Given that f(x) = x² 13x + 30 and
g(x)= x-3, find f(x) · g(x) and
express the result as a polynomial in simplest form.
Answers
The simplest polynomial form of f(x)×g(x) is x³ - 16x² + 69x - 90.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, makeup polynomials. For instance, the polynomial 3x+2x-5: A description of polynomials.So, f(x) × g(x):
Calculate as follows:
Therefore, the simplest polynomial form of f(x)×g(x) is x³ - 16x² + 69x - 90.
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Related Questions
How many dogs do they need to walk in order to pay for the box of treats?
hint:In the equation for the function representing the profit, substitute 5 for y and solve the equation for x.
hint:Round up to the nearest whole number of dogs.
Answers
The number of dogs do they need to walk in order to pay for the box of treats is 4
The function that representing the profit is
y = 3x - 5
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Here the cost for buying a box of treat = $5
Substitute the value in the function and find the number of dog that they need to walk
5 = 3x - 5
3x = 5 + 5
3x = 10
x = 10 / 3
x = 3.33
x ≈ 4
Hence, the number of dogs do they need to walk in order to pay for the box of treats is 4
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Please help!! See screenshot attached below (100 pts)
Answers
Answer:
f(2) = 0
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
Therefore, applying the factor theorem, if (x - 2) is a factor of a polynomial f(x) then f(2) = 0.
If CE and FH are parallel lines and m/CDG =
are parallel lines and m/CDG = 128°, what is mZHGD?
Answers
ALTERNATE INTERIOR ANGLES
How do work out 349 divided by 60
Answers
Answer:
5 with a remainder of 49
Step-by-step explanation:
2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
Answers
She paid $1.375 per pound of strawberries.
What is the unit rate?
When expressed rate as a fraction, a unit rate has a denominator of 1.
Since 4 pounds cost $5.50, 1 pound of strawberries will cost 5.50/ 4 ≈ $1.375.
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HELP PLEASE ILL DO ANYTHING ONE MCRIB BURGER
Answers
The solutions for the graphed linear inequality are (-4, 0), (-1, 4), (0, 0), and (-2, 0). The correct options are A. (-4, 0), B. (-1, 4), C. (0, 0), and E. (-2, 0)
Determining the solutions of a linear inequality from a graphFrom the question, we are to determine all of the solutions for the linear inequality whose graph is given
To do this, we will find the points that fall in the solution region (shaded portion of the graph)
A. (-4, 0)The point (-4, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
B. (-1, 4)The point (-1, 4) falls in the solution region. Thus, it is a solution for the linear inequality.
C. (0, 0)The poi0nt (0, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
D. (4, -1)The point (4, -1) does not fall in the solution region. Thus, it is not a solution for the linear inequality.
E. (-2, 0)The poi0nt (-2, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
F. (0, -2)The point (0, -2) does not fall in the solution region. Thus, it is not a solution for the linear inequality.
Hence, the solutions are (-4, 0), (-1, 4), (0, 0), and (-2, 0).
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Find the angle between each of these pairs of vectors:
A = -2.00 i + 6.00 j and B = 2.00 i - 3.00 j
Answers
The angle of pairs = 170.
The characteristics of the scalar product allows to find the angle between the two vectors is:The scalar product is the product between two vectors whose result is a scalar.
A . B = |A| |B| cos θWhere A and B are the vectors, |A| and |B| are the modules of the vectors and θ at the angle between them.
The vector is given in Cartesian coordinates and the unit vectors in these coordinates are perpendicular.
i.i = j.j = 1 i.j = 0 A . B = (4 i - 4j). * -5 i + 7j) A . B = - 4 5 - 4 7 A. B = -48We look for the modulus of each vector.
|A| = 4 √2 |B| = 8.60We substitute. -48 = 4√2 8.60 cos θ -48 = 48.66 cos θ θ = cos⁻¹ θ = 170ºIn conclusion using the dot product we can find the angle between the two vectors is:
Hence, the angle θ = 170º
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6 sqrt 44z + sqrt 99z
Answers
Answer: 15√11z
Step-by-step explanation:
Calculate ending inventory and COGS using FIFO and LIFO methods for ABC Inc.
On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
Answers
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO, which means First-in, First-out, computes the cost of goods sold based on the assumption that the physical flow of goods sold depends on the earlier inventory in stock.
FIFO can be applied under both the perpetual and periodic inventory systems, unlike LIFO.
LIFO means Last-in, First-out, and as a cost flow assumption assigns the cost of goods sold based on the latest inventory purchases.
LIFO cannot be used under the perpetual inventory system.
Date Activities Units Unit Rate Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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Joey has 80 pens and 30 of them are red. What percent are red?
Answers
Answer:
Step-by-step explanation:
Drag each tile to the correct box. Not all tiles will be used.
Consider the recursively defined function below.
f(1) = = 10
f(n) 2.2 f(n-1), for n = 2, 3, 4, ...
Create the first five terms of the sequence defined by the given function.
Answers
The first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22 f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.
What is a sequence?
A collection of events or items that occur one after the other in a specific order is referred to as a sequence.
Here, we have
Given the function is f(n) = 2.2 [ f(n-1) ] Here, f(1) = 10 then we have to create the first five terms of the sequence defined by the function.
Since f(1) = 10
f(2) = 2.2 [ f (2-1) ] = 2.2× [ f (1) ]
= 2.2 × 10 = 22
f (3) = 2.2 [ f (3-1)] = 2.2 × [ f (2) ]
= 2.2 × 22 = 48.4
f(4) = 2.2 [ f(4-1) ] = 2.2× [ f(3)]
= 2.2 × 48.4 = 106.48
f(5) = 2.2 [ f(5-1) ] = 2.2× [ f(4)]
2.2× 106.48 = 234.256
Hence the first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22 f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.
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If you make $4 on a sale of one share of stock that you bought for $22, what is your ROI?
Answers
Answer:
$26
Step-by-step explanation:
Lee.com accepted a $70,000, 634% , 120-day note on July 26. Lee discounted the note on October 28 at LB Bank at 6%. What proceeds did Lee receive? (Use Days in a year table) (Round your answer to the nearest cent.)
Answers
On October 28, Lee received proceeds of $71,153.66 from the discounted note.
What is note discounting?Discounting a note involves receiving immediate cash by selling it to a financial institution at a discount.
The implication of discounting a note is that the receiver gets less than the maturity value.
The maturity value is the face value of the note plus the computed interest.
Face value of the note receivable = $70,000
Interest rate = 6.34%
Note period = 120 days
July 26 - October 28 = 94 days
Maturity value of the note receivable = The Face Value + Interest
= $71,459.07 [$70,000 + ($70,000 x 6.34% x 120/365)]
Bank discount rate = 6%
The discount period from October 28 to Nov 22 = 26 days (120 - 94)
Bank discount = Maturity Value x Discount Rate x Discount Period
= $305.41 ($71,459.07 x 6% x 26/365)
Proceeds = Maturity value - Bank discount
= $71,153.66 ($71,459.07 - $305.41)
Thus, by discounting the note receivable at LB Bank at 6%, Lee received $71,153.66 instead of the $71,459.07 it would have received at maturity.
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If y varies directly as x, find the constant of variation k and the direct variation equation for the situation.
y=2 when x= 10
Answers
Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.
What is meant by variation equation?A variation is a relationship between one set of values for one variable and another set of values for another variable. Variation in direct. If m is a nonzero constant and b = 0, then the function y = mx (often written y = kx) is a direct variation of the equation y = mx + b. If y varies directly as x and y = 6 when x = 2, the constant of variation is k = 3. As a result, the equation for this direct variation is y = 3x.The direct variation equation is a two-variable linear equation given by y = kx, where k is the constant proportionality. In a coordinate plane, the direct variation graph is a straight line.Therefore,
y=0.25 x
the initial statement is y ∝ x
to convert to an equation multiply by k the constant of
⇒ y=k x
to find k use the given condition
y=0.5 when x=2
[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]
the equation is y = 0.25x
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The variation equation is [tex]y=\frac{1}{5} x[/tex]
What do you mean by direct variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first changes and decreasing when the first changes. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity.The mathematical relationship between the two quantities in the direct variation formula makes it so that one of the variables is a constant multiple of the other. The sign "∝" is used to indicate that two quantities are directly proportional to one another or directly varying from one another. Assuming that x and y are two quantities that are directly varying, they are stated as follows: y∝ xThe direct variation formula is expressed as follows when the proportionality sign is omitted.Calculation
Given, y =2 and x=10
we know the direct relation in y∝ x
so, y = kx, where k is the proportionality constant
2= k*10
k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]
Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]
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The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c).
Temperature: Days:
50-59 5
60-69 309
70-79 1496
80-89 1521
90-99 533
100-109 6
(a) Approximate the mean and standard deviation for temperature.
B) Use the frequency histogram of the data to verify that distribution is bell shaped. Yes or No
C) According to the Empirical rule, 95% of the days in the month will be between what two temperatures?
Answers
Regarding the data-set of the temperatures, it is found that:
a) The mean and the standard deviation are given as follows:
Mean: 80.41Standard deviation: 8.33.b) The histogram is bell shaped.
c) 95% of the days will be between 63.75 ºF and 97.07 ºF.
How to obtain the mean and the standard deviation?The first step towards obtaining the mean and the standard deviation is obtaining the relative frequencies, which are the absolute frequencies divided by the number of observations.
The number of observations is:
5 + 309 + 1496 + 1521 + 533 + 6 = 3870.
Considering the midpoint of each interval, the following distribution is built:
P(X = 54.5) = 5/3870 = 0.0013.P(X = 64.5) = 309/3870 = 0.0798.P(X = 74.5) = 1496/3870 = 0.3866.P(X = 84.5) = 1521/3870 = 0.3930.P(X = 94.5) = 533/3870 = 0.1377.P(X = 104.5) = 6/3870 = 0.0016.The mean is given by the sum of each value multiplied by it's relative frequency, hence:
E(X) = 54.5 x 0.0013 + 64.5 x 0.0798 + 74.5 x 0.3866 + 84.5 x 0.3930 + 94.5 x 0.1377 + 104.5 x 0.0016 = 80.41.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their relative frequencies, as follows:
S(X) = sqrt((54.5-80.41)² x 0.0013 + (64.5-80.41)² x 0.0798 + (74.5-80.41)² x 0.3866 + (84.5-80.41)² x 0.3930 + (94.5-80.41)² x 0.1377 + (104.5-80.41)² x 0.0016) = 8.33.
From the histogram, most values are around the mean, with a small percentage of around 0.3% around the bounds, accordingly with the Empirical Rule, hence the distribution is normal.
By the Empirical Rule, a percentage of 95% of the observations is within two standard deviations of the mean, hence:
80.41 - 2 x 8.33 = 63.75.80.41 + 2 x 8.33 = 97.07.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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4x7 = 2x + 15
Does the equation have one
none, or infinite solutions?
Explain why.
Answers
Answer:
There is only one solution
Step-by-step explanation:
4x - 7 = 2x + 15
+7 +7
4x = 2x + 22
-2x -2x
2x = 22
divide by 2 into both sides
x = 11
Since there is only one answer, there is only ONE solution.
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=990 and x=581 who said "yes." Use a 95% confidence level.
Answers
The 95% confidence interval for the proportion of respondents who say yes is of:
(0.5562, 0.6176)
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters, which are the sample size and the estimate, are given as follows:
[tex]n = 990, \pi = \frac{581}{990} = 0.5869[/tex]
The lower bound of the interval is of:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 - 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.5562[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 + 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.6176[/tex]
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Can I have some help asap?
Answers
Answer:
I will help you okay????
Dog food comes in two different sized bags. The 4 lb bag sells for $19.49 while the 30 lb bag sells for $73.99. Which is cheaper per pound and by how much?
Answers
Answer:
30 lb bag is cheaper by about $2.40
Step-by-step explanation:
to find per pound we divide
19.49/4= 4.8725
$4.87per pound
$73.99/30=2.46633
$2.47 per pound
30 lb bag is cheaper per pound
4.87-2.47=2.40
hopes this helps please mark brainliest
Which represents the solutions of the graphed system of equations y=x2+2x-3 and y=x-1?
Answers
Answer:
second option
Step-by-step explanation:
the solution to the system of equations is at the points of intersection of the two graphs.
the graphs intersect at (- 2, - 3 ) and (1, 0 ) , then
the solutions are (- 2, - 3 ) and (1, 0 )
find the amount on $ 6,250 at 8%p.a compounded annually for 2 years. also, find the compounded intrest
Answers
The Compound Interest is $7,290.00.
What is Compound Interest?In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
Given:
P= 6250
T= 2 years
r = R/100
r = 8/100
r = 0.08 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 6,250.00[tex](1 + 0.08/1)^{(1)(2)[/tex]
A = 6,250.00(1 + 0.08)²
A = $7,290.00
Hence, The Compound Interest is $7,290.00.
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3 times 4 times 4 times 3 times 3 times 4 = 3 (to the power of x) times 4 (to the power of y)
Answers
The value of 3 times 4 times 4 times 3 times 3 times 4 in exponent is 3³ × 4³
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the expression given is 3 times 4 times 4 times 3 times 3 times 4. It should be noted that the 4 occurs three times as well as the 3.
Therefore, this will be 3³ × 4³.
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How many hour is 4:30 until 6:00
Answers
Answer: 1 hour and 30 minutes or 1.5 hours
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Division A of Aztec Manufacturing purchases materials to be used in production from an outside supplier for $20 per unit. The same materials are produced by Division B. Division B incurs variable costs of $10 per unit. Currently, Division B is able to sell only 320,000 units to outside buyers out of 400,000 units produced. In this situation, if a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A, by what amount would Division B's operating income increase? a.$160,000 b.$960,000 c.$640,000 d.$800,000
Answers
The operating income of Division B will increase by $640,000
How to calculate the increase in Division B's operating income?
Given that: Division B incurs variable costs of $10 per unit and a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A
This cost of production by division B is:
cost = $10 × 80,000 = $800,000
Division B uses a transfer price of $18 per unit. That is:
Selling price = $18 × 80,000 = $1,440,000
Operating income increase = Selling price - cost
Operating income increase = $1,440,000 - $800,000 = $640,000
Therefore, Division B's operating income increase will be $640,000
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18
8. Carey bought a $2,100 computer system on the installment plan. He made a $400 down
payment, and he has to make monthly payments of $79.50 for the next two years. How much
interest will he pay?
Answers
Answer:
$208
Step-by-step explanation:
$79.50 x 24 = 1908
$1908 + 400 = 2308
$2100/2308 = 9%
Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.
What is Interest?Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.
Total number of monthly payments
= 12 months/year x 2 years
= 24 months
and, Monthly payment amount = $79.50
Total amount paid in monthly installments
= Monthly payment amount x Total number of monthly payments
= $79.50 x 24
= $1,908
Next, we can subtract the initial down payment from the total amount paid to find the interest paid:
Total interest paid = Total amount paid - Down payment
= $1,908 - $400
= $1,508
Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.
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1. Solve the equation (9-6p) =
-11 for p.
Answers
Answer:
p=p=10/3
Explanation:
9-6p =-11=p=10/3
The probability that a 50-year-old male in the U.S. will die within one year is about 0.00142. An insurance company is preparing to sell a 50-year-old male a one-year, $60,000 life insurance policy. How much should it charge for its premium in order to have an expectation of $0 for the policy (i.e., make no profit and make no loss)? (Round your answer to the nearest dollar.)
Answers
They should charge for its premium in order to have an expectation of $0 for the policy is $85.
Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of alive 100-0.00142
= 0.99858
P(A)=0.99858A+0.00142(A+60000)
Put A=0, in the obtained function, we get
P(0)=0.99858(0)+0.00142(0+60000)
=0.00142×(60000)
=$85.2
= $85
Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.
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rewrite 3x+4y>8 in slope intercept form
Answers
Answer: y > -3/4x + 2
Step-by-step explanation:
41% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
P(3)=
P(x >4)=
P(x<9)=
Answers
The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is;
(a) exactly three = 0.1314
(b) at least four = 0.7953
(c) less than eight = 0.93382
How to solve Binomial Probability Distribution Problems?The binomial probability distribution is the probability of exactly x successes on n repeated trials, with p probability. The formula is;
P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)
We are given;
p = 41% = 0.41
n = 12
Thus;
1) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is exactly three;
P(3) = ¹²C₃ * 0.41³ * (1 - 0.41)^(12 - 3)
P(3) = 0.1314
2) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is at least four;
P(x ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
P(x ≥ 4) = 0.7953
3) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is less than eight using binomial probability calculator is;
P(X < 8) = 0.93382
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What are the answers to 3, 4, and 5? Thank you.
Answers
The missing terms in the two column proof are;
Reason 4; Opposite Angles
Reason 5; AAS Congruency Postulate
How to carry out two column proof of triangles?From the given image, we want to use the two column proof to prove that ΔAEC ≅ ΔDEB.
Now, we have the two column proof as follows;
Statement 1; AC ║ BD
Reason 1; Given
Statement 2; AC ≅ BD
Reason 2; Given
Statement 3; ∠ACE ≅ ∠DBE
Reason 3; Alternate angles
Statement 4; ∠AEC ≅ ∠BED
Reason 4; Opposite Angles
Statement 5; ΔAEC ≅ ΔDEB
Reason 5; AAS Congruency Postulate
The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.
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