Answer:
(x-3)(x+i)(x-i)
Step-by-step explanation:
[tex]x^3-3x^2+x-3[/tex]
We apply grouping method
We group first two terms and last two terms
[tex](x^3-3x^2)+(x-3)[/tex]
Take out GCF x^2 from first group. Also take out 1 from second group
[tex]x^2(x-3)+1(x-3)[/tex]
[tex](x-3) (x^2+1)[/tex]
Now we factor x^2 + 1
We use difference of square formula
a^2 - b^2 = (a+b)(a-b)
x^1 + 1 can be written as [tex]x^2 - (-1)[/tex], the value of -1 is i^2
[tex]x^2 +1 = x^2 -(-1) = x^2 - i^2[/tex]
x^2 - i^2 = (x+i)(x-i)
Final answer is (x-3)(x+i)(x-i)
The complete factorization of the polynomial x^3 - 3x^2 + x - 3 is (x - 3)(x^2 + 1). The process involves grouping and factoring out common terms.
The question asks for the complete factorization of the polynomial x^3 - 3x^2 + x - 3. To factor this polynomial, we are looking for factors of the lowest possible order that will multiply together to give us the original polynomial. Let's first look for a common factor in all the terms. In this case, there isn't a common factor except for 1, so we move on to finding factors through other means such as grouping.
We can attempt to group terms to facilitate the factoring process:
First, consider the polynomial in two parts (x^3 - 3x^2) and (x - 3).Within the first group (x^3 - 3x^2), we can factor out an x^2, which gives us x^2(x - 3).The second group is already in the form (x - 3), mirroring the (x - 3) factor we found in the first group.We then combine these to get the full expression x^2(x - 3) + (x - 3).Next, we can factor out the common (x - 3) term from both groups, obtaining (x - 3)(x^2 + 1).The polynomial x^3 - 3x^2 + x - 3 can now be expressed as the product of (x - 3) and (x^2 + 1). This represents the polynomial in its factored form using real coefficients.
What side lengths should be used to model a rectangle with an area of x2 + 3x – 10 square units?
x – 5 and x + 2
x – 2 and x + 5
x and x + 3
x + 3 and x – 10
The side lengths of the rectangle are (x - 2) and (x + 5)
What are areas?The area of a shape is the amount of space on the shape
The area of the rectangle is given as;
[tex]Area = x^2 + 3x - 10[/tex]
Expand the expression
[tex]Area = x^2 + 5x - 2x - 10[/tex]
Factorize the expression
[tex]Area = x(x + 5) - 2(x + 5)[/tex]
Factor out x + 5
[tex]Area = (x - 2)(x + 5)[/tex]
Hence, the side lengths of the rectangle are (x - 2) and (x + 5)
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The side lengths that model a rectangle with an area of x^2 + 3x – 10 are x + 5 and x – 2, obtained by factoring the quadratic expression.
Explanation:To find the side lengths of a rectangle that model an area of x2 + 3x – 10 square units, we need to factor this quadratic expression. Factoring involves finding two binomials that when multiplied together, give the original quadratic expression. The factors of -10 that add up to 3 (the coefficient of the middle term) are 5 and -2. Therefore, the factored form of x2 + 3x – 10 is (x + 5)(x – 2), meaning the side lengths that can be used to model this rectangle are x + 5 and x – 2.
if i need 5 tomatoes to feed 7 people, how many tomatoes do i need to feed 100 leople
Rewrite the equation so that y is a function of x 5y-2x=15
Alex is saving money because she would like to purchase the new video gaming system that everyone has been talking about. After two weeks of saving, she had $47. After 24 weeks of saving, she had $430. Approximately how many dollars per week did Alex save on average between weeks 2 and 24?
Divide and write the result in standard form: 3-i/1+5i
A. 1/13 +8/13i
B. -1/13+8/13i
C. 1/13-8/13i
D. -1/13-8/13i
Final answer:
The division of the complex numbers (3 - i) by (1 + 5i) results in the standard form -1/13 - 8/13i, by multiplying both the numerator and denominator by the conjugate of the denominator. The correct answer is option D.
Explanation:
To divide the complex number 3 - i by 1 + 5i, we should multiply numerator and denominator by the conjugate of the denominator to get rid of the imaginary part in the denominator:
Multiply both top and bottom by the conjugate of the denominator, which is 1 - 5i.(3 - i) * (1 - 5i) = 3 - 15i - i + 5i2
Since i2 = -1, it simplifies to:
3 - 16i - 5 = -2 - 16i
(1 + 5i) * (1 - 5i) = 1 - 5i + 5i - 25i2
Similarly, it simplifies to:
1 + 25 = 26
Divide the top result by the bottom result:(-2 - 16i) / 26 = -2/26 - 16i/26
Simplify the fractions:
-1/13 - 8/13i
The standard form of the result is -1/13 - 8/13i, which corresponds to option D.
Pablo is a technical writer who works 7.5 hours per day. He spends twice as much time on writing tasks as he does on other work tasks. How much time per day does he spend on writing tasks?
Which value represents |7.8|?
The value of |7.8| is 7.8 because the absolute value of a number is the non-negative value of that number without regard to its sign.
The student has asked what the value of |7.8| is. The absolute value, denoted by the vertical bars, refers to the distance of a number from zero on the number line without considering direction. Therefore, the absolute value of 7.8 is 7.8 itself, regardless of any negative sign. It's because the absolute value of a positive number is the number itself, and the absolute value of a negative number is the positive version of that number.
Gordon Rosel went to his bank to find out how long it will take for $2,500 to amount to $3,090 at 6% simple interest. Calculate the number of years. (Round time in years to the nearest tenth.)
A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "Seven-eighths of my cats plus five." How many cats does the nemesis have?
The question presents a riddle that can be solved by setting up and solving an algebra equation. Based on the provided information, the solution to the problem is that the nemesis has 40 cats.
Explanation:The problem describes a riddle: "Seven-eighths of my cats plus five." This scenario is a typical mathematical representation of an algebra problem where you need to find the total number of cats.
Let us denote the total number of cats as 'C'. According to the riddle, 7/8 of the cats plus 5 equals the total cats. As per this, the equation can be written as 7/8*C + 5 = C. Solving this will lead us to find the number of cats.
Subtract 7/8*C from both sides of the equation: 5 = C - 7/8*C, which simplifies into: 5 = 1/8*C. To solve for 'C', we then multiply both sides of the equation by 8: 5*8 = C. Hence, the nemesis has 40 cats.
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which rate converts to a unit rate of 65 miles per hour
845,001 rounded to the nearest ten thousand
Answer:
850,000
Step-by-step explanation:Meow
The planet Mars has two moons – Phobos and Deimos. Phobos has a mass of 10.8 × 1015 kilograms, and Deimos has a mass of 2.0 × 1015 kilograms. How much greater is the mass of Phobos than the mass of Deimos?
Answer:
mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.
Step-by-step explanation:
The planet Mars has two moons Phobos and Deimos.
Mass of Phobos = 10.8 × 10¹⁵ Kilograms
Mass of Deimos = 2 × 10¹⁵ Kilograms
So the difference in the masses of the moons
= 10.8 × 10¹⁵ - 2 × 10¹⁵
= (10.8 - 2) × 10¹⁵
= 8.8 × 10¹⁵ Kilograms
Therefore, mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.
the length of a banquet table is 3 feet longer than 5 times it's width. if the perimeter is 54 feet. What are the dimensions of the table?
elizabeth plans to hand out door prizes as the guest arives. every 6th guest will receive a mug and every 9th guess will receive a t shirt . Elizabeth believe that the 12th guess will both receive a t shirt and a mug . is she correct or incorrect. show your work and explain your reasoning
The formula d = rt gives the distance traveled in time t at rate r. A bicyclist rides for 1.5 hours and travels 25 miles.
What was her average speed?
Answer:
16 2/3
Step-by-step explanation:
The bicyclist's average speed was 16.67 miles per hour
The student asks about the average speed of a bicyclist who traveled for 1.5 hours and covered 25 miles. The average speed can be found using the formula v = d/t, which suggests speed (v) equals distance (d) divided by time (t). To solve for the bicyclist's average speed, we'll insert the given values into the formula.
Here's the step-by-step calculation:
Identify the given variables: d = 25 miles and t = 1.5 hours.
Substitute the values into the formula: v = 25 miles / 1.5 hours.
Calculate the quotient to find the average speed: v = 16.67 miles per hour (rounded to two decimal places).
Therefore, to find the bicyclist's average speed, divide the distance traveled, 25 miles, by the time spent, 1.5 hours, which yields an average speed of 16.67 miles per hour.
Alan bought 3 pencils and a notebook. The notebook cost $6, and he spent a total of $12. How much did each pencil cost? Use p to represent the cost of each pencil. A. ; each pencil cost $2.50. B. ; each pencil cost $1.50. C. ; each pencil cost $2. D. ; each pencil cost $2.
Cost of each pencil will be $2
What is Linear Equation ?A linear equation is an equation in which the highest power of the variable is always 1 .
Number of pencil bought = 3
Number of notebook bought = 1
Cost of each notebook = $6
Cost of each pencil = ? let say its = x
Total money spent = $12
according to question , linear equation will be :
3* (x) + 1 * (6) = 12
3x = 6
x = 2
cost of each pencil will be $2
answer is d) $2
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Using simple linear regression, calculate the trend line for the historical data. say the x axis is april = 1, may = 2, and so on, while the y axis is demand. (round your intercept value to the nearest whole number and slope value to 2 decimal places.
Round 915 to the nearest ten
write an equation of the circle that is tangent to both axes with radius sqrt5 and center in quadrant 3
He total cost (in dollars) of producing xx coffee machines is c(x)=2300+40x−0.9x2. c(x)=2300+40x−0.9x2. (a) find the exact cost of producing the 21st machine.
$2743.1 .
Cost of producing 21st machine = $2743.1 .
What is function?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input.When f and its derivatives are substituted into the equation, a solution is a function y=f(x) that satisfies the differential equation.The highest order of any derivative of the unknown function that appears in the equation is the order of a differential equation.Given function,
c(x)=2300+40x−0.9x².
To find the cost of producing the 21st machine,
We have to find c(21).
c(21) = 2300+40(21)−0.9(21)²
= 2300 + 840 - 0.9 x 441
= 2300 + 840 - 396.9
= $2743.1
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Final answer:
To find the exact cost of producing the 21st coffee machine, substitute x = 21 into the given cost function, resulting in a cost of $2743.1.
Explanation:
The question asks for the exact cost of producing the 21st coffee machine given the cost function c(x) = 2300 + 40x - 0.9x². To find this, we substitute x = 21 into the cost function.
First, let's plug in x = 21 into the cost function:
c(21) = 2300 + 40(21) - 0.9(21²)c(21) = 2300 + 840 - 0.9(441)c(21) = 3140 - 396.9c(21) = 2743.1Therefore, the exact cost of producing the 21st machine is $2743.1.
please help!!ASAP!!!!!!!
Simplify 2(x + y) + 3(x + y)
0.059 seconds into milliseconds
0.059 seconds is equal to 59 milliseconds.
Explanation:Unit conversion is the process of changing the measurement units of a quantity from one system to another. It is essential for comparing and working with measurements expressed in different units. Common examples include converting between metric and imperial units for length (e.g., meters to feet) or weight (e.g., kilograms to pounds).
Accurate unit conversion is crucial in fields like science, engineering, and international trade.Thus for the given case, 0.059 seconds is equal to 59 milliseconds.
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What is 265888 rounded to nearest ten thousands
how do i solve it 1.2c=0.6
If A=4-3i, M=-4+i, S=i, and$P=2, find A-M+S-P.
Please help!
The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
As per the given values,
A=4-3i, M= -4+i, S=i, and P=2
Put the above values into A - M + S - P as
4 - 3i - (-4 + i) + i - 2
⇒ 4 - 3i + 4 - i + i - 2
⇒ 4 - 2 + 4 - 3i
⇒ 6 + 3i
Hence "The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i".
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41>6m-7 help please
An animal shelter that only cares for cats and dogs has 8 fewer dogs than cats. The animal shelter has 12 dogs.
Use the five-step problem-solving plan.
How many cats are at the animal shelter?
The expression -3m - [2m + (5 - m)] + 7 was simplified as 2 - 4m.
Question: The expression -3m - [2m + (5 - m)] +7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.
Answer may include:
If the expression has been simplified correctly, then the expressions will be equivalent.
The expressions will have the same value when numbers are substituted in for the variable m.
Choose a value for m and substitute in to both expressions.
Simplify each expression using the order of operations and show they are the same value.
The given expression is simplified correctly.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is -3m-[2m+(5-m)]+7
= -3m-2m-5+m+7
= (-3m-2m+m)-5+7
= -4m+2
= 2-4m
Hence, the given expression is simplified correctly.
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"Your question is incomplete, probably the complete question/missing part is:"
The expression -3m-[2m+(5-m)]+7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.
sophia used 1/3 of an ounce of cheese to make 1/12 of a pound of pizza dough. How many ounces of cheese are needed to amke a pound of pizza dough