the function y=2^x
    13·1 answer
  • On January 1t 2014, approximately 450 thousand buildings in the United Statcs (US) had sola panels. This number increased by a t
    11·1 answer
  • For each of the following situations, identify the response variable and the populations to be compared, and give
    12·1 answer
  • Please help Fast! I’d appreciate it! Correct answer I will mark brainlist!
    8·1 answer
  • (х-y)²-3(x-y) how do you factorise this equation?​
    6·1 answer
  • Which equation represents a line passing through the points (8, 16) and (-1,-11)?
    8·1 answer
  • Please help divide 10u^2− 4u/2u
    12·1 answer
  • 7 of 9
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!