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slava [35]
3 years ago
14

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 t imes the l

argest integer?
Mathematics
2 answers:
givi [52]3 years ago
7 0
The answer is x= 5 
Hope this helps!
frozen [14]3 years ago
6 0
Consecutive positive integers will be three numbers right in a row on the number line.

x= 1st integer
x+1= 2nd integer
x+2= 3rd integer

product= multiply
less than= subtraction
is= equal sign


FIRST INTEGER
(x)(x + 1)= (5)(x + 2) - 5
multiply both sets of parentheses 1st

(x*x) + (x*1)= (5*x) + (5*2) - 5
multiply within parentheses

x^2 + x= 5x + 10 - 5
combine like terms

x^2 + x= 5x + 5
subtract 5x from both sides

x^2 - 4x= 5
subtract 5 from both sides

x^2 - 4x - 5= 0
factor

(x + 1)(x - 5)= 0
set each parentheses equal to 0

x + 1= 0
x= -1

x - 5= 0
x= 5 first integer

***since the integers are positive, x has to be equal to 5, not -1

SECOND INTEGER
= x + 1
= 5 + 1
= 6 second integer

THIRD INTEGER
= x + 2
= 5 + 2
= 7 third integer


ANSWER: The smallest of three consecutive positive integers is 5.

Hope this helps! :)

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Factor the polynomial, x2 + 5x + 6
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Answer:

Choice b.

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Step-by-step explanation:

The highest power of the variable x in this polynomial is 2. In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to 0.)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to 0. The discriminant of this polynomial is (5^{2} - 4 \times 1 \times 6) = 1.

\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}.

Similarly:

\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}.

By the Factor Theorem, if x = x_{0} is a root of a polynomial, then (x - x_0) would be a factor of that polynomial. Note the minus sign between x and x_{0}.

  • The root x = -2 corresponds to the factor (x - (-2)), which simplifies to (x + 2).
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Verify that (x + 2)\, (x + 3) indeed expands to the original polynomial:

\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}.

4 0
2 years ago
What’s the answer ????
Temka [501]

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0.16*100 = 16 which would allow us to say 16/100

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I used the area calculators on Goggle

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