Final answer:
The quotient when dividing 6x³ + 13x² + x - 2 by x - 1 is 6x² + 19x + 20, and the remainder is 18. This solution can be found using synthetic division.
Explanation:
The question asks to find the quotient and remainder when the polynomial 6x³ + 13x² + x - 2 is divided by x - 1. To solve this, we can use polynomial long division or synthetic division. As the divisor is in the form of x - a, where a is 1, synthetic division is a streamlined approach.
We set up our synthetic division with 1 as our key number outside the division symbol and the coefficients of our polynomial (6, 13, 1, -2) inside:
Bring down the 6.
Multiply 1 by 6 to get 6, add this to the next coefficient 13 to get 19.
Continue the process: Multiply 1 by 19 to get 19, add this to 1 to get 20.
Repeat: Multiply 1 by 20 to get 20, add this to -2 to get 18.
The numbers now inside the division symbol represent the coefficients of the quotient polynomial, giving us 6x² + 19x + 20 with a remainder of 18. Therefore, the quotient is 6x² + 19x + 20, and the remainder is 18.
A quantitative variable that has a finite or countable number of values is called
A quantitative variable with a countable number of values is known as a discrete variable, which includes whole number counts such as the number of yellow M&Ms or total M&Ms in a sample
A quantitative variable that has a finite or countable number of values is called a discrete variable. Quantitative discrete data such as the number of phone calls received each day can only take certain numerical values, which are typically integers like zero, one, two, or three. This is different from continuous data, which can take any value within a certain range, like weight or percentage values that can include fractions and decimals.
For example, in the case of counting M&Ms, the number of yellow M&Ms and the total number of M&Ms would be discrete data because they can only be whole numbers. In contrast, the weight of the M&Ms in ounces and the percentage that are red are examples of continuous data because these can take on any value, including fractions, within the range.
The distinction between discrete and continuous data is important for selecting appropriate statistical methods for analysis, as certain methods are more suitable for discrete data, while others are better for continuous data
What is the value of x?
A. 68°
B. 62°
C. 112°
D. 124
If 3 is added to twice a number and this sum is multiplied by 2, the result is the same as if the number is multiplied by 3 and 4 is added to the product. what is the number?
The unknown number(n) is equal to - 2 satisfying asked statement.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the unknown number be 'n'.
Given, If 3 is added to twice a number,
and this sum is multiplied by 2,
the result is the same as if the number is multiplied by 3
and 4 is added to the product.
∴ (2n + 3)×2 = n×3 + 4.
4n + 6 = 3n + 4.
4n - 3n = 4 - 6.
n = - 2.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ5
What equation do you use to find average speed?
what is the light from a lazer pointer a point, line, line segment, ray or plane?
jackson wants to divide 3\4 pound box of trail mix into small bags each of the bags will hold 1/12 pound of trail mix how many bags of trail mix can jackson fill
There are 5 participants in a potato sack race. find the number of orders in which the participants can finish
5 x 4 x 3 x 2 x 1 = 120
120 different ways
the greatest common factor of 162, 378, and 414
Which function is a quadratic function
Answer:
[tex]p(x)=-5x-x^2[/tex]
C is correct
Step-by-step explanation:
Quadratic function: A polynomial whose degree is 2 called quadratic function.
Degree = It is highest power of the polynomial.
We have to check the degree of each option.
Option 1: [tex]c(x)=6x+3x^3[/tex]
Degree = 3
Option 2: [tex]d(x)=x-8x^4[/tex]
Degree = 4
Option 3: [tex]p(x)=-5x-x^2[/tex]
Degree = 2
Option 4: [tex]k(x)=2x^2+9x^4[/tex]
Hence, [tex]p(x)=-5x-x^2[/tex] has degree 2. It would be quadratic function.
Suppose the measure of an angle is 67 degrees what is the measure of its complementary angle
PLEASE HELP! What is the equation of this line? y = 2x y=−12x y=12x y=−2x Graph of a line passing through the origin and the point begin ordered pair 2 comma 4 end ordered pair
we know that
The line passing through the origin [tex](0,0)[/tex] and the point [tex](2,4)[/tex]
If the equation of the line passes through the origin
then
the equation of the line represent a direct variation
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
The constant k is equal to the slope m
with the point [tex](2,4)[/tex] find the constant of proportionality k
[tex]y/x=k[/tex]
substitute
[tex]4/2=k[/tex]
[tex]k=2[/tex]
The linear equation is equal to
[tex]y=2x[/tex]
therefore
the answer is
[tex]y=2x[/tex]
The required equation of the line passing through the origin and point (2, 4) is y = 2x.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
Given, a line passes through origin (0, 0) and point (2, 4).
So slope is = (y₂ - y₁)/(x₂ - x₁) = (4 - 0)/(2 - 0) = 2.
Let the required equation of the line be y = mx + b.
∴ 4 = 2×2 + b.
b = 0.
So, the equation is y = 2x + 0 ⇒ y = 2x.
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ2
ana made 12 rainbow loom bracelets in 3 hours. how many can she make in 15 hours
Mr. johnson earns $100,000 per year. each year he spends $70,000 and saves $30,000. he pays a 5 percent sales tax on all of his spending. assuming this is the only tax he pays, his average tax rate out of his income is
Average tax rate out of Mr. Johnsons earning is equals to $3500.
What is tax rate?
" Tax rate is the process of finding the percentage of amount of earnings to be taxed."
According to the question,
Given,
Total money earned by Mr. Johnson per year = $100,000
Every year amount he spend = $70,000
Every year amount he saved = $30,000
Percentage of sales tax on his spending paid by Mr. Johnson = 5%
Average tax rate = 70,000 × ( 5 / 100)
= $3,500
Hence, average tax rate out of Mr. Johnsons earning is equals to $3500.
Learn more about tax rate here
https://brainly.com/question/24734294
#SPJ2
Which algebraic expression has no like terms?a.-x+4y-6x+9 B.-4x+y+4y C.-3xy-8+xy+y^2 D.-x+7+3xy-4y
Answer:D
Step-by-step explanation:
The area of a rectangle is 440 square inches. The length of the rectangle is 29 inches more than its width. What is the length of the rectangle?
the length of the rectangle is either -11 inches or 40 inches.
Let the length of the rectangle be L.Let the width of the rectangle be W.Given the following data;
Area of rectangle = 440 square inchesTranslating the word problem into an algebraic equation, we have;
[tex]L = W + 29[/tex]
To find the length of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
[tex]Area = L * W[/tex]
Substituting the values into the formula, we have;
[tex]440 = (W + 29) * W\\\\440 = W^{2} + 29W[/tex]
Rearranging the equation, we have;
[tex]W^{2} + 29W - 440 = 0[/tex]
W e would solve the quadratic equation by factorization;
[tex]W^{2} + 40W - 11W - 440 = 0\\\\W(W + 40) - 11(W + 40)\\\\(W + 40)(W- 11)[/tex]
Width, W = -40 0r 11 inches.
Next, we would find the length of the rectangle;
When Width, W = -40;
[tex]L = W + 29[/tex]
[tex]L = -40 + 29[/tex]
Length, L = -11 inches
When Width, W = 11;
[tex]L = W + 29[/tex]
[tex]L = 11 + 29[/tex]
Length, L = 40 inches
Therefore, the length of the rectangle is either -11 inches or 40 inches.
Find more information: https://brainly.com/question/16309520
express 3.01 as a mixed number
Answer:
3 1/100
hope this is helpful!
A rectangle has a length of 6cm by 8cm. Which is the length of a diagonal of the rectangle?
A.10cm
B.14cm
C.24cm
D.28cm
E.48cm
Answer:
Your answer would be A 10cm
I need help with the functions and graphing
hello i was trying to get the understanding on how is 4-6+6=4,,,,,,,my answer (4-6=2+6=8) but me being in high school i know its not that easy.... So someone please break it down please???
Which of the following best defines the two quantities that are measured to find the call rate of a phone company? The quantity of price measured in dollars depends on the quantity of time measured in minutes. The quantity of time measured in minutes depends on the quantity of price measured in dollars. The quantity of time measured in minutes depends on the quantity of speed measured in calls per minute. The quantity of speed measured in calls per minute depends on the quantity of time measured in minutes.
Answer:
A. the quantity of price measured in dollars depends on the quantity of time measured in minutes.
Step-by-step explanation:
The following best defines the two quantities that are measured to find the call rate of a phone company:
A. the quantity of price measured in dollars depends on the quantity of time measured in minutes.
In this way we can determine that how much money will it cost in dollars for each minute of phone call.
Is the function g(x)= - 6x– 5 6 linear or nonlinear?
Explain how to compare 0.7 and 5/8.
Write this number using digits: four million, ninety-eight thousand, seven hundred sixty-two
A copy machine makes 44 copies per minute. how long does it take to make 154 copies?
Final answer:
It takes 3.5 minutes for a copy machine to make 154 copies at a rate of 44 copies per minute.
Explanation:
To find out how long it takes for a copy machine to make 154 copies at a rate of 44 copies per minute, we need to perform a division calculation. First, we divide the total number of copies needed (154 copies) by the rate at which the machine produces copies, which is 44 copies per minute.
The calculation is as follows:
154 copies ÷ 44 copies per minute = 3.5 minutes.
This means it would take the copy machine 3.5 minutes to produce 154 copies.
The measure of a and the measure of b are complementary. the measure of a is 8 times the measure of
b. find the measurement of each angle.
A total of 308 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was three times the number of adult tickets sold. how many adult tickets were sold?
Follow below steps;
The student is asking how many adult tickets were sold for a school play if a total of 308 tickets were sold and the number of student tickets sold was three times the number of adult tickets sold. To solve this problem, we will use algebra to set up an equation.
Let's define x as the number of adult tickets sold. Since the number of student tickets is three times that amount, we can say that 3x represents the number of student tickets sold. The total number of tickets sold is the sum of adult and student tickets, which is given by the equation x + 3x = 308.
To find the value of x, we combine like terms:
x + 3x = 4x4x = 308x = 308 \/ 4x = 77Therefore, the number of adult tickets sold was 77.
-10x+5y=0 -4x-6y=54 find the solution of this system of equations
13(21−3a)=6−a
no solution
−1
0
all real numbers
Answer:
No solution hope this helps:)
Step-by-step explanation:
14+3x−7=7x+7−4x14+3x-7=7x+7-4x is always, sometimes or never true.
Find the middle term of ([tex]( x^{2}+2) ^{20}
[/tex]