The synthetic division (x²+9) by (x-3) has a quotient of x+3 and the remainder of 18
How to use synthetic division to solve polynomials?
Synthetic division is a way of performing the division of polynomials, with less writing and fewer calculations than the long division method
Given: (x²+9) ÷ (x-3)
The numerator can be written as p(x)= x²+9
The zero of the denominator g(x) is 3 (Note: the sign changed)
The coefficients of p(x) are arranged as follows, with the zero of g(x) on the left:
3 | 1 0 9
|________
The first coefficient after the bar is "dropped" to the last row.
3 | 1 0 9
|___________
| 1
The dropped number is multiplied by the number before the bar, and placed in the next column
3 | 1 0 9
| 3
|___________
| 1
An addition is performed in the next column
3 | 1 0 9
| 3
|___________
| 1 3
The previous two steps are repeated and the following is obtained:
3 | 1 0 9
| 3 9
|___________
| 1 3 18
Here, the last term (18) is the remainder while the rest are the coefficients of the quotient
The terms are written with increasing degree from right to left beginning with degree zero for the remainder and the result
1x + 3 | 18
Where the quotient q(x) = x+3 and the remainder r(x) = 18
Therefore, the quotient is x+3 and the remainder is 18
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Graph this function:
y = |x − 3| + 1
Click to plot the vertex first.
Given function:
y = |x − 3| + 1
Table:
x y
1 3
2 2
3 1
4 2
5 3
Here the vertex is (3,1).
Graph is in the image uploaded.
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in a shipment of 54 vials, only 16 do not have hairline cracks. if you randomly select one vial from the shipment, what is the probability that it has a hairline crack?
The probability that it has a hairline crack is 19/27.
Given that;
In a shipment of 54 vials, only 16 do not have hairline cracks.
Let shipment of 54 Vials;
x(s) = 54
Let,' A ' be the event that selects 16
x(A) = 16
P(A) = x(A) / x(s)
= 16/54
But only 16 don't have hairline Crakes;
To solve a given case;
The probability that it has a hairline crack is:
P(A') = 1 - P(A)
= 1- 16/54
P(A') = 19/27
Hence, the probability that it has a hairline crack is 19/27.
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An emperor penguin dive down into the ocean at a contant rate. From the urface, he dive 1,760 feet in 8 minute. The number −1,760 repreent the location of the penguin in relation to the urface. What number repreent the location of the penguin in relation to the urface 2 minute after beginning hi dive?
The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.
First, we will calculate the speed of the penguin. The speed is represented by the variable "s".
s = 1,760/8
s = 220 feet per minute
The location of the penguin after 2 minutes is calculated below.
d = 2×s
d = 2×220
d = 440
Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
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-3(4x-7) please answer quickly!!
b According to estimates, there are over 300 million people living in the Unite
States. How many Neyland Stadiums would it take to hold 300 million people
Answer:
it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps
Step-by-step explanation:
Finding the derivatives using The Chain Rule
a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².
b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².
How to determine the derivative of a function by chain rule
Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:
df / dx = (df / du) · (du / dx)
a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:
F'(x) = [2 · g(x) + 6] · g'(x)
F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²
b) Now we proceed to expand the polynomial in its standard form:
F'(x) = [(2 / 3) · x³ + 7] · x²
F'(x) = (2 / 3) · x⁵ + 7 · x²
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The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12. What is the remaining credit after 81 minutes of calls?Calling Time In MinutesRemaining Credit In Dollars$
The remaining credit after 81 minutes of calls is $17.04.
Given that, the remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Let x be the number of minutes and y be the number of dollars.
According to question, the ordered pair is
(44, 22.96) and (68, 19.12)
The point slope form is (y-y1)=m(x-x1)
Slope = (y2-y1)/(x2-x1)
= (19.12-22.96)/(68-44)
= -3.84/24
m= -0.16
Put m= -0.16 and (x1, y1)=(44, 22.96), we get
(y-22.96)=-0.16(x-44)
When x=81
y-22.96=-0.16(81-44)
⇒ y-22.96=-0.16×37
⇒ y-22.96=-0.16×37
⇒ y-22.96=-5.92
⇒ y=-5.92+22.96
⇒ y=17.04
Therefore, the remaining credit after 81 minutes of calls is $17.04.
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Complete the equation so that it has no solution.
9(x – 4) – 5x =__x-30
For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
As given in the question,
Given equation is equal to :
9 ( x - 4) - 5x = _ x - 30
Simplify Left hand side of the given equation we get,
9 ( x - 4) -5x
= 9x - 36 - 5x
Collect the like terms we have,
9x - 5x - 36
= 4x - 36
Now compare left hand side and right hand side to get no solution of the equation,
4x -36 = _x -30
Blank should be filled by 4
Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
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An adult sleeps about 480 minutes per day an infant sleeps about 820 minutes per day about how many more minutes does an infant sleep than an adult in one week. What is the given information that will be used to solve the problem?
Answer:2380 minutes. By saying how many more minutes does an infant sleep than an adult in one week impies that you have to subtract how long an adult sleeps taken away from the amount of time an infinte sleeps. Once you get the answer you multiply it by seven.
Step-by-step explanation:
Answer:340 minutes
Step-by-step explanation:you subtract the amount an infant sleeps (820 minutes) by the amount an adult sleeps (480 minutes)
820-480=340
The first container has 3 gallons 3 quarts 1 pint of diesel fuel, the second container has 5 gallons 2 quarts of diesel fuel, and the third container has 6 gallons 1 quart 1 pint of diesel fuel. what is the total quantity of diesel fuel?
The total quantity of diesel fuel is 15.75 gallons.
The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.
1 quart = 0.25 gallon
For first container, 3 quarts = 0.25 × 3
3 quarts = 0.75 gallon
For second container, 2 quarts = 0.25 × 2
2 quarts = 0.5 gallon
For third container, it has 0.25 gallon
1 pint = 0.125 gallon
For first and third container, it has 0.125 gallon
So, amount of diesel fuel in first container = 3 + 0.75 + 0.125
Amount of diesel fuel in first container = 3.875 gallons
Amount of diesel in second container = 5 + 0.5
Amount of diesel in second container = 5.5 gallons
Amount of diesel in third container = 6 + 0.25 + 0.125
Amount of diesel in third container = 6.375 gallons
So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375
The total quantity of diesel fuel = 15.75 gallons
Hence, the total quantity is 15.75 gallons.
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For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.
Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.
50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.
It will be demonstrated by:
1 - p = 1 - 10% = 1 - 0.10 = 0.90
np = 50 × 0.1 = 5. This suggests the number of victories.
Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.
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The question is -
For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?
at a certain university, the average attendance at basketball games in the previous year was 3000 spectators per game. the athletic director claims that the attendance this season is up from last year. for the first 14 games of the current year, there has been an average of 3200 spectators per game with a standard deviation of 450. using a significance level of .05, does this sample data provide evidence to support the athletic director's claim?
The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.
Hypothesis:
H₀ : μ = 3000
H₁ : μ > 3000
The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.
The following information is provided:
s = 450
x = 3200
n = 14
Therefore, test statistics will be:
t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66
The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.
0.0601 is the p-value.
We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.
Since p =.0601, the director's assertion cannot be supported by the available data.
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What is the sum of the 9th square number and the 5th cube number?
Answer:
Step-by-step explanation:
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equations that are quadratic in form include:
A. x⁴ – 6x²– 27 = 0
D. 6x⁴ = -x² + 5
E. 8x⁴ + 2x² – 4x = 0
What is a quadratic equation?A quadratic equation simply refers to the equation which is in an algebraic equation that is of the second degree.
It should be noted that a quadratic equation is in the form of ax² + bx + c = 0.
In this situation, a and b are the coefficients while c is the constant in the equation.
Therefore, based in the information given, the correct options are A, D, abd E.
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Answer:
The equations that are quadratic in form include:
A. x⁴ – 6x²– 27 = 0
D. 6x⁴ = -x² + 5
E. 8x⁴ + 2x² – 4x = 0
Step-by-step explanation:
10 POINTS!
What is the equation of the line in standard form?
(-3,2) and (2,-1)
Answer: y = -.06x + 0.2
Step-by-step explanation: Find the slope by plugging in the given values to the slope formula to find that the slope is -0.6. Next, determine the y-intercept is b=y1−m⋅x1: b = 2 - (-0.6) ⋅ (-3) = 0.2 Finally, the equation of the line can be written in standard form y= -0.6x + 0.2.
I need help understanding domain and range better. I am in algebra 1 in high school freshmen
The domain and the range of a function have the concepts given as follows:
Domain: input values of a function/relation.Range: output values of a function/relation.What are the domain and range of a function?The domain of a function or of a relation is the set that contains all possible input values. Hence, among possible representations, we have that:
In a graph, the domain is composed by the values of x.In a relation of points (x,y), the domain is also composed by all the values of x.For a function, the domain is composed by all values that respect the restrictions of a function. For example, in a fraction, the domain is composed by all values for which the denominator is not zero.The range of a function or of a relation is the set that contains all possible output values. Hence, among possible representations, we have that:
In a graph, the domain is composed by the values of y.In a relation of points (x,y), the domain is also composed by all the values of y.For a function, the range is composed by all the numeric values assumed by the function inside it's domain.More can be learned about the domain and the range of a function or of a relation at https://brainly.com/question/10197594
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Solve for x:-
[tex]\sf 5 + 2x = 2x + 6[/tex]
Answer:
No solution (0 = 1)
Step-by-step explanation:
Given equation,
→ 5 + 2x = 2x + 6
Then the value of x will be,
→ 5 + 2x = 2x + 6
→ 2x = 2x + 6 - 5
→ 2x - 2x = 1
→ 0 = 1
Hence, there is no solution.
[tex]\boxed{\begin{array}r \large{ \tt solution \: : } \: \: \: \: \: \\ \\ { \longrightarrow5 + 2x = 2x + 6} \\ \\ \\ ( \sf 2x \: \: present \: \: on \sf\: \: both \: \: \\ \sf sides \: \: of \: \: equality \: \: \: \\ \sf \: \: gets \: \: \sf canceled\: \: out) \\ \\ \sf \longrightarrow5 \neq6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \: \: therefore \: \: there \: \: is \\ \tt no \: \:solution \: \: for \: \: x \: \: \\ \\ \tt that \: \: is \: \: no \: \: value \: \: \: \: \\ \tt \: of \: \: x \: \: that \: \: satisfies \\ \tt the \: \: given \: \: equation\end{array} }[/tex]
These points are linear.
Find the slope.
x 56 7 8 9
y| 11 | 16 | 21 | 26 | 31
Hint: First calculate the change
between each y-value.
[?]
Slope =
The slope is m = 5.
What is slope?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.
We have to find the slope of the points given.
First to find the change between each y - value.
16 - 11 = 5
21 - 16 = 5
26 - 21 = 5
31 - 26 = 5
So the change between each y - value is 5.
Now, to find the slope of the points.
Since,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]
Hence, the slope of the given points is 5.
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Answer:
The answer is 5
Step-by-step explanation:
Though there is also a bottom number, just put a 1 in the bottom number
in which of the following african countries is the population growth rate above 2.5% and life expectancy at least 61 years old?
Answer: Ethiopia has a population growth rate above 2.5% and a life expectancy of 61 years old
how heavy a load (in pounds) is needed to pull apart pieces of douglas fir 4 inches long and 1.5 inches square? data from students doing a laboratory exercise are given.
With the help of binomial distribution we can conclude our answer.
What is binomial distribution?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability displaystyle q=1-pq=1-p). This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution. The popular binomial test of statistical significance is based on the binomial distribution. [1]A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.acc to our question-
The confidence interval can be found out using,
Confidence interval = Mean ± MOE = 30,800 ± 1,314.8079 = 29,485.192 , 32,114.8Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).
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Use the information given to enter an equation in standard form.
Slope is 6, and (1, 8) is on the line.
Answer:
y=6x+2
Step-by-step explanation:
y=mx+c
8=6(1)+c
8=6+c
c=2
y=6x+2
Check the month and dollar value that represent a correct ordered pair. In April, Cathy's Clothmart had a profit of $3,000. In May, the profit was $4,000. In June, the profit was $5,000. April May June July $1,000 $2,000 $4,000 $6,000
The Cathy's Clothmart job had a profit comprises of pairings of the form (x,y), where the two integers are paired because of some relation.
In this instance, the relation is effectively "in month x it truly had a profit y" The ordered pairs are then, in a really significant sense, (April, 3000), (May, 4000), and (June, 5000). The ordered pairs can be written as follows if the month's number is used to identify them: (4,3000), (5,4000), They generally believed that both kinds of ordered pairings are generally correct.
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May, 4,000
The only correct pair is may and 4,000 because the other options don't have the proper profit to represent the corresponding months.
Is it a, b, or c, and if A what goes in the box
Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.
Given equation,
[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]
For values (-∞,-7)
equation stands true
For values (-7,5)
equation stands false
For values (5,12)
equation stands true
For values (12,∞)
equation stands false
Hence, x ∈ (-∞,-7)∪(5,12).
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Find quotient of 1/3 divided by 5/6
Answer:
2/5
Step-by-step explanation:
flip 5/6 to become 6/5 then cross reduce then cross multiply
ESSENTIAL
Chuck
Match up each scenario with the equation that models the word problem.
Skate rental charges an additional $3.
Jeff is 3 years less than Tony's age.
Marie buys balloons for a party that
are $3.00 each.
Intro
y=x+3
y=x-3
y = 3x
Done
En this is the answer
The following are the equations which matches the given word problems:
a. Skate rental charges an additional $3 :
y = x+3
b. Jeff is 3 years less than Tony's age:
y=x-3
c. Marie buys balloons for a party that are $3.00 each:
y = 3x
Given, we have the word problems:
a. Skate rental charges an additional $3 :
here, based on the fixed charge, additional charge is taken as $3.
let the total charge be represented as y and
x represent the fixed charge,
hence the equation we get is:
y = x+3
b. Jeff is 3 years less than Tony's age.
let y represent the age of Jeff
and x represent the age of Tony.
hence we frame the equation as:
y = x - 3
c. Marie buys balloons for a party that are $3.00 each:
let the cost of the balloon be represented as y
and x represent the number of balloons Marie wants to buy for $3 each.
hence the equation we frame is:
y = 3x
Hence we get the required equations.
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Write 8433 in scientific notation.
I know the answer but can someone give me an explanation and steps.
Answer:
8.433 to the power of 4
Step-by-step explanation:
The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.
Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?
The graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
The system of equation are
-3x + y = 3
-x + 2y = -4
Here we have to use the substitution method
-3x + y = 3
y = 3 + 3x
Substitute the value of y in the second equation
-x + 2(3 + 3x) = -4
-x + 6 + 6x = -4
-x + 6x = -4-6
5x = -10
x = -10/5
x = -2
Substitute the value of x in the first equation
-3x + y = 3
-3(-2) + y = 3
6 + y = 3
y = 3 - 6
y = -3
Hence, the graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
The complete question is:
Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?
a) On a coordinate plane, 2 lines intersect at (3, 0).
b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
c) On a coordinate plane, 2 lines intersect at (negative 1.5, 1).
d) On a coordinate plane, 2 lines intersect at (1.5, 2.5).
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Answer:
B
Step-by-step explanation:
both point intersect at ( -2, -3)
There are 95 males and 125 females participating in a marathon. What
percent of the participants are female? Round your answer to the nearest
hundredth.
Answer: 55.56%
Step-by-step explanation:
To find the percentage, we need to do part over whole. Part being the females and the total marathon runners being the total. So that would be 95/95+125, then 95/225, then 55.555555 and repeating. Then we would round that to 55.56%.
suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. how many times would we have to flip the coin in order to obtain a 99% confidence interval of width of at most .18 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation) a) 164 b) 205 c) 167 d) 212 e) 202 f) none of the above
The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.
Hence, Option F is correct answer.
In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.
[tex]\pi[/tex] ± z[tex]\sqrt{\frac{\pi \p(1-\pi )}{n} }[/tex]
z is the z-score that has a pvalue of [tex]1-\frac{\alpha }{2}[/tex]
Since, the coin is fair, so [tex]\pi =0.5[/tex].
The margin of error is:
[tex]M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}[/tex]
99% confidence level:
So [tex]\alpha =0.01[/tex] ,z is the value of Z that has a p value of 1-[tex]\frac{0.01}{2}[/tex]=0.995,
so Z= 2.575
How many times would we have to flip the coin ?
We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.
n is found when M=0.18 .
So
M=[tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
[tex]0.18=2.575\sqrt{\frac{0.5*0.5}{n} }[/tex]
[tex]0.18\sqrt{n} =2.575*0.5[/tex]
[tex]\sqrt{n}=\frac{2.575*0.5}{0.18}[/tex]
[tex]\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}[/tex]
n = 51.16
Thus, we have to flip the coin at least 52 times.
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Determine the value of y for the inequality 2 times the quantity y plus one third end quantity is greater than two thirds. Y is greater than negative 1 over 36 y is less than negative 1 over 36 y > 0 y < 0
The solution to the inequality is y < -12 ( y less than negative 12).
Given inequality is;
y + 15 less-than 3
y+15<3
For solving the inequality, we will subtract 15 from both sides in order to find y.
Subtracting 15 from both sides of inequality
The solution to the inequality is y < -12 ( y less than negative 12).
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