The expression for the synthetic division is 10n³ + 8n² -10 - 0
What is synthetic division?Synthetic division can be defined as a mathematical way to divide a polynomial by a given binomial x - c
Given that, c is a constant.
The steps to take in synthetic division;
Set up the synthetic divisionBring down the leading coefficient to the bottom rowMultiply c by the value just written on the bottom row Add the column created in step 3Repeat until doneGiven the polynomial;
(10n^3*18n^2-2n-10)/(n+1)
[tex]\sqrt[n + 1]{10n^3 + 18n^2 -2n - 10}[/tex]
- 1 coefficient of dividend
10 18 -2 -10
____-10_-8__10_________
10 8 -10 0
The quotient becomes;
10n³ + 8n² -10 - 0
Hence, the expression is 10n³ + 8n² -10 - 0
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Four students set up a lemonade stand. At the end of the day,their profit is $17. 52. How much money do they have when the profit is split equally?
Answer:
$4.38
Step-by-step explanation:
17.52/4=4.38
the quotient of y and 4 is at most 19
The inequality of the statement is y/4 ≤ 19
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement represented as
the quotient of y and 4 is at most 19
The variable in the above statement is y
This means that the quotient of y and 4 cannot exceed 19
The term cannot exceed implies less than or equal to
So, we have the following representation
y/4 ≤ 19
Hence, the statement is
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This is for geometry I need to know step by step appreciate it
For the given similar triangles, the value of x = 5.
What are similar triangles used for?Similar triangles share the same associated angle measurements and proportional side lengths.
Due to their similar shapes, two figures that are not always the same size can appear comparable. We might claim, for instance, that all circles are equivalent. Squares and equilateral triangles share similar characteristics. Although similar figures need not be congruent in order to be comparable, congruent figures are always comparable.
Despite having the same shape, similar triangles have different diameters. In identical triangles, corresponding angles are equal. In analogous triangles, the ratio of the corresponding sides is the same. Any pair of equivalent sides' squares and any comparable triangle's area have the same ratio.
As the given triangles are similar,
the sides are in same ratio,
⇒ 56 / 8x - 5 = 24 / 15
⇒ 8x - 5 = 35
⇒ 8x = 40
⇒ x = 5
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The equation of the line is ____?
Answer:
Step-by-step explanation: using the y-intercept form, I see the y-intercept is 40 , at the point (0,40)
and we have a point (4,160), so
slope = (160-40)/(4-0) = 30
equqtion: y = 30x + 40 or 30x - y = -40
Jasmine's average speed was 33 3/4 miles per hour.
How far did she travel if it took her 3 1/5 hours?
A. 79 1/2 miles
B. 89 1/2 miles
C. 98 miles
D. 108 miles
The distance travelled by Jasmine in 3 1/5 hours is 108 miles.
What is the distance travelled by Jasmine in the given time?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Speed = 33 3/4 miles per hourElapsed Time = 3 1/5 hoursDistance = ?Plug in given values into the above equation and solve for distance.
Speed = Distance / time
Distance = Speed × Time
Distance = 33 3/4 × 3 1/5
Convert to improper fraction
Distance = (33 × 4 + 3)/4 × ( 3 × 5 + 1)/5
Distance = 135/4 × 16/5
Distance = 2160 / 20
Distance = 108 miles
Therefore, the distance covered is 108 miles.
Option D) 108 miles is the correct answer.
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Solve each trigonometric function IN THE INTERVAL [0, 2)
3 sec2x − 2 tan2x − 4 = 0
The intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The trigonometric function is given below.
3 sec2x − 2 tan 2x − 4 = 0
Simplify the equation, then we have
3 sec2x − 2 tan 2x − 4 = 0
3 / cos 2x − 2 sin 2x / cos 2x = 4
3 − 2 sin 2x = 4 cos 2x
(3 − 2sin 2x)² = 16 cos² 2x
The graph of the functions is drawn below.
From the graph, the intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.
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4(2x – 5) = 4
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work.
The equation has one solution
The solution to the equation is x = 3
How to solve the equation4(2x – 5) = 4
To solve this, we would first have to open the bracket.
4 * 2x - 4*5 = 4
8x - 20 = 4
We would want to have the variable x stand on its own
so we take like terms
8x = 4 + 20
8x = 24
To get the value of x divide through the equation by 8
x = 24 / 8
x = 3
The solution is just one at x = 3
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$37 dinner; 15% tip what can I do to get the answer
Answer: $5.55
Step-by-step explanation: 15% = 0.15
37 / 0.15 = 5.55
Between the hours of 10 P.M. and 6 A.M., the temperature decreases an average of a degree per hour. How long, in hours and minutes, will it take for the temperature to decrease by 5 °F ?
Algebraic equation:
solution:
Answer:
5 hours
OR
300minutes
Step-by-step explanation:
1 degree lost 1 hour
5 degrees lost (5×1) hours
5hours
1 hour=60 minutes
5hours= (5×60)
300minutes
What is the quotient of 154,504 divided by 28 using standard algorithm
Answer
5518
28/154504
154504
1 4 0
1 4 5
1 4 0
5 0
2 8
2 2 4
2 2 4
0
Please help I need the answers ASAP.
Question 6:
The relationship between ∠2 and ∠7 is that they are corresponding angles.
Question 8:
Since ∠1 and ∠2 are alternate exterior angles, m∠2=m∠1 so 180°
Question 9:
Options A, C, and D are correct.
*Note*
For option B the angles are supplementary.
For option E the angles are vertical angles.
Question 10:
∠1 and ∠2 lie in the interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal.
Help me please and thank you !!!!
The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]
What is a positive exponent?A positive exponent indicates that the base should be multiplied by that many.
An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. Negative exponents like xn can be rewritten as 1 / rs. As an illustration, qr^-4 s^6 q ^-8 s^6 q^-1 rs^6
The Power Rule for Exponents is a further exponent rule that follows from this. You multiply the exponents while keeping the base constant to simplify a power of a power. As an illustration, b for any positive s^6 q ^-8 s^6 q^-1 rs^6 number x and integers q and s.
⇒ qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹
⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹
⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹
⇒ qr⁻⁸ × r⁻⁴ × s⁹
[tex]$ \Rightarrow \frac{1}{q^8} \times \frac{1}{r^4} \times s^9[/tex]
[tex]$ \Rightarrow \frac{s^9}{q^8r^4}[/tex]
Thus , The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]
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+
At a sale this week, a sofa is being sold for $173.60. This is a 72% discount from the original price.
What is the original price?
The original price of the sofa before the discount is $241.11.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Let the original price of the sofa be x.
Given that 72% of the original price is $173.60, this can be written mathematically as follows:
72/100 × x = 173.60
72x = 17360
x = 241.11
Hence, the original price of the sofa before the discount is $241.11.
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Suppose your friend's parents invest $10,000 in an account paying 6% compounded annually. What will the balance be after 7 years?
The account balance will be $
(Round to the nearest cent as needed.)
The balance will be $15,036.30 after 7 years.
What is Compound Interest?Compound interest, also known as interest on principle and interest, is the practise of adding interest to the principal amount of a loan or deposit.
We have,
P = $10,000
R= 6%
T= 7 years
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt[/tex]
A = 10,000.00(1 + 0.06/1)⁷
A = 10,000.00(1 + 0.06)⁷
A = $15,036.30
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the proportion of defective electronic items in a shipment has the beta distribution. find the probability that at least 30% of the items in the shipment are defective (round off to second decimal place).
The probability that at least 30% of the items in the shipment are defective is 0.7360.
The beta distribution with parameters (3,3) is the conjugate prior for the binomial distribution with a probability of success of p, where 0<p<1.
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of Bernoulli trials. A Bernoulli trial is a random experiment with two possible outcomes: success or failure. In the context of the problem you presented, success would be a defective item, and failure would be a non-defective item.
To find the probability that at least 30% of the items in the shipment are defective, we can use the cumulative distribution function (CDF) of the beta distribution. The CDF of the beta distribution is given by:
F(x;a,b) = (x^(a-1) * (1-x)^(b-1)) / B(a,b)
where x is the proportion of defective items, a and b are the shape parameters, and B(a,b) is the beta function.
We want to find P(X >= 0.3) where X is the proportion of defective items. Substituting the values for a, b, and x we get
P(X >= 0.3) = 1 - P(X < 0.3)
= 1 - F(0.3;3,3)
= 1 - ((0.3^(3-1) * (1-0.3)^(3-1)) / B(3,3))
= 1 - ((0.3^2 * 0.7^2) / (1/6))
= 1 - ((0.09 * 0.49) / (1/6))
= 1 - (0.044/0.1666)
= 1 - 0.2640
= 0.7360
Therefore, The probability that at least 30% of the items in the shipment are defective is 0.7360.
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PLLZZZ HELP!!!
20. The bee population in a certain area is declining at an uninhibited rate of 36. 5% per year. How long will it take for that population to be one-fourth of the initial population?
5. 9 years
1. 6 years
11. 3 years
3. 8 years
The time that it would take for the population to decrease by one fourth is 3 years. Option C
What is population growth?
We know that when we talk about population growth, we are talking about the increase in the population of the species and this can be regarded as a kind of an exponential growth problem.
We know that we can write;
P = Poe^-rt
P = population at time t
Po = initial population
r = population growth rate
t = time taken
Then we have that at the said time, P = 1/4Po
Hence;
1/4Po = Poe^-0.365t
1/4 = e^-0.365t
0.25 = e^-0.365t
ln0.25=ln e^-0.365t
-1.386 = -0.365t
t = 3 years
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6. Four friends are going into business together and have agreed to evenly
split the rental cost of their new company's office space. Each friend
wants to pay no more than $80 per month for their share of the rental
cost. What inequality represents the situation, where x is the total cost of
renting the office space?
Answer: C.
Step-by-step explanation:
since the four friends are SPLITTING the rental cost, it would be dividing.
Then, since it says NO MORE THAN it would be less than or equal to as the symbol for the inequality.
Claire has no more than $45 to spend on a new dress. If x represents the amount Claire can spend, which inequality represents the possible prices of the new dress?
The possible prices of the new dress must be any value less than or equal to $45.
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Start with the inequality x ≤ 45
This inequality states that x must be less than or equal to 45.
Therefore, the possible prices of the new dress must be any value less than or equal to $45.
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please help i’m so bad at geometry
Answer:
what is the question the website is blocked
Step-by-step explanation:
A desk is on sale for $480 , which is 50% of the regular price.
What is the regular price?
Answer: $960
Step-by-step explanation:
Regular Price = x
x*0.5 = 480
x = 960
Answer:
$960
Step-by-step explanation:
Since 480 dollars is half (50%) of the regular price...
you can find the total price by dividing 480 by 0.50 (50%)
or multiplying 480 by 2. You end up getting an answer of $960.
if she needs to allocate her waking time of 15 hours between these two activities, how much studying is she going to do per day?
She would be doing 9 hours of studying per day and 6 hours of other activities. This is because 15 hours divided by 9 hours of studying and 6 hours of other activities would equal the same amount of time allocated to each activity.
The amount of studying she is going to do per day is 9 hours, and the amount of other activities she is going to do per day is 6 hours. This means that she will be dedicating roughly 60% of her waking hours to studying and 40% to other activities. This is a good balance between the two activities, and it will ensure that she is able to adequately focus on both her studies and other activities.
This balance will also help her to stay motivated and not become overwhelmed by her studies. Having a set amount of time for both activities will also help her to organize her day and stay on track. It will give her a sense of structure and allow her to plan her day accordingly.
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Please help I really need it
Kelly's brothers age after 4 2/3 is 23 12/24 years.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
We have ;
Kelly's Brother is 18 7/8 year old.
We have to calculate;
His age after 4 2/3 years.
So,
⇒ 18 7/8 + 4 2/3
⇒ 151/8 + 14/3
⇒151 x 3 + 14 x 8/24
⇒453 + 112 /24
⇒565/24
⇒23 13/24 year old
Hence , his age after 4 2/3 is 23 13/24 years.
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Find the selling price cost to store 30$markup 120%
well, the selling price is simply $30 plus 120% of that, hmmm what's 120% of 30 anyway?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{120\% of 30}}{\left( \cfrac{120}{100} \right)30}\implies 36~\hfill \underset{selling~price}{\stackrel{30~~ + ~~36}{\text{\LARGE 66}}}[/tex]
a fictional country has a population of 5 million people and a net immigration rate of 1 person per 1000 people. the population is only increasing due to immigration. how long will it take the country's population to double?
The time it takes for the country's population to double is 1000 years. The total population would be 10 million people.
How to calculate the population growth?We can calculate the population growth by
P = P₀ × r × t
Where
P = population growthP₀ = current populationr = growth raten = number of periodsSuppose that immigration is the only factor of population growth. We have
Net immigration rate, i = r = 1/1000The current population, P₀ = 5 million peopleFind the time that takes the country's population to double!
To make the country's population double, the population growth should be also 5 million people.
The formula would be
5,000,000 = 5,000,000 × 1/000 × t
t = 1,000/1
t = 1,000 years
Hence, the country's population will be double after 1,000 years.
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kieron has 13 workers he can use for a job. he knows 6 workers would take 14 and a half days. show he has enough workers to finish the job in 7 days
To complete the piece of work Kieron needs 12.42 workers. He able to complete the work in 7 days.
What is the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that 6 workers would take 14 and a half days.
In other words, to complete a piece of work in 14.5 days he needs 6 workers.
Now apply the unitary method,
To complete a piece of work in 1 day he needs 6×14.5 workers.
To complete a piece of work in 7 days he needs (6×14.5)/7 workers.
= 12.42
He has 13 workers and to complete the piece of work he needs 12.42 workers. Thus he was able to complete the work in 7 days.
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Can someone write an equivalent expression to 8(y - 7)?
Answer: 8y-56
Step-by-step explanation: the equivalent expression is 8y-56
Answer: 8y - 56
Step-by-step explanation: Hello! Here are the steps to solve this:
8(y - 7) Use the distributive property, distribute 8 to y and 8 to -7
8y - 56 8 x y = 8y, 8 x -7 = -56
8y - 56 is an equivalent expression to 8(y - 7) because it is simplified. I hope this helps!
Please help me this is driving me crazy
Answer:
24 days = 1500 tables
25 days = Fewer than 1500 tables
Step-by-step explanation:
So we have the inequality of < which is fewer than. Let's start by labeling all the numbers given.
What we want to find is how many days, so we'll make days = x
2100 is the initial and they sell 25 a day... 25 a x.
Combining them all we get a basic inequality of:
2100 - 25x < 1500
Let's get X alone.
Subtracting 2100 from both sides gives you
-25x < -600.
We have negatives on both sides. For me, if I see that, I make both of them positive;
25x < 600
Last step is to divide the 25 out of the X which means you'll divide 25 by 600 also
X = 24
Which means day 24 will be exactly 1500. We wanted fewer though, so adding a day gives you an answer of 25 days.
How do you isolate the variable in x + 5 = 12?
The distance between 2 cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers.
Write you answer as a number without units.
Answer: 70
Step-by-step explanation:
70 kilometers if 3.5 centimeters is the distance and each centimeter represents 20 kilometers, 3.5 times 20 is equal to 70
Jason planted 11 packs of seeds in his 4 garden's he planted the same amount of seeds in each garden how many packs of seeds were planted in each garden
If Jason planted 11 packs of seeds in his 4 garden's he planted the same amount of seeds in each garden then the number of packs of seeds were planted is 2.74 pack for each garden .
the number of packs of seed planted by Jason is = 11 packs ;
the number of gardens in which the seeds are planted is = 4 garden ;
the amount of packs planted in each garden can be calculated by the expression on dividing "number of seed packs" by "number of gardens" ;
⇒ (number of seed packs)/(number of gardens) ;
Substituting values of number of seed pack and number of garden ,
we get ;
= 11/4 = 2.74 .
Therefore , Jason planted 2.74 packs of seed in each garden .
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