The degree of a polynomial is the highest power of the polynomial.
The polynomial is [tex]\mathbf{P(x) = (x + 3)^4}[/tex]
The degree is given as:
[tex]\mathbf{n = 4}[/tex]
The zero is given as:
[tex]\mathbf{x = -3}[/tex]
Add 3 to both sides
[tex]\mathbf{x + 3= 0}[/tex]
From the question, we understand that the polynomial has a single zero.
So, the polynomial is:
[tex]\mathbf{P(x) = (x + 3)^n}[/tex]
Substitute 4 for n
[tex]\mathbf{P(x) = (x + 3)^4}[/tex]
Hence, the polynomial is [tex]\mathbf{P(x) = (x + 3)^4}[/tex]
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(a) I wanted to determine how much water my sprinkler was using, so I set out a bunch of empty cat food cans at various distances from the sprinkler and noted how high the water was in each can after one hour. My sprinkler reaches from 0 feet to 16 feet away from the sprinkler. The data are given in Table 1. The sprinkler distributes water in a circular pattern, so I assumed that points the same distance from the sprinkler received the same amounts of water. One way to use the data in Table 1 to estimate how many cubic feet of water my lawn got from my sprinkler in one hour is to write down an integral for the volume of water using the method of shells, and then use a right-endpoint Riemann sum to approximate this integral. Give your answer in decimal form rounded to the nearest cubic foot.
(b) My neighbor decided to collect the same data for her watering. Her sprinkler reaches from 0 feet to 21 feet away from the sprinkler, but she did not set out the cans at evenly spaced distances and so the calculation is a bit more complicated. The data are given in Table 2.Use the data in Table 2 to estimate how many cubic feet of water her lawn got from her sprinkler in one hour. Again, write down an integral for the volume of water using the method of shells, and then use a right-endpoint Riemann sum with subintervals of different lengths to approximate this integral. Give your answer in decimal form rounded to the nearest cubic foot.
Answer:
a) 108 ft
Step-by-step explanation:
2pi (x*f(xi)........)*deltax
x is the point in the table
so for the first three points
2pi(2*f(2)+4*f(4)+6*f(6).....)*2
and so on for the rest
make sure you convert f(x) into feet, for example (2, 2.1) do 2.1/12
first point in equation
2pi(2*(2.1/12)+....)*2
Sophia wants to buy collector boxes that can hold 6 dolls each. How many boxes will Sophia need to buy for her collection of 168 dolls?
A 21
B 28
C 34
D 1,008
what is the equivalent fraction of 6/20 with a denominator of 10
Answer:
3/10
Step-by-step explanation:
I will give you BRAINLYEST if you answer this. (I did not get an answer the first time that I asked this)
What is the sign of the product (3) × (−25) × (7) × (−24)?
Positive, because the products (3) × (−25) and (7) × (−24) are negative and the product of two negative numbers is positive
Positive, because the products (3) × (−25) and (7) × (−24) are positive and the product of two positive numbers is positive
Negative, because the products (3) × (−25) and (7) × (−24) are negative and the product of two negative numbers is negative
Negative, because the products (3) × (−25) and (7) × (−24) are positive and the product of two positive numbers is negative
Answer:
Positive, because the products (3) × (−25) and (7) × (−24) are negative and the product of two negative numbers is positive
Step-by-step explanation:
(3) × (−25) × (7) × (−24) =(-75)(negative)×(-168)(negative)=12 600(positive)
Find the product (answer )
-3/10 x 7/10
A) 21/100
B) 4/10
C) -21/100
D) -2/5
Answer:
[tex]C) -21/100=-0.21[/tex]
Step-by-step explanation:
[tex]→\frac{- 3}{10} \times \frac{7}{10} [/tex]
[tex]→ \frac{ - 3 \times 7}{10 \times 10} [/tex]
[tex] →\frac{ - 21}{100} [/tex]
Answer:
[tex]c) \frac{ - 21}{100} [/tex]
Step by step Explanation:[tex] \frac{ - 3}{10} \times \frac{7}{10} = \frac{ - 21}{100} \: \: \\ option \: c \: is \: correct[/tex]
The functions r and s are defined as follows.
r(x)= -2x-2
s(x)=2x² +2
Find the value of s (r (2)).
[tex]r(x) = -2x-2\\ s(x) = 2x^2+2[/tex]
[tex]s\big(r(2)\big) = s(-2\cdot 2-2) = s(-4-2) = s(-6) = 2\cdot(-6)^2+2 = 2\cdot 36+2 =\\ = 72+2 = 74[/tex]
[tex]\Rightarrow \boxed{s\big(r(2)\big) = 74}[/tex]
Answer:
74Step-by-step explanation:
Given functions:
r(x) = -2x - 2 s(x) = 2x² + 2Find s(r(2)) in steps:
r(2) = -2*2 - 2 = - 4 - 2 = - 6s(r(2)) = s(- 6) = 2(-6)² + 2 = 72 + 2 = 74Greatest common factor of 30 and 75
Step-by-step explanation:
The prime numbers 5 and 3 are both factors that are common to 30 and 75. The product of these factors is 3×5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15.
Answer:
the Greatest common factor of 30 and 75 is 15
Step-by-step explanation:
The product of these factors is 3×5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15.
can anyone heelp me pls
Answer: lotion- semisolid
capsule- solid
suspension- liquid
Step-by-step explanation:
What is the decimal equivalent of 9.7 X 10^5
Answer:
B)
Step-by-step explanation:
9.7×10⁵= 970000
Hope this helped you- have a good day bro cya)
4-8m=-8-5m what is m
Answer:
-9m-4
Step-by-step explanation:
Move the -4 to the right hand side by adding 4 to both sides, like this: To the left hand side:
-4 + 4 = 0
9m ‹ 5m
Yesterday, Maura made $142 at her waitressing job. $67 was tips, and the rest was her regular rate of $10 per hour. How long did Maura work yesterday?
If Maura made $142 at her waitressing job. $67 was tips, and the rest was her regular rate of $10 per hour then she worked for 7.5 hours.
The total amount she made is the sum of her tips and her regular rate:
Total Earnings = Tips + Regular Rate
Given that:
Tips = $67
Regular Rate = $10 per hour
Total Earnings = $142
We can set up the equation:
142 = 67 + 10h
Now, solve for "h" (the number of hours Maura worked):
10h = 142 - 67
10h = 75
h = 75 / 10
h = 7.5
Hence, Maura worked for 7.5 hours yesterday.
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What single decimal multiplier would you use to increase by 15% followed by a 14% increase?
9514 1404 393
Answer:
1.311
Step-by-step explanation:
That multiplier is the product of the multipliers for each of the increases:
(1 +15%)(1 +14%) = 1.15×1.14 = 1.311
A class is selling magazines as a fund raiser. of the 500 magazines sold, allie sold 1/7 of them. Gary sold 0.085 of the magazines. rob sold 9/100 of the magazines, and felisha sold 0.185 of the magazines. who sold the most magazines?
PLS ANSWER QUICKLY THANK YOU :)
Answer:
Felisha
Step-by-step explanation:
What is the distance between points B and C
Answer:
5
Step-by-step explanation:
I hope this helps
yea xxx
At a recent meeting at the American College of Asthma, Allergy, and Immunology, researchers reported that allergy vaccinations are effective in treating sinusitis (inflammation of the membrane lining the facial sinuses) in individuals predisposed to allergies. Specifically, the researchers reported that of individuals predisposed to allergies find relief from their sinusitis after allergy vaccinations. Suppose that this number is accurate and that individuals predisposed to allergies are chosen at random and given allergy vaccinations.
a. Estimate the number of individuals in the random sample who do not find relief from their sinusitis by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable).
b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution.
HELP MEEEEEEE (−4)÷(14)(−2)
quotient of 820 and 0.10=
Answer:
The quotient of 820 and 0.10 is 8200
hi I was just a little bit of time with my module and I didn't know what is answer of the module now please please be sure of the answer please I want to know the answer please can I
1. 5 x 4 = A. 20
2.
[tex] \frac{2}{5} \times 25 = 2 \times 5 = 10[/tex]
the answer is D. 25
3.
[tex] \frac{3}{5} \div 15 = \frac{3}{5} \times \frac{1}{15} = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} [/tex]
the answer is A. 1/25
4.
[tex]4 \div \frac{1}{2} = 4 \times \frac{2}{1} = 8[/tex]
the answer is C. 8
5.
[tex]9 \div \frac{1}{3} = 9 \times \frac{3}{1} = 27[/tex]
the answer is D. 27
6.
[tex]20 \div \frac{1}{4} = 20 \times \frac{4}{1} = 80[/tex]
the answer is D. 80
7.
[tex] \frac{9}{10} \div \frac{1}{2} = \frac{9}{10} \times \frac{2}{1} = \frac{18}{10} = \frac{9}{5} = 1 \frac{4}{5} [/tex]
the answer is C. 1 4/5
8.
[tex]9 \div \frac{3}{2} = 9 \times \frac{2}{3} = \frac{18}{ 3} = 6[/tex]
the answer is B. 6
9.
[tex] \frac{3}{4} \div \frac{3}{8} = \frac{3}{4} \times \frac{8}{3} = 2[/tex]
the answer is A. 2
pls help me i need to finish this
Answer:
-1 = -2
0 = 0
1 = 2
2 = 4
Step-by-step explanation:
-1 x 2 = -2
0 x 2 = 0
1 x 2 = 2
2 x 2 = 4
Since the equation says y = 2x, you must multiply every x factor by 2 to get your answer.
-kiniwih426
Create and solve another problem about Jeremiah and his lemonade stand which requires multiplying decimals
Answer:
116 ounces
Step-by-step explanation:
Hope this helps.
Cómo hallar el alcance de una función cúbica?
Answer:
Cómo hallar el alcance de una función cúbica? or How to find the scope of a cubic function?
Step-by-step explanation:
To find the scope of a cubic function, we first need to understand what the term "scope" refers to. In mathematics, the scope of a function refers to the range or set of all possible values that the function can take.
For a cubic function, which is a polynomial of degree three, the scope can vary depending on its coefficient values. Generally, a cubic function will have an infinite scope which means it can take on any real value. This is because the degree of the polynomial is odd and therefore the function's graph will extend to both positive and negative infinity.
However, if there are additional conditions or constraints given for the cubic function, such as restricted coefficients or a limited domain, then the scope may be constrained accordingly. It is important to analyze the specific details of the cubic function in order to determine any limitations on its scope within a defined range.
Question is incomplete the complete question is
One similarity Egypt has to the U.S. federal government?
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Mr. Jones' recipe calls for 1.04 tablets per day. Based on this information, how many tablets should Mr. Jones take per day?
Due to the fact that no one can consume .04 of a tablet, we can round down this answer to 1. Even if we were told to round to the tens place, we would still be unable. Remember, 5 or above, give it a shove, 4 or below, let it go. This means that Mr. Jones should take C- 1 tablet per day.
I hope I've helped! :)
Classify each term in the expression 3+6ab+c as a constant term or a variable term.
Answer: 3 is constant term, 6ab is variable term, and C is variable term
Answer:
3: Constant term, 6ab: Variable term, C: Variable term
Step-by-step explanation:
If you can help please and thanks
Answer:
Cost of each pendant = $2.80
Step-by-step explanation:
Since we're given information regarding the total cost of beads, $13.20, and the total cost of beads and pendants for all 4 necklaces, $24.40:
Let b = beads
p = pendants
C = total cost of beads and pendants for all 4 necklaces.
b + p = C
$13.20 + p = $24.40
$13.20 - $13.20 + p = $24.40 - $13.20
p = $11.20 (This represents the total cost of 4 pendants).
To find out the cost of each pendant, divide $11.20 by 4:
$11.20 ÷ 4 = $2.80
Therefore, the cost of each pendant is $2.80.
Answer:
I'm 50% sure it's $7.52 though I may be wrong
help with 5a, to find the values of x
what number is in the Tenths place for 315.84
Answer:
The number in the tenths place is 8
Step-by-step explanation:
Answer:
8.
Step-by-step explanation:
The first number after the decimal represents the tenths place. 315.84 8 is right after the decimal so it's in the tenths place.
A square field is 30 m long.Find the length of wire required to fence it with 4 rounds
Answer:
120m
Step-by-step explanation:
because 30×4 is 120
Who do you agree with? Explain why.
David states -15 divided by a negative integer will produce a positive quotient less than or equal to 15.
Lesly states -15 divided by a negative integer will produce a positive quotient greater than or equal to 15.
Evaluate the expression when b=3 and c=6.
Answer:
8
Step-by-step explanation:
dear! mam /sir!
solution;
given: b=3 and c=6.
=(6^2-4*3)/3
=(36-12)/3
=24/3
=8
hope it hlps..thank u!!
The difference between a number and −22 is equal to the number times 11.
Answer:
The equation looks like this x-(-22)=11x
The answer for the equation is x=11/5
Step-by-step explanation:
Difference between a number (x) and -22
Difference means subtract so x subtracted by -22
x-(-22)
Is equal to: which means you put a =
the number times 11
number is x so x times 11 is 11x
The equation looks like this:
x-(-22)=11x
simplify
x+22=11x
Move x to the other side:
22=10x
Divide 10 on both sides:
x=22/10
Simplify
x=11/5
Hope this helps!
Answer:-11/5
Go Step-by-step-
The difference... -
between a number and 22.... n-22
equal to number times 11...
n-22=11n
subtract n
-22=10n
x=-11/5