The revenue function is a quadratic equation and the graph of the function
has the shape of a parabola that is concave downwards.
The correct responses are;
(a) R = -x² + 82·x(b) $1,645(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.(d) R = -1·(x - 41)² + 1,681(e) 41(f) $1,681Reasons:
The given function that gives the weekly revenue is; R = x·(82 - x)
Where;
R = The revenue in dollars
x = The number of lunches
(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;
R = x·(82 - x) = 82·x - x²
Which gives;
R = -x² + 82·xWhere, the constant term, c = 0
(b) When 35 launches are sold, we have;
x = 35
Which by plugging in the value of x = 35, gives;
R = 35 × (82 - 35) = 1,645
The revenue when 35 lunches are sold, R = $1,645
(c) The given function for R is R = x·(82 - x) = -x² + 82·x
Given that the leading coefficient is negative, the shape of graph of the
function R is concave downward, and therefore, the graph has only a
maximum point.
(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;
(h, k) = The vertex of the equation
a = The leading coefficient
The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;
R = x·(82 - x) = -x² + 82·x
At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;
[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]
Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]
The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681
Which gives;
(h, k) = (41, 1,681)
a = -1 (The coefficient of x² in -x² + 82·x)
The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41
Therefore;
The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681
The maximum revenue of the company is $1,681Learn more about the quadratic function here:
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Laurie wants to join the basketball team. Her parents ask her to figure out how much it will cost. Laurie knows that she has to pay an activities fee of $42 plus a fixed amount for each tournament. Write a formula that describes how much it will cost to join the team. Let's let:
c=cost for each tournament
n=number of tournaments the team plays
t=total amount to join the team
The Formula:
t = cn + 42
lcm of 5,12 and 20????,
Answer: 60
Step-by-step explanation:
WILL GIVE BRAINLIEST!
Answer:
425
Step-by-step explanation:
225/24 then multiply the answer by 40
1) -4/3
2) -3/4
3) 10/17
4)17/10
Answer:
boom bam ba boom bam ba
Answer: -3/4
Step-by-step explanation:
The y value is decreasing by -0.75
-3.75 - 0.75 = -4.5
-4.5 - 0.75 = -5.25
-5.25 - 0.75 = -6
ect.
-0.75 in fraction form is -3/4
PLEASE HELPPPP. I really need it
Answer:
Option 4: (0, 5]
Step-by-step explanation:
Given the inequality notation, 0 < x ≤ 5 :
Definitions:open- and closed-parenthesis "( )"We know that using the open- and closed-parenthesis, "( )" are used to express interval notation for which the endpoints are not included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, less than (>) or greater than (<), as you do not include the endpoints when these inequality symbols are used.
open- and closed-brackets "[ ]"In contrast, the open- and closed-brackets, "[ ]" are used to express interval notation for which the endpoints are included as part of the solution. Hence, the open- and closed-parenthesis are associated with the inequality symbols, less than or equal to (≤), and greater than or equal to (≥).
Explanation:In the inequality notation, 0 < x ≤ 5, the endpoints are 0 and 5.
The inequality symbol between 0 and x is "<," which means that we must use an open parenthesis, " ( " for the endpoint, 0.
While the inequality symbol between x and 5 is "≤," which means that we must use an closed bracket, " ] " for the endpoint, 5.
Therefore, the correct answer is Option 4: (0, 5].
Luke portrays this time in Jesus’ ministry as very successful, but he starts giving hints of things to come. For instance, after the healing of the boy, Jesus seems to randomly say that he is going to be betrayed. Why would Jesus have picked that time to say such a thing? I think Jesus picked this time to warn the disciples about what was going to happen.
Factorise it
(x + 2y)² – (x – 2y)²
[tex]\text{Given that,}\\\\(x+2y)^2 - (x-2y)^2\\\\=(x+2y +x -2y)(x+2y -x+2y)~~~~;[a^2 - b^2 = (a+b)(a-b)]\\\\=(2x)(4y)\\\\=8xy[/tex]
PLEASE HELPPP
ILL GIVE 5 STARS TY
Answer:
14
Step-by-step explanation:
4^2=16
16/2=8
8+6=14
Answer:
[tex]14[/tex]
Step-by-step explanation:
This equation would be easier to do if it was: [tex]6+\frac{4^2}{2}[/tex]
So first you have to cancel out: [tex]\frac{4^2}{2}[/tex] so that would become [tex]6+8[/tex]
Finally [tex]6+8=14[/tex]
There you go brainliest pls
A vehicle was travelling at a speed of 72km per hour. What distance did it cover in 2 hours? A. 158km B. 148km C. 168km D. 144km
Answer:
D. 144km
Step-by-step explanation:
If the vehicle travels 72km every hour, in two hours, it will drive 144km. (72x2=144)
Please help!! Thank you!!!!
Answer:
total cost = 10 • months + 100
Step-by-step explanation:
The $100 application fee is extra, only needed to pay once. The $10 per month is multiplication. $10 • the number of months.
PLEASE HELP ME WITH THIS! I NEED TO PASS THIS ASAP
Answer:
The Y-Int. is 60
Step-by-step explanation:
0 marks the x axis, which leads me to believe 60 is the Y-int so (0,60)
I need help with pre calculus.
Problem 1
Answer: Choice A. (0,9)---------------------
Explanation:
The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.
Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...
m = (y2-y1)/(x2-x1)
m = (11-15)/(-4-(-6))
m = (11-15)/(-4+6)
m = -4/2
m = -2
Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)
y = mx+b
b = y-mx
b = 15-(-2)*(-6)
b = 15-12
b = 3
The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.
Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.
The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).
So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).
=========================================================
Problem 2
Answer: Choice Ax is any real number but x cannot equal -2, -1 or 1.---------------------
Explanation:
Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get
g(x) = x^3+2x^2-x-2 = (x+2)(x+1)(x-1)
The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.
So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".
Side note: We don't involve the numerator function at all.
=========================================================
Problem 3
Answer: Choice B. 2x+1 and x-3---------------------
Explanation:
The height is x, which we can factor out like this
2x^3-5x^2-3x
2x^2*x - 5x*x - 3*x
x(2x^2-5x-3)
Effectively you would use the distribution rule in reverse.
Now let's factor the remaining expression in the parenthesis.
I'll use the factor by grouping method.
2x^2-5x-3
2x^2-6x+1x-3
(2x^2-6x) + (1x-3)
2x(x-3) + 1(x-3)
(2x+1)(x-3)
Therefore, the full factorization is
x(2x+1)(x-3)
which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.
You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.
ILL GIVE BRAINLIEST TO THE RIGHT ANSWER!!!!!
Write an equation involving absolute value for the graph.
Answer:
-3<lxl<5
Step-by-step explanation:
take least number than use x in absolute value bars than take highest number sorry if this is wrong I'm just a kid
Help!!!! Need this asap!!!
Answer:
the graph is in link
Step-by-step explanation:
y ..... means full line and shading above the line
Y< ......means doted line and shading below the line
A) solution is overlapping shaded part
B) (10,5)
plug in point in inequalities and check if it's true; if it's true you showed that solution is correct
1. 5-1/2*10 + 2 1/2
5 -5 + 2 1/2
5 -2 1/2 TRUE
2. 51/5*10 + 6
5< 2 + 6
5< 8 TRUE
A BCC professor decides to grade his class as following: 20 percent for homework assignments, 10 percent for quizzes, 25 percent for a midterm, and 45 percent for the final exam. A student receives 90 for homework, 95 for the quizzes, 85 for the midterm and 84 for the final exam. What will be the student’s class grade?
Class grade: ?
Answer:
86.55%
Step-by-step explanation:
Basically what you would do is take each percentage and turn it into decimal percent. after that, you multiply it with the respective numbers, like:
90 × 0.20= 18
95 × 0.10= 9.5
85 × 0.25= 21.25
84 × 0.45= 37.8
Adding these numbers together, you could get 86.55, or 86.55%.
Help w exponential functions pls
Answer:
Step-by-step explanation:
"end behavior" means what the is graph doing if you keep going off the page.
The symbol "x approaches negative infinity" is going off the page to the left. Both graphs are going up, up, up as you look at the x's going off the page to the left. See image.The last point of the g(x) on the table, when it's on the graph, you can see that curve hit bottom and turned up. So g(x) is going up, up, up as you look at all the x's going to the right. However the original graph, the green graph f(x), well, it's kind of flat, but it IS going down, down, down as you go off the page to the right.
So the end behavior is the same as x approaches negative infinity and different as x approaches infinity.
After the math contest, Basil noticed that there were four extra-large pizzas that were left untouched. In addition, another three slices of pizza were uneaten. If there were a total of 51 slices of pizza left, how many slices does an extra-large pizza have
s = number of slices for a large pizza
so if "s" is the number of slices in 1 large pizza, the total for 1 pizza will just be 1s, for two pizzas will be 2s and so on, so for 4 pizzas the total will just be 4s.
we also know there were an extra 3 slices, and we also know that whatever 4s is plus 3 will give us the total of 51 slices of pizza.
[tex]4s + 3 = 51\implies 4s = 48\implies s = \cfrac{48}{4}\implies \boxed{s = 12}[/tex]
The probability of randomly meeting someone with a phone number that ends in 3 is
Answer:
0,1,2,3,4,5,6,7,8,9
Step-by-step explanation:
: probability of meeting someone with a phone number that ends with 3 .....
= 3/total amount of no ×100
3÷10= 0.3
: 0.3×100= 30% probability.
Assuming a phone number is 10 digits long and the last digit can be any of the 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) with equal probability, the probability of randomly meeting someone with a phone number that ends in 3 is 1/10, or 0.1.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
If the phone number is 10 digits long, there are 10 possible digits that could be at the end. Since only one of those digits is a 3,
the probability of randomly selecting a phone number that ends in 3 is:
1/10 = 0.1 or 10%
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The distance between a 16 foot tall flagpole and a 40 foot tall tree is equal to the sum of the lengths of their shadows. If the flagpole casts a 18 foot shadow, find the distance from the flagpole to the tree.
Answer:
The distance from the flagpole to the tree is 27 ft
Step-by-step explanation:
what are the measurements of 1 and 2?
Answer:
8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces
HELP PLEASE!! WILL GIVE BRAINLIEST TO CORRECT QNSWER.
Use the quadratic formula to find the solution to the quadratic equation given below.
x²-x+¼=0
3. The lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for $24.00 each and slices of cheesecake for $3.50 each. If they want to raise at least $700, how many of each could they sell?
Part A: List three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal of raising at least $700.
Part B: Write an inequality to represent the situation.
Part C: Graph the inequality and shade where the solutions are. y X
Part D: What is the difference in the amount of money raised for ordered pairs falling on the line and the ones that fall in the shaded area?
Part E: What do the x- and y-intercepts represent?
To reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.
To determine, if they want to raise at least $ 700, how many of each could they sell, listing three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal, the following calculation must be performed:
C + S = 700 24 x 20 = 480 700 - 480 = 220 / 3.5 = 62.85 24 x 10 = 240 700 - 240 = 460 / 3.5 = 131.42 24 x 15 = 360 700 - 360 = 340 / 3.5 = 97.14Therefore, to reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.
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−4x−2 + 3y0 if x = 2 and y = 5
Hey there!
-4x^-2 + 3y^0
= -4(2)^-2 + 3(5)^0
= -4(1/4) + 3(5)^0
= -1 + 3(5^0)
= -1 + 3(1)
= -1 + 3
= 2
Therefore, the answer should be: 2
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
. Mary has been working hard to pay her bills and as a result she has a good credit rating and has qualified for a lower interest rate credit card. She needs to move and an apartment in a good location is available now. She has money for the monthly rent but she doesn’t have enough cash right now for the month in advance and additional moving expenses. She is expecting a bonus from her job within the next couple of months that will cover these expenses. How could a credit card be a benefit in this situation?
Mary having a credit card could be beneficial to her present situation as it gives her the ability to move to the new apartment without making immediate cash payments.
What is a credit card?A credit card is a payment card issued by a bank or financial services company to a cardholder to enable the cardholder to purchase goods and services on credit and later pay for them.
Credit cards and their interest rates are issued based on the user's credit rating.
What are the benefits of credit cards?Some of the benefits that Mary can derive from using credit cards include:
Ability to move to an apartment using her credit card without making immediate cash payments from her unavailable savings.Make credit purchases and withhold cash payments.The cardholder does not necessarily have to have a checking or saving account.The credit card gives Mary increased purchasing power.Using a credit card now helps Mary to build up her credit rating for future emergencies.Thus, with a credit card, Mary can move to the new apartment by borrowing the required funds for advance payment, including additional moving expenses.
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What is the smallest integer value that makes the inequality true? 3x - 10 > 2x + 4
Answer:
x=0 is the smallest integer
Step-by-step explanation:
What expressions is equivalent to -19.2 - (-3.8)
Answer:
-19.2
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST
What is the equation of the line that passes through the point (8,-4) and has a slope of 1/2
Answer:
y = 1/2x - 8
Step-by-step explanation:
Assuming that they want the equation in slope intercept form we would use the following form: y = mx + b
where m = slope and b = y intercept.
We are given the slope and a point on the line. We need to find the y intercept. We can do this by plugging in what we are given and then solving for b.
y = mx + b
slope (m) = 1/2
x value of given point (x) = 8
y value of given point (y) = -4
- plug in these values -
-4 = (1/2)(8) + b
now solve for b
multiply 1/2 and 8
-4 = 4 + b
subtract 4 from both sides
-8 = b
So the y intercept (b) is -8
We now plug in the slope and y intercept into slope intercept form
y = mx + b
m = 1/2 and b = -8
y = 1/2x - 8 is the equation of the line that passes through the point (8,-4) and has a slope of 1/2
For more validation refer to the attached image.
[tex]\text{Given that,}\\\\(x_1,y_1) = (8,-4), ~~ \text{and slope, m} = \dfrac 12\\\\\text{Equation with given points,}\\\\y -y_1 = m(x-x_1)\\\\\implies y -(-4) = \dfrac 12 (x-8)\\\\\implies y+4 = \dfrac 12 x - 4\\\\\implies y= \dfrac 12x -4 -4 \\\\\implies y = \dfrac 12 x -8\\\\\implies y = \dfrac{x-16}2\\\\\implies 2y = x -16\\\\\implies x -2y = 16[/tex]
Find the slope of the line that passes through the pair of points (4,3) (-1,6)
Answer:
-3/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-3)/(-1-4)
m=3/(-5)
m=-3/5
(giving brainlelist if answered correctly!) which of the following inequalities is -4
?
Answer
A, B, E.
Hope you could get an idea from here.
Doubt clarification - use comment section.
A cylindrical barrel has a radius of 2.1 ft and a height of 14 ft. Doubling which dimension(s) will double the volume of the barrel?
Answer:
Step-by-step explanation:
r = 2.1 feet
h = 14 feet
V = pi r^2 h
V = 3.14 * 2.1^2 * 14
V = 193.85
Let h = 28 feet
V = pi * r^2 * h
V = 3.14 * 3.2^2 * 28
V = 387.72
If you divide 387.72 by 2 you get 193.86
The difference in the hundreds place comes about because of the rounding that took place.
The answer to your question is you must double the height,