How to factor 16x²-72xy+81y²

Answers

Answer 1

Answer: $16x^2-72xy+81y^2=(4x)^2-2\cdot4x\cdot9y+(9y)^2=(4x-9y)^2\n\n=(4x-9y)(4x-9y)\n\n\n\n(a-b)^2=a^2-2ab+b^2$

Answer 2

Answer: use the perfect square trinomial method. since 16x² is a perfect square and so is 81y² your answer would be (4x-9y)² when u multiply that out it will give u 16x²-72xy+81y²

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What is another way to say 345 centimeters?345 mm
345 cm
34.5 dl
345 cg

Answers

non of them are right unless u ment 3450 mm or u could say 3.45 meters

Answer:

3450 mm

Step-by-step explanation:

Andres bought a 5-kilogram can of peanuts for $10.55. What is the unit price?

Answers

$2.11 would be the price for a 1 kilogram can of peanuts if that is the kind of answer you are looking for :))

What are the solutions of x^2 - 5x+7 = 0 ?

Answers

Answer:

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=(-b\pm√(b^2-4ac) )/(2a)$

Algebra II

Imaginary Roots: √-1 = i

Step-by-step explanation:

Step 1: Define

x² - 5x + 7 = 0

Step 2: Identify Variables

a = 1

b = -5

c = 7

Step 3: Find solutions

Substitute [Quad Formula]: $x=(5\pm√((-5)^2-4(1)(7)) )/(2(1))$
Evaluate Exponents: $x=(5\pm√(25-4(1)(7)) )/(2(1))$
Evaluate Multiplication: $x=(5\pm√(25-28) )/(2)$
Evaluate Subtraction: $x=(5\pm√(-3) )/(2)$
Factor: $x=(5\pm√(-1) √(3) )/(2)$
Simplify: $x=(5\pm i√(3) )/(2)$

The solutions to the equation x² - 5x + 7 = 0 are:

x = (5 + i√3) / 2 or x = (5 - i√3) / 2

Option C is the correct answer.

We have,

To find the solutions of the quadraticequation x² - 5x + 7 = 0, we can use the quadraticformula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, the coefficients are:

a = 1

b = -5

c = 7

Substituting these values into the quadraticformula,

x = (-(-5) ± √((-5)² - 4(1)(7))) / (2(1))

Simplifying further:

x = (5 ± √(25 - 28)) / 2

x = (5 ± √(-3)) / 2

Since the discriminant (the value inside the square root) is negative, √(-3) is imaginary, meaning there are norealsolutions to this quadratic equation.

The solutions exist in the complex number system.

So,

√-1 = i

x = (5 ± i√3) / 2

This can be written as,

x = (5 + i√3) / 2

and

x = (5 - i√3) / 2

Thus,

The solutions to the equation x² - 5x + 7 = 0 are:

x = (5 + i√3) / 2 or x = (5 - i√3) / 2

Learn more about solutionsofequations here:

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The gross salary was increased twice during the year. First by 8%, then again by 10%.Its final amount was 10,098. Calculate the amount of the original gross salary.

Answers

Answer:

$8,500

Step-by-step explanation:

Let the original gross salary be "X" dollars.

First, it was increased by 8%, which can be calculated as 1.08 times the original salary:

1.08 * X

Then, this new amount was increased by 10%, which can be calculated as 1.10 times the previous amount:

1.10 * (1.08 * X)

The final amount is given as $10,098:

1.10 * 1.08 * X = 10,098

Now, solve for X:

1.188 * X = 10,098

Divide both sides by 1.188 to find X:

X = 10,098 / 1.188

X ≈ 8,500

So, the original gross salary was approximately $8,500.

In ΔOPQ, p = 180 inches, q = 120 inches and ∠O=171°. Find the length of o, to the nearest inch.

Answers

Given:

In ΔOPQ, p = 180 inches, q = 120 inches and ∠O=171°.

To find:

The length of o, to the nearest inch.

Solution:

According to cosine formula,

$a^2=b^2+c^2-2bc\cos A$

Using cosine formula in ΔOPQ, we get

$o^2=p^2+q^2-2pq\cos O$

On substituting the values, we get

$o^2=(180)^2+(120)^2-2(180)(120)\cos (171^\circ)$

$o^2=32400+14400-43200(-0.9877)$

$o^2=46800+42668.64$

$o^2=89468.64$

Taking square root on both sides.

$o=√(89468.64)$

$o=299.113$

$o\approx 299$

Therefore, the length of o is about 299 inches.

Answer:299

Step-by-step explanation:

You deposit 350 in an account that pays 3% annual intrest. Find the balance afer 2 years if the intrest is compounded

Answers

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \n\n A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\n P=\textit{original amount deposited}\dotfill &\$350\n r=rate\to 3\%\to (3)/(100)\dotfill &0.03\n n= \begin{array}{llll} \textit{times it compounds per year}\n \textit{annually, thus once} \end{array}\dotfill &1\n t=years\dotfill &2 \end{cases} \n\n\n A=350\left(1+(0.03)/(1)\right)^(1\cdot 2)\implies A=350(1.03)^2\implies A=371.315$

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