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Nastasia [14]
3 years ago
7

Let x^2 +11x=3 ​.

Mathematics
2 answers:
Mashutka [201]3 years ago
5 0

We have been given an equation x^2 +11x=3. We are asked to complete the square for the given equation.

To complete the square for our given equation, we need to add the half the square of x term on both sides.

We can see that coefficient of x term is 11, so we need to add half the square of 11 on both sides.

(\frac{11}{2})^2  

Let us simplify (\frac{11}{2})^2.

\frac{11^2}{2^2}=\frac{121}{4}

Upon adding \frac{121}{4} on both sides, we will get:

x^2 +11x+\frac{121}{4}=3+\frac{121}{4}

Now we will make a common denominator for right side.

x^2 +11x+\frac{121}{4}=\frac{12}{4}+\frac{121}{4}

x^2 +11x+\frac{121}{4}=\frac{133}{4}

Therefore, our equation would be x^2 +11x+\frac{121}{4}=\frac{133}{4}.

tensa zangetsu [6.8K]3 years ago
3 0
The answer is x^2+11x+(121/4)=(143/4)

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I believe that the answer to the question would be 4.5
5 0
3 years ago
Find the smallest positive integer k such that 3240/k is a square number
sashaice [31]

Answer:

10

Step-by-step explanation:

First, factorize the number 3,240:

3,240=2\cdot 1,620=2\cdot 2\cdot 810=2\cdot 2\cdot 2\cdot 405=2\cdot 2\cdot 2\cdot 2\cdot 5\cdot 81=2^3\cdot 5\cdot 9^2

So,

3,240=2^2 \cdot 2\cdot 5\cdot 9^2=18^2\cdot 10

Now consider the fraction

\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{k}

If k = 10, then

\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{10}=18^2

is a square number.

For all k < 10, the fraction tex]\dfrac{3,240}{k}[/tex] is not a square number (this follows from factorization).

Or you can simply check the values of the fraction for all k < 10:

  • k = 1, \dfrac{3,240}{1}=3,240 is not a square number;
  • k = 2, \dfrac{3,240}{2}=1,620 is not a square number;
  • k = 3, \dfrac{3,240}{3}=1,080 is not a square number;
  • k = 4, \dfrac{3,240}{4}=810 is not a square number;
  • k = 5, \dfrac{3,240}{5}=648 is not a square number;
  • k = 6, \dfrac{3,240}{6}=540 is not a square number;
  • k = 7, \dfrac{3,240}{7} is not a square number;
  • k = 8, \dfrac{3,240}{8}=405 is not a square number;
  • k = 9, \dfrac{3,240}{9}=360 is not a square number.
5 0
3 years ago
The population of coyotes in the northwestern portion of Alabama is given by the formula p (t )equals (t squared plus 100 )ln (t
elena-14-01-66 [18.8K]

Answer:

The rate of change of the Coyote population in 2002 is 32

Step-by-step explanation:

Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2

The formula is given as;

P(t) = (t^2 + 100) ln (t + 2)

The rate of change refers to the first integral of the formula;

Thus we need to calculate this by the use of product formula;

The first differential of t^2 + 100 is 2t

while that of ln(t + 2) is 1/(t + 2)

P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)

Now, we substitute 2 for the value of t here.

P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))

P’(2) = 4 ln 4 + 104(1/4)

P’(2) = 4ln 4 + 26

P’(2) = 5.55 + 26 = 31.55 which is approximately 32

8 0
3 years ago
Peter says if you subtract 13 from my number and multiply the difference by -6, the result is -42. What is Peters's number?
qwelly [4]
I think the answer is 20, may be wrong tho
3 0
3 years ago
Read 2 more answers
Help plss I only need 5
pochemuha

Answer:

Acute scalene triangle

Step-by-step explanation:

The triangle is acute because all of the angles are less than 90 degrees.

It is scalene because the 3 sides are all different lengths.

4 0
3 years ago
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