Answer:
C.
Step-by-step explanation:
Two lines, R and M, are represented by the following equations:
Line R: 2x + 2y = 18
Line M: x + y = 9
Which statement is true about the solution to the set of equations? (4 points)
A.There is no solution.
B.It is (18,9).
C.There are infinitely many solutions.
D.It is (9, 18).
The answer is C. There are infinitely many solutions.
Nina opened a savings account and deposited $300.00. The account earns 4% interest, compounded monthly. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike?
Answer:
up to $338.18
Step-by-step explanation:
Use the compound amount formula:
A = P(1 + r/n)^(n*t), where r is the interest rate as a decimal fraction and n is the number of compounding periods per year.
Here, A = $300(1 + 0.04/12)^(12*3), or
A = $300(1.0033333)^*36, or
A = $300(1.127) = $338.18
Nina will be able to spend up to $338.18 on a new bike.
Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.
cos−1(StartFraction 6.9 Over 12 EndFraction)
cos−1(StartFraction 9.8 Over 12 EndFraction)
sin−1(StartFraction 6.9 Over 12 EndFraction)
sin−1(StartFraction 9.8 Over 12 EndFraction)
tan−1(StartFraction 6.9 Over 9.8 EndFraction)
To find measure of angle BAC in a right triangle, we can use the trigonometric functions cos⁻¹(6.9/12), sin⁻¹(6.9/12), and tan⁻¹(6.9/9.8), corresponding to the sides AC and CB with respect to the hypotenuse AB.
Explanation:To find the measure of angle BAC in triangle ABC where angle ACB is a right angle, we can use the trigonometric ratios involving the sides of the triangle. Given that AB is the hypotenuse, CB is the adjacent side to angle BAC, and AC is the opposite side to angle BAC, we can use the following expressions:
cos⁻¹(⅓6.9/12): This represents the cosine of angle BAC, since cosine is the ratio of the adjacent side to the hypotenuse.sin⁻¹(⅓6.9/12): This represents the sine of angle BAC, since sine is the ratio of the opposite side to the hypotenuse.tan⁻¹(⅓6.9/9.8): This represents the tangent of angle BAC, since tangent is the ratio of the opposite side to the adjacent side.Using any of these trigonometric functions, we can calculate the measure of angle BAC by inputting the ratios into a calculator that has the capability to compute the inverse trigonometric functions.
The pie chart shows information about the grades achieved by all of the candidates in Keval's school who took AS Level English in 2015. 8 candidates achieved grade C. Work out the number of candidates in Keval's school who took AS Level English in 2015, showing your working out (2 marks)
Answer:
you have to put the pie chart to get an answer
Step-by-step explanation:
Suppose that 200 flies are ee, 150 flies are ee, and 150 flies are ee. calculate the frequencies of the 3 genotypes for this population. do not leave your answers as fractions!
Complete Question
Imagine a large Source [tex](S_o)[/tex] population of 500 files at a particular time we will call [tex]T_s[/tex].The files have brown ebony bodies. Suppose that 200 flies are ee, 150 flies are Ee, and 150 flies are EE. calculate the frequencies of the 3 genotypes for this population. do not leave your answers as fractions!
Answer:
The frequency of genotype ee is [tex]f_{ee}= 0.4[/tex]
The frequency of genotype Ee is [tex]f_{Ee} = 0.3[/tex]
The frequency of genotype EE is [tex]f_{EE} = 0.3[/tex]
Step-by-step explanation:
From the question we are told that
The number of files with genotype ee is [tex]ee = 200[/tex]
The number of files with genotype Ee is [tex]Ee = 150[/tex]
The number of files with genotype [tex]EE[/tex] is [tex]EE = 150[/tex]
The frequency of genotype ee is mathematically evaluated as
[tex]f_{ee} = \frac{200}{500}[/tex]
[tex]f_{ee}= 0.4[/tex]
The frequency of genotype Ee is mathematically evaluated as
[tex]f_{Ee} = \frac{150}{500}[/tex]
[tex]f_{Ee} = 0.3[/tex]
The frequency of genotype EE is mathematically evaluated as
[tex]f_{EE} = \frac{150}{500}[/tex]
[tex]f_{EE} = 0.3[/tex]
Our school had a pizza party.The school ordered 847 slices of pizza for the party. The students ate 628 slices. How many slices of pizza are left over?
Answer:
209
Step-by-step explanation:
837-628
F(x)=x^2 - 1/x - 4
Can someone please help me with this
deon buys candy that cost $6 per pound. he will buy at most 7 pounds. write answer as inequality
Answer:
x ≤ 42 dollars
Step-by-step explanation:
Deon will buy at most 7 pounds, and we know that it costs 6 per pound, so we multiply 7 and 6 to get 42. Deon will not buy over 7 pounds, so that means less than or equal to.
A play started at 2:35 P.M after the play was over , Jamie talked to a friend for 15 minutes She left the theatre at 4:10 P.M how long was the play? Would fine this super helpful thank you so much
Answer:
1 hour 20 minutes
Step-by-step explanation:
The play started at 2:35 PM.
After the play, Jamie talked to her friend for 15 mins and then left the theater at 4:10 PM.
She started talking to her friend once the play was over, hence, to find the time she started talking, we subtract 15 mins from 4:10 PM:
H M
04 : 10
- 00 : 15
03 : 55
She started talking around 3:55 PM.
Hence, to find how long the play lasted:
H M
03 : 55
- 02 : 35
01 : 20
Hence, the play lasted for 1 hour 20 minutes.
What is the slope of the line that passes through the points (-9, -3) and (1, -3)?
Write your answer in simplest form.
Answer:
The slope is 0.
Step-by-step explanation:
m= (y2-y1)/(x2-x1).
y2 is -3, y1 is -3.
x2 is 1 and x1 is -9.
m= -3 -(-3)/ 1- (-9)
m= 0/10
m=0
The slope of the line that passes through the points (-9, -3) and (1, -3) is 0 because the y-coordinates of both points are the same and this results in a 'change in y' of 0.
Explanation:In mathematics, the slope of a line passing through two given points can be calculated by the formula: (y2 - y1) / (x2 - x1). Where y2 and y1 represent the y-coordinates of the two points and x2 and x1 represent the x-coordinates of the two points. However, in this particular case, we see that the y-coordinates of both points (-9, -3) and (1, -3) are the same as -3.
This means our 'change in y', or (y2 - y1), is equal to zero (-3 - -3 = 0). Any fraction with 0 as the numerator (0 divided by any number) is itself equal to 0. Therefore, the slope of the line that passes through the points (-9, -3) and (1, -3) is 0.
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Purse A which contains $1,000 today. If you leave it alone, it will contain $1,200 tomorrow (by magic). The next day, it will have $1,400. This pattern of $200 additional dollars per day will continue. Purse B which contains 1 penny today. Leave that penny in there, because tomorrow it will (magically) turn into 2 pennies. The next day, there will be 4 pennies. The amount in the purse will continue to double each day. How much money will be in each purse after a week? After two weeks? The genie later added that he will let the money in each purse grow for three weeks. How much money will be in each purse then? Which purse contains more money after 30 days?Purse A which contains $1,000 today. If you leave it alone, it will contain $1,200 tomorrow (by magic). The next day, it will have $1,400. This pattern of $200 additional dollars per day will continue.
Purse B which contains 1 penny today. Leave that penny in there, because tomorrow it will (magically) turn into 2 pennies. The next day, there will be 4 pennies. The amount in the purse will continue to double each day.
How much money will be in each purse after a week? After two weeks?
The genie later added that he will let the money in each purse grow for three weeks. How much money will be in each purse then?
Which purse contains more money after 30 days?
Answer:
After a Week(7 days)
[tex]Purse \:A: \$2200\\Purse B: \$0.64[/tex]
After 2 Weeks(14 days)
[tex]Purse \:A: \$3600\\Purse B: \$81.92[/tex]
After 3 Weeks(21 days)
[tex]Purse \:A: \$5000\\Purse B: \$10485.76[/tex]
After 30 days
[tex]Purse \:A: \$6800\\Purse B: \$5368709.12[/tex]
Therefore, Purse B contains more money after 30 days.
Step-by-step explanation:
Purse A
The amount of money($1000) in purse A for each consecutive day grows with $200. The sequence is written as:
1000,1200,1400,...
This is an arithmetic sequence with the first term being $1000 and the common difference $200.
Therefore, for any number of day, n, the amount of money in the purse,
[tex]T_n=1000+200(n-1)[/tex]
Purse B
1 Penny=$0.01
The amount of money(1 Penny) in purse B for each consecutive day doubles. The sequence is written as:
0.01,0.02,0.04,...
This is a geometric sequence with the first term being $0.01 and the common ratio 2.
Therefore, for any number of day, n, the amount of money in purse B,
[tex]T_n=0.01(2)^{n-1}[/tex]
After a Week(7 days)
[tex]Purse \:A: T_7=1000+200(7-1)=\$2200\\Purse B: T_7=0.01(2)^{7-1}=\$0.64[/tex]
After 2 Weeks(14 days)
[tex]Purse \:A: T_{14}=1000+200(14-1)=\$3600\\Purse B: T_{14}=0.01(2)^{14-1}=\$81.92[/tex]
After 3 Weeks(21 days)
[tex]Purse \:A: T_{21}=1000+200(21-1)=\$5000\\Purse B: T_{21}=0.01(2)^{21-1}=\$10485.76[/tex]
After 30 days
[tex]Purse \:A: T_{30}=1000+200(30-1)=\$6800\\Purse B: T_{30}=0.01(2)^{30-1}=\$5368709.12[/tex]
Final answer:
After calculating daily increases for Purses A and B over several time frames, it's evident that Purse B, which doubles its amount every day, holds a vastly greater sum after 30 days, illustrating the power of compound interest.
Explanation:
Calculating Growth in Purses A and B
Let's start by determining the amount in each purse after one week (7 days) and after two weeks (14 days). Purse A gains $200 more each day, starting with $1,000 on day 1. Purse B's amount doubles every day, beginning with 1 penny on day 1.
For Purse A, we can calculate the total after one week as:
$1,000 + (6 days × $200/day) = $1,000 + $1,200 = $2,200
After two weeks (14 days):
$1,000 + (13 days × $200/day) = $1,000 + $2,600 = $3,600
For Purse B, since the amount doubles each day, we use the power of 2 to represent the growth:
After one week (7 days):
1 penny × [tex]2^6[/tex] = 64 pennies (because we don't count the first day)
After two weeks (14 days):
1 penny × [tex]2^13[/tex]= 8,192 pennies, or $81.92
After three weeks (21 days) for Purse A we get:
$1,000 + (20 days × $200/day) = $1,000 + $4,000 = $5,000
And for Purse B:
1 penny × [tex]2^{20}[/tex] = 1,048,576 pennies, or $10,485.76
Now, let's see which purse contains more money after 30 days:
Purse A: $1,000 + (29 days × $200/day) = $1,000 + $5,800 = $6,800
Purse B: [tex]1 penny \times 2^{29} = 536,870,912 \ pennies \, \ or\ \$\ 5,368,709.12[/tex]
After 30 days, Purse B contains significantly more money due to the power of compound interest.
Find the percent markdown for an $80 jacket that is in sale for $48
Answer:
40 percent off
Step-by-step explanation:
40 percent off 80.00 is 48.00
A couple plans on having three children. Which of the following represents the sample space for the genders of the three children? To simplify this question, we will use the binary definition of gender, with representing boy and representing girl. A (68B, BBG, BGG, GGG) B.(B,G) C.(BB, BG, GB, GG) D. (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG) E. (BG, BG, BG)
Grace is having trouble deciding what to order for dessert. The options are 4 different flavors of ice cream, 3 different flavors of cake, or 2 different flavors pie. If she were to choose one item at random, what is the probability that she will choose a cake?
Answer: The probability that she would choose cake is 0.33 (or 33%)
Step-by-step explanation: The number of all possible outcomes is given as follows;
4 (ice cream) + 3(cake) + 2(pie), that is 4 + 3 + 2 = 9
This means there is a possibility of 9 different outcomes if she decided to choose her dessert at random.
However, there are 3 flavors of cake available which means the possibility of choosing cake is 3.
Therefore the probability that she will choose a cake is give as,
P(Cake) = Number of required outcomes/Number of all possible outcomes
P(Cake) = 3/9
P(Cake) = 1/3 or 0.33
Therefore the probability that she would choose cake is 0.33 or 33%
The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How fast did Sean drink the slushy?
The initial amount of slushy in the cup is 600 mm.
A linear equation has the following form:
y = mx + b
where y and x are variables, m represents the rate of change, and b represents the initial value of y.
Let y be the amount of slushy remaining in the cup (in milliliters) and x the time (in seconds).
The y intercept on the graph is 600.
As a result, the initial amount of slushy in the cup is 600 mm.
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The following question may be like this:
Sean drank a slushy as fast as he could.
The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How much slushy was initially in the cup?
PLS HELPP Mr. Clark needed to rent a moving van. Company A charges a rate of $90 per hour plus a $50 truck
fee. Company B charges $70 per hour plus a $90 truck fee. For what number of rental hours is the cost
for both companies the same?
Answer:
2 hours
Step-by-step explanation:
According to the information provided you can say that for company A, the total cost is equal to 90 for the number of hours plus the 50 fee. For company B, the total cost is equal to 70 for the number of hours plus 90.
90x+50= 70x+90
x= number of rental hours
Then, you have solve for x:
90x-70x=90-50
20x=40
x=40/20
x= 2
The cost for both companies is the same for 2 rental hours.
Answer:
h = 2 hrs
Step-by-step explanation:
Mr Clark needed to rent a moving Van.
Company A charges
cost = 50 + 90(h)
where
h = number of hours used
Company B charges
cost = 90 + 70(h)
where
h = number of hour used
The number of rental hours when both companies cost is same is when both the cost equation is equal to each other.
Therefore,
50 + 90(h) = 90 + 70(h)
50 - 90 = 70h - 90h
-40 = -20h
divide both sides by -20
h = -40/-20
h = 2 hrs
Select the choice that translates the following verbal phrase correctly to algebra:
8 times the total of x and 3
A. 8(x + 3)
B. 8x + 3
C. (8x) ⋅ 3
D. 8 + x(3)
Answer:
8(x+3)
Step-by-step explanation:
The Reason being it is the total of x and 3 times 8.
For it to be 8x+3 you would write it eight times x plus three or eight x plus three
Option A - 8 (x + 3) correctly represents the verbal phrase.
We have the following statement -
8 times the total of x and 3
We have to select the choice that translates the above verbal phrase correctly to algebra.
Rephrase the following verbal phrase into mathematical form - ' n times the sum of a and b '.The mathematical statement for the above phrase is - n x (a + b)
In the question given to us we have - 8 times the total of x and 3
The mathematical statement for the above phrase will be -
8 (x + 3)
Hence, Option A correctly represents the verbal phrase.
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what the value of the expression -2(-7/9 divided 1/3)
Answer:
lol i need
Step-by-step explanation:
ez calps plue
Answer:
14/27
Step-by-step explanation:
let me know if this is right
A row of plaques covers 252 square feet of space along a wall.
If the plaques are 6 feet tall, what length of the wall do they cover?
The length of the wall that the plaques will cover is feet long.
Answer:
252/6=42
Step-by-step explanation:
BRAINLIEST PLZ
Answer:
The length of the wall that the plaques will cover is 42 feet long.
Step-by-step explanation:
Wall is rectangular in shape
So Area = length × width
252 = 6 × length
length = 252/6
length = 42
The radius of a circle is 7 ft. Find its area to the nearest tenth.
The required area of the circle with a radius of 7 ft is given as 153.9 ft².
What is an area circle?The area of the circle is given by the pie times square of the radius. Or defined as the area enclosed within the circumference of the circle.
here,
Area of the circle = πr²
From the given data radius is 7ft,
plugging the value in the area formula of the circle,
Area of the circle = 3.14 × 7² = 153.9 ft²
Thus, the required area of the circle with a radius of 7 ft is given as 153.9 ft².
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What is 10^3 x 10^9 with a single exponent ?
10^3 x 10^9 = 10^12
Step-by-step explanation:
Given that,
10^3 x 10^9
The bases of the 2 terms are same (10) and the power of the terms are 3 and 9
As the base of the 2 terms are same and the bases are in multiplication form we can add up the powers.
So,
10^3 x 10^9 = 10^(3+9)
= 10^12
least to greatest. 26.2, 262%, 2 3/5 (two and three fifths)
in all decimal or percent form please and i need an answer soon please help!!!
Answer:
Step-by-step explanation:
BACD
Final answer:
The numbers from least to greatest are 2.62 (262%), 2.6 (2 3/5), and 26.2.
Explanation:
To arrange the numbers 26.2, 262%, and 2 3/5 from least to greatest in all decimal or percent forms, we need to convert them into the same form.
First, we know that 262% as a decimal is 2.62. The mixed number 2 3/5 can be converted to a decimal by dividing the numerator by the denominator and adding it to the whole number, resulting in 2 + 0.6 = 2.6.
Now we have the numbers in decimal form: 26.2, 2.62, and 2.6.
To order them from least to greatest:
2.62 (262%)2.6 (2 3/5)26.2When converting back to percent form, remember to multiply by 100. Thus, 2.62 is already given as 262%, and 2.6 becomes 260%.
What’s the measure of angle C if tan C = 0.5773
Answer:
C =29.998°
Step-by-step explanation:
To find the measure of angle C if tan C = 0.5773, we will follow the steps below;
tan C = 0.5773
take the tan⁻¹ of both-side of the equation
that is;
tan⁻¹ tan C = tan⁻¹0.5773
On the left-hand side of the equation tan and tan⁻¹ will cancel-out leaving us with just c
C = tan⁻¹0.5773
C =29.998°
C≈30°
What method can be used to write the equation of a line in slope-intercept form given two points?
A. Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
B. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
C. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
D. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Answer:
The Answer is the first one, A
Step-by-step explanation:
Answer:
a.
Step-by-step explanation:
Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
16x+9=8x+46 can someone help?
Answer:
37/8
Step-by-step explanation:
Subtract 8x from both sides and get 8x+9=46 subtract 9 from both sides and get 8x=37 divide by 8 and get 37/8
Answer:
x=4.625
Step-by-step explanation:
16x+9=8x+46
-8x
8x+9=46
-9
8x=37
/8
x=4.625
Find the simplified product where x=0: √5x (√8²−2√x)
Answer:
D Is the answer on edge
Step-by-step explanation:
hope this helps!
The product of the polynomials √(5x) and √(x²) - 2√(x) will be 8√(5x) - 2x√5.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The polynomials are given below.
√(5x) and √(8²) - 2√(x)
The product of the polynomials √(5x) and √(x²) - 2√(x) will be given as,
⇒ [√(5x)] [√(8²) - 2√(x)]
⇒ √(5x)√(8²) - 2√(x)√(5x)]
⇒ 8√(5x) - 2x√5
The product of the polynomials √(5x) and √(x²) - 2√(x) will be 8√(5x) - 2x√5.
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how can u change this rhombus so that its also a square
A.make to sides longer
B.make all right angles
C.make all sides longer
D.make all angles wider
Answer:
Make all sides right angles
Step-by-step explanation:
Answer: B.
Step-by-step explanation:
A square must have 4 right angles and perpendicular congruent diagonals which already meets the requirements of a rhombus.
When making a batch of orange juice for her basketball team Jackie used 5 times as much water as concentrate. There were 32 more cups of water than concentrate. How much juice did she make in all? She poured the juice in 2 quart containers how many containers could she feel?
Answer:
48 cups of orange juice, 24 containers.
Step-by-step explanation:
Given:
Jackie used 5 times as much water as concentrate to make orange juice.
There were 32 more cups of water than concentrate.
Question asked:
How much juice did she make in all ?
She poured the juice in 2 quart containers how many containers could she fill ?
Solution:
Let concentrate used in the juice = [tex]x[/tex]
As Jackie used 5 times as much water as concentrate:
Then water used in the juice = [tex]5x[/tex]
According to question:
To make orange juice 32 more cups of water used than concentrate is equals to to make orange juice, Jackie used 5 times as much water as concentrate, we will write this as:-
[tex]x+5x=x+x+32\\6x=2x+32\\[/tex]
Subtracting both sides by [tex]2x[/tex]
[tex]4x=32\\[/tex]
Dividing both sides by 4
[tex]x=8[/tex]
Concentrate used in the juice = [tex]x[/tex] = 8 cups
Water used in the juice = [tex]5x[/tex] = [tex]5\times8=40\ cups[/tex]
Total quantity of juice =8 + 40 = 48 cups
Thus, she made 48 cups of orange juice for her basketball team.
Now, as she poured the juice in 2 quart containers, we have to find number of containers could be filled, we will simply divide total quantity of juice by 2 quart
Number of 2 quart containers = 48 cups [tex]\div[/tex] 2 = 24 containers
Thus, she can fill 24 containers.
What is the formula to find the vertex of a parabola?
Answer:
y = a(x - h)^2 + k (please give branliest)
Step-by-step explanation:
(h,k) are coordinates of a point on the parabola
this is derived by ax^2 + bx + c
The formula to find the vertex of a parabola is x = -b/(2a) and y = f(x). The vertex of a parabola is represented by the coordinates (x, y).
Explanation:The formula to find the vertex of a parabola is x = -b/(2a) and y = f(x). In the equation of a parabola y = ax² + bx + c, the vertex can be found by substituting the x-coordinate from the formula into the equation to get the y-coordinate. So, the vertex of a parabola is represented by the coordinates (x, y).
A motel finds it can rent 180 rooms when the room rate is $ 60 per day. For each $ 2 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .
Answer:
$7,200
Step-by-step explanation:
r=p × n
where
r=revenue
p = price per item
n = number of items sold
A change in price changes quantity ( number sold)
Variable x changes with price, then
Let
p+x=a dollar price increase
p-x= a dollar price decrease
n+x= an increase in quantity sold
n-x= a decrease in quantity sold
Therefore,
A $2 dollar increase in price=p+2x
2 decrease in room quantity sold= n-2x
Substituting in the above equation
r=(p+2x)*(n-2x)
P=$60
n=180
Then
r=(60+2x)*(180-2x)
r=10,800-120x+360x-4x^2
r=-4x^2-240x+10,800
Solve the quadratic equation
The maximum value of x in the vertex = - b/2*a
Where
b=240
a=-4
Value of x=-240/2*(-4)
X=30
r=-4x^2-240x+10,800
=-4(30)^2-240(30)+10,800
=-4(900)-7200+10,800
=3,600-7200+10800
=$7,200
The rate that maximises revenue=$7,200
Answer:
The rate that maximizes revenue is $14,000
Step-by-step explanation:
First of all, you should know that the income equation is:
R = p * n
where:
p = price per item n = number of items soldOn the other hand, if p + x means a price increase, while n - x means a decrease in the number of an item sold.
In this case, reference is made to rooms, where 60 + 2x is the increased price and 180-2x is the decrease in rooms for rent.
So:
R=(60+2x)*(180-2x)
Expressing this in another way, applying distributive property:
R=60*180+60*(-2)x+2x*180+2x*(-2)x
R=10,800+240x-4x² equation (A)
This is a quadratic equation that is graphically represented by a parabola. If a, the coefficient that accompanies the term x², has a positive value, the parabola will be oriented upwards. On the contrary, if a has a negative value, the parabola will be oriented downwards. In this case, the value of a is -4, with the parabola facing down. The vertex is a point that is part of the parabola, which has the value as ordered minimum or maximum function. In this case, since the parabola faces downward, the vertex will be its maximum value.
The value of x in the vertex is [tex]-\frac{b}{2*a}[/tex]. In this case:
a=-4b=240Replacing:
[tex]x=-\frac{240}{2*(-4)}[/tex]
Solving:
x=40
To find the rate that maximizes income you simply replace this value in equation (A)
R=10,800+240*40-4*(40)²
R=14,000
The rate that maximizes revenue is $14,000