Answer:
Step-by-step explanation:
A polynomial is a finite sum of terms in which all variables have whole number exponents and no variable appears in a denominator.
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The leading term in a polynomial is the term of highest degree.
The constant term in a polynomial is the term without a variable.
Polynomials: YES or NO
3x½
NO - exponent is not a whole number
polyd
NO - the variable is in the denominator
-3x2
YES - satisfies the polynomial definition
polyd1
NO - the square root of x can be written with a fractional exponent of x.
2x-3
NO - exponent is not a whole number.
Negative exponent places x3 in denominator.
polyrad3
YES - the exponent of x is 1 which is OK.
The coefficient being radical 3 is not a problem.
Classification by Terms
monomial
one term: 12, 4x, x2, -5xy
binomial
two terms: 2x - 1, x2 - 4
trinomial
three terms: x2 + 2x + 1
polynomial - one or more terms: polynomial means "many", but it can also be one term.
The ending of these words "nomial"
is Greek for "part".
Classification by Degree
Linear - degree of 1 or 0: 3x + 1 or 12
Quadratic - degree of 2: 2x2 - x + 7
Cubic - degree of 3: 3x3 + 4x2 + 3x + 5
definition The degree of a term with whole number exponents is the sum of the exponents of the variables, if there are variables. Non-zero constants have degree 0, and the term zero has no degree. Example: 6x2 has a degree of 2; 4x2y3 has a degree of 5 (the sum of 2 and 3).
definition
The degree of a polynomial is the highest degree of its terms.
Example: 3x2 + 4x + 1 has a degree of 2; x3 - x2 + 5x - 2 has a degree of 3
The standard form of a polynomial is when all like terms are combined and the degrees are arranged in descending order.
Polynomial: 2x + 3x5 + 4x3 - 8
Standard form: 3x5 + 4x3 + 2x - 8
3x5 + 4x3 + 2x1 - 8x0
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Will we ever really use the degree?
Knowing the "degree" of a polynomial function will let you determine the most number of solutions the function may have, and the most number of times the function will cross the x-axis.
FYI: The standard form of a polynomial is formally written as anxn + an - 1xn - 1 + ... + a2x2 + a1x + a0, where n is a non-negative integer, and a0, a1, a2, ..., an are real number constant coefficients with an ≠ 0.
bullet Polynomials and Closure:
Polynomials form a system similar to the system of integers, in that polynomials are closed under the operations of addition, subtraction, and multiplication.
CLOSURE: Polynomials will be closed under an operation if the operation produces another polynomial.
• Closure under Addition: (2x2 + 3x + 4) + (x2 - 5x - 3) = 3x2 - 2x + 1
When adding polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the sum has variables and exponents which are already classified as belonging to polynomials. Polynomials are closed under addition.
• Closure under Subtraction: (2x2 + 3x + 4) - (x2 - 5x - 3) = x2 + 8x + 7
When subtracting polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the difference has variables and exponents which are already classified as belonging to polynomials. Polynomials are closed under subtraction.
• Closure under Multiplication: (x + 1)(x2 + 4x + 3) = x3 + 5x2 + 7x + 3
When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. Remember that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under multiplication.
What about division?
Polynomials are NOT closed under division. Look at this simple counterexample:
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When dividing variables with exponents, there is the possibility of creating a negative exponent. Negative exponents are not allowed in polynomials.
Can someone tell me what I’m doing wrong
Answer:
In the key it states that each dot is 2 students. So when counting how many people have a foot size you have to account for the fact that each point represents two people
Step-by-step explanation:
In a diagram which of the following statements are false
Answer:
1 and 4 are vertical angles. thats false.
edit: nvm.
Start with the base. What is the approximate area of the base of the water tower? Use 3.14 for pi. Be sure to include units in your answer.
Answer: Pi times (25 squared)
Step-by-step explanation:
Answer:
it might be 78.5
Step-by-step explanation:
Which value of x is a solution of the inequality?
−2x<−18
Question 5 options:
x=8
x=32
x=2
x=−27
Answer: 8 is what I’m guessing but when I did the math I got 9 so I don’t know if I’m wrong or u put the wrong number
Step-by-step explanation:
This is the start of the question, thanks again!
10 POINTS! WILL GIVE BRAINLIEST! Write the Inequality! Thank you!
Freddie went to cover 72 miles riding his bike. so far he has covered 48 miles at minimum, how many more miles does Freddie need?
Answer:
24? Thats easy
Step-by-step explanation:
Answer:
24 that ez Ez im not sure
On Monday, the temperature at 10 a.m. at Sam’s house was –6° Fahrenheit. The
temperature at 2 p.m. at Sam’s house was 2° Fahrenheit. Which statement about the
change in temperature from 10 a.m. to 2 p.m. at Sam’s house is true?
Question 1 options:
The temperature decreased by 12° Fahrenheit.
The temperature decreased by 4° Fahrenheit.
The temperature decreased by 3° Fahrenheit.
The temperature decreased by 8° Fahrenheit.
Answer:
8
Step-by-step explanation:
to find the answer, subtract the second amount (2) from the first amount (-6), -6 - 2 = -8, the temperat decreased by 8
Evaluate each expression for the value given z/4;z=824
Answer:
their is no answer
Step-by-step explanation:
Cheddar cheese costs $4.25 per pound. Write an equation best represents y, the total cost of x pounds of cheddar cheese and type out your reason (justify) for your answer.
How do i find the answer??
Answer:
y=4.25x
Step-by-step explanation:
x will represent the number of pounds of cheddar that you have. so whatever the value of X is, 4.25 would be multiplied by X. This problem does not provide a value for x, but say you had 4 pounds of cheese (x=4), the problem would become y=4.25(4) because you would plug 4 in where x is.
4.25(4)= 17 and therefore Y would equal 17.
DO NOT EXPLAIN WILL GIVE BRAINLIEST
Answer:
D
Step-by-step explanation:
Has already given the answer
PLZ HELP MEEE I REALY NEED IT PLZ SHOW YOUR WORK I NEED THE WORK TO BE SHOWN!!!
Answer:
C
Step-by-step explanation:
if lettuce is 69 percent then you add that up to be equal to
Sam bought a new bicycle on sale that was originally $160 but was 20% off. He was also charged 6.5% sales tax. How much did Sam pay in total after the discount and tax?
dsjihgnvosjdiufabnvoilasdb ill give brainley
Answer:
-876 would be the right answer
Can someone please help me!?
WILL MARK BRAINLIEST :)
Answer:
Which question?
Step-by-step explanation:
PLZ HELP I NEED IT DONE
Answer:
2y+12
4(1/2y+3)
4(1/2y-4+7)
Step-by-step explanation:
I'm sure of it
Answer:
There are Three equivalents form are :
1. The first one
2. The fifth one
3. The sixth one
I will write it in below
Step-by-step explanation:
[tex]1. \: \: \: \: \: \: \: \: \: \: \: \: 4( \frac{1}{2} y - 4 + 7) \\ 2. \: \: \: \: \: \: \: \: \: \: \: \: 4( \frac{1}{2} y + 3) \\ 3. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2y + 12[/tex]
The best unit of measure for the liquid in an eyedropper is the liter.
True.
False.
Answer:
True. Can i have brainliest
Step-by-step explanation:
Is an Obtuse triangle a Acute triangle? Yes or no? And why or why not?
Answer:
No, this is because the word obtuse is in the name obtuse triangle as well as it being a whole different angle than an acute angle. Obtuse angles are are greater than 90 degress but less than 180 while the acute angle is less than 90.
Step-by-step explanation:
who ever gets this right will get a brainlest
Answer:
15%nririrjeieieirirjr
The second hand on a clock is 8 cm long.
What is the distance the tip of the second travels in 10 minutes?
Give correct answer I will give you Branist
Answer:8
Step-by-step explanationesporq eñ relokrr co:
Answer:
This is just a guess. I think .4 feet.
Only number 17 ! (if you do number 18 I´ll give brainliest)
(no files or links)
Answer:
B and D
Step-by-step explanation:
When you simplify 6/12 and 10/12 you get 1/2 and 5/6. When you simplify 12/24 and 20/24 you get 1/2 and 5/6 again. Therefore, the answers are B and D.
Answer:
B- 6/12 and 10/12
D- 12/24 and 20/24
Step-by-step explanation:
Simplify the fractions
A- 8/16= 1/2
10/16= 5/8
B- 6/12= 1/2
10/12= 5/6
C- 5/10= 1/2
8/10= 4/5
D- 12/24= 1/2
20/24= 5/6
Therefore the answer is B and D.
You don't have to explain
DONT BE SO NEGATIVE..............
ಠ_ಠ plss help(will report if a scam)
Answer:
.
Step-by-step explanation:
Does x=4 make x + 9 = 13 a true equation?
Answer:
yes
Step-by-step explanation:
if x=4 then x+9=13 is equal to 4+9=13
which is true
will give brainliest
Answer:
36 in
Step-by-step explanation:
4*3=12, 12*3=36. also plz give me brainliest.
Answer:
[tex]\frac{9}{16} in^3[/tex]
Step-by-step explanation:
First we need to find the volume of the cube. To do so, we need to multiply length × width × height
[tex]\frac{3}{4} * \frac{3}{4} * 1 = 0.5625[/tex]
Convert to a fraction
[tex]9/16 = 0.5625 = \frac{9}{16}[/tex]
Since we can not simplify this fraction to [tex]\frac{1}{4}[/tex] that is our answer. Since these cubes are in inches we need to add inch/in to the end. Also since this is the 3D cube we need to add ^3
[tex]\frac{9}{16} in^3[/tex]
William has a fish tank that has a volume of 3,825 cubic inches. The base has a width of 12.5 inches and a length of 24 inches. What is the height of the fish tank?
Answer:
12.75
Step-by-step explanation:
3,825 / 12.5 / 24 = 12.75
can someone pls help
What percent of students selected Fall?
Answer:
48%
Step-by-step explanation:Because its 48 out of 100
Answer:
48%
Step-by-step explanation:
If I had a 68.0% D+ and I had one missing assignment worth 30 points. If I got a 30 on another assignment 30/30 and still have the missing assignment. What grade will I have?
Please Help
Answer:
C- or C+ or B-
Step-by-step explanation:
The ratio that compares the measurements of a model and the real object is called what?
Answer:
Unit Scale
Step-by-step explanation:
A unit scale is a ratio that compares the dimensions of an actual object to the dimensions of a scale drawing or model that represents the actual object. Neither value in a unit scale has to equal 1.
Please answer! Brainliest will be given, thanks :)
Answer:
2600, 3400, 5000, 7000
Step-by-step explanation:
This equation can be simplified to 200n + 1000. Now we can just plug in the amount of customers. 200 * 8 + 1000 = 2600. 200 * 12 + 1000 = 3400. 200 * 20 + 1000 = 5000, and 200 * 30 + 1000 = 7000.
