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Alexxandr [17]
2 years ago
14

Can you please help me give the Complete solution (nonsence report )​

Mathematics
1 answer:
Tasya [4]2 years ago
7 0

\huge \boxed{\mathfrak{Question} \downarrow}

  • Factorise the polynomials.

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

__________________

<h3><u>1. x² + 4x + 4</u></h3>

{x}^{2}  + 4x + 4

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+4. To find a and b, set up a system to be solved.

a+b=4  \\ ab=1\times 4=4

As ab is positive, a and b have the same sign. As a+b is positive, a and b are both positive. List all such integer pairs that give product 4.

1,4  \\ 2,2

Calculate the sum for each pair.

1+4=5  \\ 2+2=4

The solution is the pair that gives sum 4.

a=2 \\  b=2

Rewrite x² + 4x + 4 as (x² + 2x) + (2x + 4)

\left(x^{2}+2x\right)+\left(2x+4\right)

Take out the common factors.

x\left(x+2\right)+2\left(x+2\right)

Factor out common term x+2 by using distributive property.

\left(x+2\right)\left(x+2\right)

Rewrite as a binomial square.

b. \:  \:  \boxed{ \boxed{{(x + 2)}^{2} }}

__________________

<h3><u>2. x² - 8x + 16</u></h3>

x ^ { 2 } - 8 x + 16

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+16. To find a and b, set up a system to be solved.

a+b=-8  \\ ab=1\times 16=16

As ab is positive, a and b have the same sign. As a+b is negative, a and b are both negative. List all such integer pairs that give product 16.

-1,-16  \\ -2,-8  \\ -4,-4

Calculate the sum for each pair.

-1-16=-17  \\ -2-8=-10  \\ -4-4=-8

The solution is the pair that gives sum -8.

a=-4  \\ b=-4

Rewrite x²-8x+16 as \left(x^{2}-4x\right)+\left(-4x+16\right).

\left(x^{2}-4x\right)+\left(-4x+16\right)

Take out the common factors.

x\left(x-4\right)-4\left(x-4\right)

Factor out common term x-4 by using distributive property.

\left(x-4\right)\left(x-4\right)

Rewrite as a binomial square.

d. \:  \:  \boxed{\boxed{\left(x-4\right)^{2} }}

__________________

<h3><u>3. 4x² + 12xy + 9y²</u></h3>

4 x ^ { 2 } + 12 x y + 9 y ^ { 2 }

Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=2x and b=3y.

e. \:  \: \boxed{ \boxed{\left(2x+3y\right)^{2} }}

__________________

<h3><u>4. x⁴ - 2x² + 1</u></h3>

x ^ { 4 } - 2 x ^ { 2 } + 1

To factor the expression, solve the equation where it equals to 0.

x^{4}-2x^{2}+1=0

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 1 and q divides the leading coefficient 1. List all candidates p/q.

± \: 1

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

x=1

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x⁴-2x²+1 by x-1 to get x³+x²-x-1. To factor the result, solve the equation where it equals to 0.

x^{3}+x^{2}-x-1=0

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -1 and q divides the leading coefficient 1. List all candidates p/q.

± \:  \: 1

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

x=1

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x³+x²-x-1 by x-1 to get x²+2x+1. To factor the result, solve the equation where it equals to 0.

x^{2}+2x+1=0

All equations of the form ax²+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 2 for b and 1 for c in the quadratic formula.

x=\frac{-2±\sqrt{2^{2}-4\times 1\times 1}}{2}  \\

Do the calculations.

x=\frac{-2±0}{2}  \\

Solutions are the same.

x=-1

Rewrite the factored expression using the obtained roots.

\left(x-1\right)^{2}\left(x+1\right)^{2}  \\  = a. \:  \:  \boxed{ \boxed{\left(x^{2}-1\right)^{2}}}

__________________

  • <em>Refer to the attached picture too.</em>

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Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace t
34kurt

Answer:

The probability is 0.0775

The expected value is 4.75 clubs

The standard deviation is 1.8875 clubs

Step-by-step explanation:

The variable X follows a binomial distribution, because we have n identical and independent events (19 cards) with a probability p of success and 1-p of fail (there is a probability of 1/4 to be club and 3/4 to be diamond, heart or spade). Then, the probability that x of the n cards are club is:

P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\P(x)=\frac{19!}{x!(19-x)!}*0.25^{x}*(0.75)^{19-x}

So, the probability P of drawing at least 8 clubs is:

P = P(8) + P(9) + P(10) + ... + P(18) + P(19)

Replacing, the values of x, from 8 to 19, on the equation above, we get:

P = 0.0775

Additionally, the expected value E(x) and standard deviationS(x) for this distribution is given by:

E(x)=np = 19(0.25) = 4.75

S(x)=\sqrt{np(1-p)} =\sqrt{19(0.25)(0.75)} =1.8875

8 0
3 years ago
What types of solutions does 6x^2 - 20x + 1 have?​
elena55 [62]

Answer:

2 real solutions

Step-by-step explanation:

We can use the determinant, which says that for a quadratic of the form ax² + bx + c, we can determine what kind of solutions it has by looking at the determinant of the form:

b² - 4ac

If b² - 4ac > 0, then there are 2 real solutions. If b² - 4ac = 0, then there is 1 real solution. If b² - 4ac < 0, then there are 2 imaginary solutions.

Here, a = 6, b = -20, and c = 1. So, plug these into the determinant formula:

b² - 4ac

(-20)² - 4 * 6 * 1 = 400 - 24 = 376

Since 376 is clearly greater than 0, we know this quadratic has 2 real solutions.

<em>~ an aesthetics lover</em>

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2 years ago
Find the slope of the following points. (-20,-4) (-12,-10)
beks73 [17]

m = −3/4 is the correct answer. Hope this helps!

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Max caught 43 lb of fish in one deep sea fishing trip the fish needed to be equally separated by weight into 5 packages to sell
solmaris [256]
43÷5=8.6   he would put 8.6 lb per bag
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3 years ago
Use the Perfect Square Trinomial and provide the first step to calculating 382 without a calculator.
dusya [7]

Answer:

(40-2)^2

Step-by-step explanation:

Given: (38)^2

To find: the correct option

Solution:

A binomial polynomial is a polynomial consisting of two terms.

A trinomial polynomial is a polynomial consisting of three terms.

On multiplying a binomial (x-y) to itself, a perfect square trinomial (x-y)^2 is obtained.

Here, 38=40-2

So, (38)^2=(38)(38)=(40-2)(40-2)=(40-2)^2

Here, (40-2) is a binomial and it is multiplied to (40-2) to get a perfect square trinomial (40-2)^2

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