Find the area of a quadrilateral formed by the points of intersection of the graphs f(x) = (x − 3)(x + 1) and g(x) = 4x − 2x^2 + 6 and the points of extrema of f(x) and g(x).
Answers
Answer:
24
Step-by-step explanation:
The extrema is halfway between the roots, so for f(x), it has coordinates (1, f(1)) = (1, -4).
For g(x), we can rewrite it as -2(x²-2x-3) = -2(x-3)(x+1). We can see that the extrema has coordinates (1, 8).
Finding the intersection,
[tex](x-3)(x+1)=-2(x-3)(x+1) \\ \\ 3(x-3)(x+1)=0 \\ \\ x=-1, 3 \\ \\ x=-1 \implies f(x)=g(x)=0 \\ \\ x=3 \implies f(x)=g(x)=0[/tex]
So, we need to find the quadrilateral with vertices (1,-4), (1,8), (-1,0), and (3,0).
We observe this is a kite with diagonals of lengths 4 and 12. So, using the formula for the area of a kite, the area is 24.
Related Questions
Use this limit to find f′(11) given f(x)=sqrt(x-2)
Answers
Answer: f'(11)=1/6
Step-by-step explanation:
f(x)=sqrt(x-2)
f(x)=(x-2)^1/2
f'(x)=1/2 * (x-2)^(1/2-1)
f'(x)=1/2 * (x-2)^(-1/2)
f'(11)=1/2 * (11-2)^(-1/2)
f'(11)=1/2 * (9)^(-1/2)
f'(11)=1/2 * (9)^(1/2 * (-1))
f'(11)=1/2 * (9^1/2)^(-1)
f'(11)=1/2 * (3)^(-1)
f'(11)=1/2 * 1/3
f'(11)=1*1/(2*3)
f'(11)=1/6
Using the definition of the derivative, we have
[tex]\displaystyle f'(11) = \lim_{x\to11} \frac{\sqrt{x-2} - \sqrt{11-2}}{x - 11} = \lim_{x\to11} \frac{\sqrt{x-2} - 3}{x - 11}[/tex]
Rationalize the numerator.
[tex]\displaystyle \frac{\sqrt{x-2}-3}{x-11} \cdot \frac{\sqrt{x-2}+3}{\sqrt{x-2}+3} = \frac{\left(\sqrt{x-2}\right)^2 - 3^2}{(x-11)\left(\sqrt{x-2}+3\right)} = \frac{x - 11}{(x - 11) \left(\sqrt{x-2} + 3\right)}[/tex]
If [tex]x\neq11[/tex], we can simplify the limit to
[tex]\displaystyle f'(11) = \lim_{x\to11} \frac{x-11}{(x-11)\left(\sqrt{x-2}+3\right)} = \lim_{x\to11} \frac1{\sqrt{x-2} + 3}[/tex]
The function in the remaining limit is continuous at [tex]x=11[/tex], so we end up with
[tex]\displaystyle f'(11) = \frac1{\sqrt{11-2} + 3} = \boxed{\frac16}[/tex]
what is the image of the point (4, 0) after a rotation of 90 degrees counterclockwise about the origin
Answers
When point is rotated 90 degrees counterclockwise about the origin, point (x,y) becomes (-y,x).
Solving the QuestionWe're given
(4,0) rotated 90 degrees counterclockwise about the originMake the y-coordinate negative:
(4,0)
Switch around the coordinates:
(0,4)
Answer(0,4)
How can you represent the number of bacteria after 6 days in terms of exponents?
Answers
Answer:
b⁶
Step-by-step explanation:
Where b is the variable, we multiply b by itself six times to represent its multiplications every 6 days.
What is the five-number summary for the data set?
Answers
Answer:B
Step-by-step explanation:A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.
Could someone help me with this I will give you brainlist
Answers
Hey diddle diddle the median is the middle mode is the one that you see the most often and the range is the difference between.
And the average you just add all the numbers in the data set together and then divided by the amount of numbers in the data set.
please help my geo grade is so low
Answers
As m ∠ COD = 90°, then the angle COD is a right angle.
What kind of angle is the measure seen in the protractor?
According to geometry, angles are generated by semirrays with a common point. There are different kinds of angles concerning its measure:
Acute angle - Its measure is between 0° and 90°.Right angle - Its measure is 90°.Obtuse angle - Its measure is between 90° and 180°. Straight angle - Its measure is 180°.Based on all the information given by the protractor, we find that the measure of the angle AOD is:
m ∠ COD = m ∠ AOD - m ∠ AOC
If we know that m ∠ AOD = 115 ° and m ∠ AOC = 25°, then the measure of the angle COD is:
m ∠ COD = 115° - 25°
m ∠ COD = 90°
As m ∠ COD = 90°, then the angle COD is a right angle.
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You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $50,000, and the rate is 9.5% using ordinary interest.
You currently have some excess cash: $35,000. Due to situations beyond your control, you, as the owner, must make an immediate business decision now to pursue only one of these two choices:
1) sending all of the $35,000 to Citizens Bank as a partial payment on your loan, or
2) using the $35,000 to purchase serving supplies such as food containers, cups, and plastic dinnerware for your inventory. This is the last day to take advantage of the opportunity to save some money due to a special discount price that is "10% off" the normal cost of $35,000 for these items.
Consider these calculations:
(a)
How much interest (in $) will you save on this loan if you make the partial payment and don't purchase the additional serving supplies? (Round your answer to two decimal places.)
$
(b)
How much money (in $) will you save if you purchase the serving supplies with the discount and don't make a partial payment on the loan? (Round your answer to two decimal places.)
$
(c)
How much (in $) will you save by purchasing the discounted serving supplies rather than making the partial payment? (Hint: Find the difference between the savings on the supplies found in part (b) and the savings on the loan interest found in part (a). Round your answer to two decimal places.)
$
(d)
What other factors should you consider before making this decision?
Answers
The amount saved by repaying the loan early is $831.25
The amount of discount received by purchasing supplies is $3,500
The net amount saved by purchasing supplies rather than repaying loan is $2,668.75
What is ordinary interest?
Ordinary interest is the interest computation that is based on 360-day a year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.
Amount saved in interest=$35,000*9.5%*90/360
Amount saved in interest=$831.25
Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000
Amount saved with discount=10%*$35,000
Amount saved with discount=$3,500
The difference between discount on supplies and interest saved=$3,500-$831.25
The difference between discount on supplies and interest saved=$2,668.75
The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies
Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates
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X °
52°
230°
38°
Find the value of X.
Answers
Answer:
Step-by-step explanation:
all of the angles complete a circle so they must add up to 360 degrees.
230 + 38 + 52 + x = 360
320 + x = 360
x = 40 degrees
7 is a factor of which number?
Answers
If p=7 and q=1, what is 4pq squared + (-7)pq squared +5p?
For the exponents, I don’t know how to distribute the squared/power of two within each term.
Answers
Answer:
14
Step-by-step explanation:
q² = 1
and 1² = 1 * 1 = 1
4pq² + (-7)pq² +5p
Evaluate for p=7,q=1
(4)(7)(1²)+((−7)(7))(1²)+(5)(7)
(4)(7)(1²)+((−7)(7))(1²)+(5)(7)
=14
Tane and Pete are raising funds for their sports trip.
Between them they need to raise $1000.
There are only 5 weeks until they need the money.
Tane gets paid $15 an hour, and Pete gets paid $16 an hour as he has more experience.
Between them they work for a total of 13 hours each week.
What is the average number of hours that each of them work per week if they are to have
exactly the amount of money they need?
Answers
Answer: Tane needs to work 8 hours per week while Pete needs to work 5 hours per week
Step-by-step explanation:
T=Tane. P=Pete
5*13=65
T+P=65
15T+16P=1000
T=65-P
15(65-P)+16P=1000
975-15P+16P=1000
975+P=1000
P=25 hours for 5 weeks
T=65-25
T=40 hours for 5 weeks
P: 25/5=5 hours per week
T: 40/5=8 hours per week
Tane needs to work 8 hours per week while Pete needs to work 5 hours per week
2x + = x + 5
Solve using a mental strategy
Answers
The required solution of the given equation is 5.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The given equation is
2x + = x + 5
According to given question we have
Mental Math is an exercise where we solve mathematical equations mentally without the help of a calculator.
To do the bigger or important quantities first. This gives an estimate of the value expected. Such an approach is front end or left to right multiplication.
2x = x + 5
Substract x from both sides we get,
x=5
Therefore, the required solution of the given equation is 5.
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A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 10 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.
According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between __ years and __ years. (Round your answer to the nearest whole number)
According to Chebyshev's theorem, at least what percent of the home buyers' ages lie between 25 years and 65 years.
Answers
Step-by-step explanation:
Given that
A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 10 years.That these measures are valid for the population of all home buyers.To find
Complete the given statements about the distribution of all ages of home buyers.So, according to the question
We have,
Mean of ages = 45, andStandard deviation = 10We know that,
Chebyshev's Theorem
The smallest percentage of observations that fall within a precise range of current standard deviations from the mean is estimated by Chebyshev's Theorem. There are many different chance distributions that are covered by this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.When the distribution is not normal, Chebyshev's Theorem is used. It states that:
Measures are all within 2 standard deviations of the mean in at least 75% of cases.Measures are all within 3 standard deviations of the mean in at least 89% of cases.The percentage of measurements that are within k standard deviations of the mean is represented by an in general:[tex]P = 100(1-\frac{1}{k^2} )[/tex]
Chebyshev's Theorem is used to determine that:
At least 56% of home buyers are between the ages of 30 and 60.At least 75% of home buyers are between the ages of 25 and 65.For the 1sr item, we have to find k at P = 56,
[tex]P = 100(1-\frac{1}{k^2} )[/tex]
[tex]56 = 100(1-\frac{1}{k^2} )[/tex]
0.56 = 1 - [tex]\frac{1}{k^2}[/tex]
[tex]\frac{1}{k^2} = 0.44[/tex]
k² = 1/0.44
k = [tex]\sqrt{\frac{1}{0.44} }[/tex]
k = 1.5
The bounds are, therefore, within 1.5 standard deviations:
45 - 1.5 × 10 = 30 years old.45 + 1.5 × 10 = 65 years old.Ages 25 and 65 are both 2 standard deviations away from the mean, so:
At least 75% of the home buyers' age lie between 25 years and 65 years.Answer:
According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between 30 years and 65 years.According to Chebyshev's theorem, at least what 75% of the home buyers' ages lie between 25 years and 65 years.To learn more about Chebyshev's theorem, please click on the link:
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Suppose a computer manufacturer has the total cost function
C(x) = 76x + 3600
(in dollars) and the total revenue function
R(x) = 376x
(in dollars).
(a) What is the equation of the profit function P(x) (in dollars) for this commodity?
Answers
The equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600
It is given in the problem that,
The total cost function C(x) = 76x + 3600 (in dollars)
Also,
The total revenue function R(x) = 376x (in dollars)
We need to find the equation of the profit function P(x) (in dollars) for this commodity
First we need to understand the following terms
Cost is the price of a commodity which is paid or charged in exchange of something. Example - 1 kg of apple are of 3 Dollars
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations.
So,
The equation of the profit is given by = Total Revenue - Total Cost
P(x) = R(x) - C(x)
Putting values, we get
P(x) = 376x - (76x + 3600)
P(x) = 376x - 76x - 3600
P(x) = 300x - 3600
Hence, the equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600
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Suppose that 650lb of coffee are sold when the price is $4 per pound
Answers
Money earned = $162.50
Explanation:
650 / 4 – You make $4 for every pound sold
= 162.5
Which is $162.50
C. Julia has six novels she wants read, one of them
which is in the chest of a woman' by Efo Kodjo
Mawugbe. She plans to create a reading list of four of
these novels for an upcoming trip, and different orders
count as different lists. How many reading lists are
possible if 'in the chest of a woman' must be on the
list?
Answers
She can have 60 reading list to plan to read the 6 novels that she wants to read including the 'in the chest of a woman' in the list.
We are given that:
Number of novels that Julia wants to read = 6
She plans to read = 4
1 novel is fixed that is "in the chest of a woman' by Efo Kodjo"
We need to tell the number of possible reading list that she can have.
We will use permutation for it
By using permutation, we get that:
Number of reading list = 1 × 5 × 4 × 3
Number of reading list = 5 × 12
Number of reading list = 60 lists
Therefore, she can have 60 reading list to plan to read the 6 novels that she wants to read including the 'in the chest of a woman' in the list.
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$953 is ________% of $1717
Select one:
A. 0.6
B. 55.5
C. 0.1
D. 180.2
Answers
Step by step
$953 is _______ % of $1717
$953 = x (unknown %) of $1717
$953 = $1717x
Divide both sides by 1717 to solve for x
953/1717 = 1717/1717 x
.555 = x
To turn this into a percent, move your decimal point two places to the right
Answer is 55.5%
You can check your work by substituting 55.5% into the word problem
$953 is 55.5 % of $1717
1717 x .555 = $953
Problem solved
Express the following inequality using interval notation.
1/2x−1>7
Answers
The inequality using interval notation is (18, ∝)
How to express the inequality using interval notation?The inequality is given as
1/2x − 1 > 7
Add 1 to both sides of the inequality
So, we have
1/2x − 1 + 1 > 7 + 1
Evaluate the like terms
So, we have
1/2x > 8
Multiply through by 2
So, we have
x > 16
Using interval notation, we have
(18, ∝)
Hence, the inequality using interval notation is (18, ∝)
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James is saving $15 per week in order to purchase a gaming console. Create a table to represent the relationsip between x, the number of weeks and y, the total amount James has saved.
Answers
The total amount saved by the James is: $330.
Equation: What is it?The relationship between two expressions is expressed by the word equation. It employs many mathematical symbols, including greater-than, less-than, and equal.
The amount James has saved, according to the query, is $15 each week.
It is now time to generate the table that shows how the variable "x" and the number of weeks relate to one another.
The following are the possible possibilities for the necessary parameters "x" and "y":
x = [1 2 3 4]
y = [15 30 45 60]
The last formula may now be written as y = 15x.
The formula will be y = 15x = 15x22 = 330 dollars after 22 weeks.
As a result, the James have saved $330.
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Identify the correct justification for each step, given that m/1 = 30° and m/2 = 30°.
Answers
30 = m<1 = m<2
m<1 is equals to m<2 because these two angles are transitive property.
How to identify the correct justification for m<1 = 30° and m<2 = 30°?given that m<1 = 30° and m<2 = 30°.
m<1 = 30
m<2 equals to m<1
m<2 = 30 can be obtained by substituting 30 into the second equation.
The proof is now complete.
The Transitive Property of Equality can also be used, which asserts that if X = Y and Y = Z, then X = Y = Z. In other words, if one number is equal to another, and that other number is equal to a third, then all three numbers must be the same.
thus, 30 = m<1 = m<2, m<1 is equals to m<2 because these two angles are transitive property.
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Help me pleasseeee lelelelelele
Answers
Area of rectangle is length times width
So total are is 5*6=30
How can setting your cell phone to silent while listening help you listen actively?
Answers
Answer: Turning your cell phone off or on silent can help you listen actively because you won't have the urge to look at it unless you hear a little notification.
But honestly, whose question is this, it's so random, and I think everyone can listen with their phones out, because I pay more attention when I'm doing something like on a phone or listening to music.
Given (x,7) and (−1,y) find x and y such that the midpoint between these two points is (3,5)
Answers
The solution to the system of linear equations is (x, y) = (7, 3).
How to find the missing coordinates of the two ends of a line segmentHerein we find that the coordinates of the midpoint and part of the coordinates of the ends of the line segment are known. We must determine the values of the missing coordinates by the midpoint formula:
0.5 · (x, 7) + 0.5 · (-1, y) = (3, 5)
Which is equivalent to the system of linear equations:
0.5 · x - 0.5 = 3 (1)
3.5 + 0.5 · y = 5 (2)
The solution to the system of linear equations is (x, y) = (7, 3).
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The function F(x) = −0.005x^2 + 0.8x + 12 models the relationship between a certain vehicle’s speed and the fuel economy, where F(x) is the fuel economy in kilometres per litre and x is the speed of the vehicle in kilometre per hour.
a) Determine the average rate of change in the fuel economy in the interval of speed [60,80].
b) b) Interpret your result.
Answers
a) The average rate of change on that interval is 0.1
b) as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1
How to find the average rate of change on the given interval?For any function f(x), the average rate of change on an interval (a, b) is given by:
(f(b) - f(a))/(b - a)
In this case, the function is:
F(x) = −0.005x^2 + 0.8x + 12
And the interval is [60, 80]
Then we have:
F(60) = −0.005*60^2 + 0.8*60 + 12 = 42
F(80) = −0.005*80^2 + 0.8*80 + 12 = 44
Then the average rate of change on that interval is:
R = (44 - 42)/(80 - 60) = 0.1
b) What does that rate means?
F(x) relates the fuel economy and x the speed of the vehicle.
This means that as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1.
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The mass of a paperclip is 6.0 × 10−4 mg. If a box of paperclips has 7.23 × 104 paperclips, determine the total mass of the paperclips in the box. Write the final answer in scientific notation with the correct number of significant digits.
4.338 × 101 mg
4.3 × 101 mg
4 × 101 mg
3.62 × 100 mg
Answers
Taking into account the definition of Scientific notation, the correct answer is the first option: the total mass of the paperclips in the box is 4.338×10¹ mg.
Scientific notationScientific notation is a quick way to represent a number using powers of base 10.
The numbers are written as a product:
a×10ⁿ
where:
a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is a whole number, which is called an exponent or an order of magnitude. Represents the number of times the point decimal is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.Total mass of the paperclips
In this case, you know that:
The mass of a paperclip is 6.0×10⁻⁴ mg. A box of paperclips has 7.23×10⁴ paperclips.To know the total mass of the paperclips in the box, you must multiply the number of paperclips in the box by the mass of each paperclip:
7.23×10⁴×6.0×10⁻⁴
To multiply numbers in scientific notation, you multiply the numbers that are not powers of 10 (the numbers previously called "a") and add the exponents of 10.
(7.23×6.0)×10⁴⁻⁴= 43.38×10⁰= 4.338×10¹ mg
Finally, the correct answer is the first option: the total mass of the paperclips in the box is 4.338×10¹ mg.
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4.
Calculate 3% of $600
Answers
i used desmos calculator to calculate the answer
Hey there!
3% of $600.00
= 3% * $600.00
= 0.03 * 600
= 3/100 * 600/1
= 3(600) / 100(1)
= 1800/100
= 1800 ÷ 100 / 100 ÷ 100
= 18/1
= 18 ÷ 1
= 18
Therefore, your answer should be:
18
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HELP HELP HELP HELP HELP
please...
Answers
Answer:
-10
Step-by-step explanation:
[tex]f(x) = 2 - 3x \\ [/tex]
So,
[tex]f(4) = 2 - (3 \times 4) = 2 - 12 = - 10[/tex]
Therefore, Option A is correct
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What makes a zero? Using zero to simplify algebraic expressions
Answers
It should be noted that an algebraic expression will be equal to zero when the difference is between the same expressions.
How to illustrate the information?It should be noted that an algebraic expression simply means the expression that's used to show the relationship between the variables
In this case, the should be noted that an algebraic expression will be equal to zero when the difference is between the same expressions.
An example is illustrated as:
= 2x - 2x
= 0
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Are these ratios equivalent?
17 1
33 3
Answers
Answer:
no
Step-by-step explanation:
There is no question that is the station
Answers
Answer: lol
no question that is the station? so there's no question?
ok
Step-by-step explanation:
