write polynomial function in standard form with given zeros, x=-2,0,1
The equation for the polynomial in the standard form is:
P(x) = x^3 + x^2 - 2x
How to find the equation of the polynomial?A polynomial of degree N with the n zeros {x₁, x₂, x₃, ..., xₙ} is written as:
P(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)
That is called the factorized form of the polynomial, and we are assuming that the leading coefficient is equal to 1 just for simplicity.
In this case we have 3 zeros {-2, 0, 1}, so the polynomial is of degree 3, and we can write it as:
P(x) = (x + 2)*(x - 0)*(x - 1)
To write the polynomial in the standard form, we need to expand the product:
P(x) = (x + 2)*(x)*(x - 1)
P(x) = (x^2 + 2x)*(x - 1)
P(x) = (x^3 + 2x^2 - x^2 - 2x)
P(x) = x^3 + x^2 - 2x
That is the polynomial.
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Can you guys please help?
A science fair has 405 projects. The coordinator displays the projects in rows of 42. How many rows have exactly 42 projects?
I really do not understand this. It would really help me if after you have answered the question, you could explain how you got that answer. Thank you!
Answer: x=9
Step-by-step explanation:
To get the answer, just divide, but you must not count in the rows that have less or more than 42 projects. 405/42=xThere are 9 rows that have exactly 42 projects because 42 x 9 = 378, which is the closest we can get to 405.
What is the solution to the system of linear equations?
(–4.5, 4.25)
(–1.7, –2.8)
(0, –7)
(3, 0.5)
Answer:
−903.65625
Step-by-step explanation:
((((−4.5)(4.25))(−1.7−2.8))(0−7))((3)(0.5))
=((−19.125(−1.7−2.8))(0−7))((3)(0.5))
=(((−19.125)(−4.5))(0−7))((3)(0.5))
=86.0625(0−7)(3)(0.5)
=(86.0625)(−7)(3)(0.5)
=−602.4375(3)(0.5)
=(−602.4375)(1.5)
=−903.65625
Find the equation (in terms of
x
of the line through the points (-5,-1) and (4,-5)
Answer:
-4/9x - 16.22222
Step-by-step explanation:
Use slope formula
(-5) - (-1) = -4
4 - (-5) = 9
Remember -(-) cancel out to become positive!
The answer is
-4/9x - 16.22222
I can't approximate the 16.222, it is literally that. I did trial and error.
In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.
True
False
False, In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.
What is exponential decay function?
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time.
It can be written as y=a(1-b)x, where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.
How do you calculate an exponential function?
The equation f(x) = ax, in which the input variable x appears as an exponent, describes an exponential function. Both the exponential function and the value of x are dependent on the exponential curve.
The exponential function, which has the form, is a significant mathematical function. f(x) = ax.
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FIRST ANSWER WILL GET 100 PTS!
Eight soccer players order 14 pizzas to share equally among themselves.
How much pizza will each player receive?
Select each correct answer.
Responses
8 1/4 pizza
1 4/8 pizzas
1 4/8 pizzas
1 6/8 pizzas
Answer:
8 1/4
Step-by-step explanation:
Sould be your anwser.
Write an equation that represents the line. Use exact numbers.
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Domain : {-4, 3} and Range : {-1, 4}
What is Domain and Range ?
A relation's domain and range are established, and they consist of all ordered pairs' x and y coordinate sets, respectively.
Domain = the set of all x-coordinates Range = the set of all y-coordinatesHere, observe the line through x-axis
you'll see the it range from -4 to 3 on x-axis.
Therefore, Domain is {-4, 3}
Now, observe the line through y-axis
you'll see the it range from -1 to 4 on y-axis.
Therefore, Range is {-4, 3}
Hence, Domain : {-4, 3} and Range : {-1, 4}
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The straight line distance between the towns of Martville and Edentown is 120 miles. The straight-line distance between Martville and Newberg is 150 miles.
Which of the following represents a possible straight-line distance between Edentown and Newberg if the three towns form a right triangle on a map?
270 miles
30 miles
90 miles
135 miles
The straight-line distance between Edentown and Newberg is 90 miles. The correct option is the third option 90 miles
Calculating the straight-line distance between two townsFrom the question, we are to determine the possible straight-line distance between Edentown and Newberg if the three towns form a right triangle.
Let the straight-line distance between Edentown and Newberg be x.
Now,
Assume that the straight-line distance between Martville and Newberg is the hypotenuse of the right triangle,
Then,
From the Pythagorean theorem, we can write that
150² = x² + 120²
22500 = x² + 14400
x² = 22500 - 14400
x² = 8100
x = √8100
x = 90 miles
Hence, the straight-line distance is 90 miles
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evaluate for x=2
12x+8 divided by 4
Answer:
12x + 32
Step-by-step explanation:
Multiply 8 and 4 to get 32.
IL GIVE BRAINLIEST Question 1 of 10
Which is an expression?
A. 3 + 2 = 5
OB. 2+1>0
OC. 1+4= 2 + 3
OD. 4+6
Answer:
D
Step-by-step explanation:
A and C are equations. B is an inequality.
An expression does not have an inequality or equal sign.
Hence, D is the answer.
78x7x54x8 show your work
Answer:
235,872
Step-by-step explanation:
Simplify:
78×7×54×8
78×69
= 235,872
Answer:
235872
Step-by-step explanation:
I hope it's useful to you
Two ratios that both have values that are equal.
Group of answer choices
Measurement of a Quantity
Rate
Quantity
Equivalent Ratios
Answer:
Equivalent Ratios
Step-by-step explanation:
Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions.
The equality of two ratios is also known as proportion. The antecedent and consequent values are different.
Equivalent ratios are the same when we compare them. The two quantities of ratio should be of the same kind. To find an equivalent ratio we need to multiply.
Equivalent ratios are just like equivalent fractions. If two ratios have the same value, then they are equivalent, even though they may look very different!
Equivalent ratios or equal ratios are two ratios that express the same relationship between numbers as we covered in our tutorial on scaling up ratios.
Answer:
equivalent ratios
Step-by-step explanation:
At a local sandwich shop, 55% of customers preferred white bread over whole wheat bread. Of those who chose whole wheat bread, 61% preferred ham for the protein, and 41% of those who chose white bread preferred turkey.
What percentage of customers chose whole wheat bread with turkey? Round your answer to the nearest whole percentage.
18%
28%
39%
41%
Answer:
≈ 18%
Step-by-step explanation:
% of customers preferring whole wheat bread = 100 - 55 = 45%
% of choosers of whole wheat bread who prefer turkey = 100 - 61 = 39%
Multiply: 0.45×0.39 = .1755
Answer:
18%
Step-by-step explanation:
i took the test :)
Solve for x:-12x-14=34
Answer: x=4
Step-by-step explanation:
first you add both side by 14 to get 12x=48 then you divide both sides by 12 to get 4 so x=4
please help i will give brainliest
Explanation:
We want to prove by contradiction that corresponding angles 1 and 5 made by a transversal crossing non-parallel lines are not congruent.
To prove by contradiction, we make an assumption that results in a demonstrably false conclusion. This allows us to conclude the assumption is false.
ProofAssume angles 1 and 5 are congruent.
Then lines m and n are parallel by the converse of the corresponding angles theorem.
Lines m and n are not parallel, hence our assumption must be false.
Angles 1 and 5 are not congruent.
What is the value of (2,820/8) / 5?
[The slashes are divided by]
Answer:
70.5
Step-by-step explanation:
2,820/8 equals 352.5.
352.5/5 equals 70.5.
Which rule explains why these triangles are congruent?
What is 417 divided by 3 and what is the remainder
Answer:
139
Step-by-step explanation:
The number 417 divided by 3 gives the quotient of 139 and leaves the remainder of 0.
Given a division problem.
Here, the dividend is 417.
The divisor is 3.
It is required to find the quotient and the remainder of this division problem.
It can be done using the normal division method.
The first term of the dividend is 4.
4 = (3 × 1) + 1
So, the first digit of the quotient is 1.
The remainder, 1, goes to the other digit of the dividend and it becomes 11.
11 = (3 × 3) + 2
The second digit of the quotient is 3.
The remainder 2 goes to the last digit and it becomes 27.
27 = (3 × 9) + 0
The third digit of the quotient is 9.
The remainder is 0.
Hence, the quotient is 139 and the remainder is 0.
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please help want! easy thank you so much!!
7. Serena estimates that she can paint 40 square feet of wall space every half-hour. Can Serena paint at least 180 square feet of wall space in 2.5 hours? Why or why not?
A. Yes, 180(2.5)= 450, and 450 > 180
B. Yes, 80(2.5) = 200, and 200 > 180
C. No, 40(2.5) = 100, and 100 < 180
D. No, 80(0.5)= 40, and 40 < 180
B. Yes, 80(2.5) = 200, and 200 > 180
Step-by-step explanation:1. Addition:If Serena can paint 40 square feet in 30 minutes, then:
40 + 40 = 80 sq. ft.
30 + 30 = 1 hour
80 + 40 = 120 sq. ft.
60 + 30 = 1.5 hours
120 + 40 = 160 sq. ft.
90 + 30 = 2 hours
160 + 40 = 200 sq. ft.
120 + 30 = 2.5 hours
So, what I just did was adding the 30 minutes and the 40 square feet at the same time until I got to 2.5 hours, and seeing if I also got to 180 square feet. Which I did. I actually got to 200 sq. ft. That means our answer is B. Yes, 80(2.5) = 200, and 200 > 180
Solution:
B. Yes, 80(2.5) = 200, and 200 > 180
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Given h(x)=4x+2, find h(5)
PLEASE HELP ME
Answer:22
Step-by-step explanation:
Answer: h(5)=22
Step-by-step explanation:
h(5) is saying that x is equal to 5
replace x with 5
h(5)=4(5)+2
h(5)=20+2
h(5)=22
Give the degree of the polynomial
Answer:
10
Step-by-step explanation:
Given polynomial:
[tex]3x^2y^3+8x^3y^7[/tex]
The degree of a polynomial is the largest exponent in the function.
When a polynomial has more than one variable, add the exponents of each variable in each term.
3x²y³ has a degree of 5, since both exponents add up to 5.
8x³y⁷ has a degree of 10, since both exponents add up to 10.
So the polynomial has a degree of 10.
Find equivalent decimal number of (1100111)²and (16742)³
Answer:
[tex]1100111_2 = 103_{10}\\\\16742_3 = 7650_{10}[/tex]
Step-by-step explanation:
[tex]\textsf{I just used the programmer's version of the built-in calculator that comes with Windows}[/tex]
A gasoline tank holds 3 3/4
gallons. If 1/3 of the tank has been used,
then how many gallons have been used?
Answer:
3/5
Step-by-step explanation:
Reduce fraction to lowest terms
1 is the greatest common divisor of 41 and 12. The result can't be further reduced.
Step 2 of 2: Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
41 over 12
41
12
= 3 and 5 over 123
5
12
41 ÷ 12 = 3 remainder 5
Answer: [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
5. The population of deer in a park is growing over the years. The table below gives the population found in a
survey by local wildlife officials.
Year
2000
2003
2006
2009
Deer Population
168
216
264
312
(a) Find the average rate that the deer population is changing over each time interval below:
From 2000 to 2003
From 2003 to 2006
From 2006 to 2009
(b) Why does this calculation indicate a linear (c) Ift stands for the number of years since 2000,
relationship?
write an equation for the deer population, p, as a
function of 1.
(d) What does your model predict the deer (e) How many years will it take for the deer
population to be in the year 2014?
population to reach 500? Round to the nearest
year.
a) The average rate of change is 16.
b) The Calculation is linear because the average rate of change is same.
c) p= 16t + 168
d) The population in 2014 is 8168.
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
a) The average rate of change
From 2000 to 2003 = (216- 168)/ 3
= 16
From 2003 to 2006 = (264- 216) / 3
= 16
From 2006 to 2009 = (312- 264)/ 3
= 16
b) The Calculation is linear because the average rate of change is same.
c) From the year 2000, the intercept is 168.
So, p= 16t + 168
e) The population in 2014
p = 16(500)+ 168
= 8168.
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Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.
P(A) = 0.37, P(B) = 0.43 and P(AandB) = 0.20.
P(B | not A) =
=
The probability of B | not A i.e. P(B | not A) is 0.3651
How to find P(B | not A)?Probability is defined as the likelihood of a desired event happening.
Given that: P(A) = 0.37, P(B) = 0.43 and P(AandB) = 0.20.
We want to find P(B | not A)
Remember: P(A | B) = P(A n B) / P(B)
Thus, P(B | not A) = P(B and not A) / P(not A)
P(not A) = 1 - P(A) = 1 - 0.37 = 0.63
P(B and not A) = P(B) - P(A and B) = 0.43 - 0.20 = 0.23
Hence,
P(B | not A) = P(B and not A) / P(not A) = 0.23 / 0.63 = 0.3651
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can someone help me? I can't get rid of this test and it won't let me do it, I really don't know what to do and my grades will start to go down because I can't do it. (sorry if none of this makes sense)
Answer:
Step-by-step explanation:
There is no question to help with? Maybe ask your teacher or computer guy.
1
Rebecca has 3 boxes of shells
with 30 shells in each box.
Which equation can be used
to find the total number of
shells in Rebecca's boxes?
A3 x 3 + 0 =
B3+3 x 10 =
3x3 + 10 =
3 x 3 x 10
Answer:
Step-by-step explanation: the answer is 90
the answer is 3 x 3 x 10 because she has 3 boxes and 30 shells in each box. 30 divided by 3 is 10 therefore you would multiply 3 by 3 to get 9 then multiply 9 times 10 to get 90.
A shipment of 50 inexpensive digital watches, including 7 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected?
0.8926 is the probability that the shipment will be rejected.
What does the math term "probability" mean?
Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
The probability that a digital watch is defective p = 10/50 = 0.2
n = 10
Using the binomial probability formula
P(x) = ⁿCₓ pˣ ( 1 - p)ⁿ⁻ˣ
Let x be the random variable that represents the number of defective watches.
The probability that the shipment will be rejected
P(x ≥ 1 ) = 1 - P(0)
= 1 - ¹⁰C₀ ( 0.2)⁰ ( 0.8)¹⁰
= 1 - ( 0.8)¹⁰
= 0.8926258176 ≈ 0.8926
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Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
The value of x in the statement negative 3 less than 4.9 times a number x is the same as 12.8 is 2.
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.
Given a statement negative 3 less than 4.9 times a number, x, is the same as 12.8 this can be numerically expressed as,
4.9x - (- 3) = 12.8.
4.9x + 3 = 12.8
4.9x = 12.8 - 3.
4.9x = 9.8.
x = 9.8/4.9.
x = 2.
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