The function f(x) = −x2 60x − 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired. determine the vertex, and explain what it means in the context of the problem.
Answers
In the context of this problem, the vertex represents the maximum profit the shop can make by repairing windshields. The vertex of a quadratic function is a point on its graph where the function reaches its maximum or minimum value.
To determine the vertex of the function f(x) = -x^2 + 60x - 116, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = -1, b = 60, and c = -116.
Using the formula, we can calculate x = -60/(2*(-1)) = 30. This means that the vertex of the function occurs at x = 30.
To find the corresponding y-value of the vertex, we substitute x = 30 back into the function: f(30) = -(30)^2 + 60(30) - 116 = -900 + 1800 - 116 = 784.
Therefore, the vertex of the function is (30, 784).
In the context of the problem, the vertex (30, 784) represents the number of windshields repaired (x) and the corresponding monthly profit (y) at which the shop makes the maximum profit. The x-coordinate of the vertex, 30, represents the number of windshields at which the shop can maximize its profit. The y-coordinate of the vertex, 784, represents the maximum profit in dollars that the shop can make by repairing that number of windshields.
It's important to note that the negative coefficient of x^2 (-1 in this case) indicates a downward opening parabola, meaning that the maximum profit occurs at the vertex. The shop can use this information to determine the optimal number of windshields to repair in order to maximize its profit.
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Related Questions
At the local pizzeria, a slice of pizza costs $3.00. if there are eight slices in one pizza . how much would two whole pizzas cost?
Answers
Answer:
48 dollars
Step-by-step explanation:
3 x 8 = 24
24 x 2 = 48
Two whole pizzas will cost forty-eight dollars
Answer:
48 dollars
Step-by-step explanation:
because for each slice is 3 dollars and there is 8 slices in 1 pizza so 8*3=24 so for 1 whole pizza its 24 dollars and because we want 2 we multiply it by 2 so 24*2= 48 so for 2 whole pizzas it equals 48 dollars.
A easier way, in 2 pizzas there is a total of 16 slices so 16*3= 48
The point (5,1) is equidistant from (1,y) and (10, -3). determine the value of y.
Answers
The value of y in the given coordinate points is 5.
Value of y
The value of y in the given coordinate points is calculated as follows;
Point (5,1) is equidistant from (1,y) and (10, -3).
The value of y is calculated as follows;
(x₁ + x₂)/2, (y₁ + y₂)/2 = (5, 1)
(y - 3)/2 = 1
y - 3 = 2
y = 5
The coordinates points are (1, 5) and (10, - 3)
Thus, the value of y in the given coordinate points is 5.
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PLEASE HURRY
no links please!
Answer the questions to show how Adam could find the area of the scale drawing, and then use this strategy to find the area of the electronics board.
1. What is the area of the board shown on the scale drawing? Explain how you found the area. ( 3 points)
2. How can Adam use the scale factor to find the area of the actual electronics board? remember, he used a different method than jason. ( 3 points)
3. What is the area of the actual electronics board. (4 points)
Answers
1. The area of the scale drawing is 1800 cm².
2. We can multiply the dimensions of the drawing by the scale factor of 5.
3. The area of the actual board is 45000 cm².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know, The area of a rectangle is (length×width).
1. Therefore, The area of the scale drawing is (50×36) cm².
= 1800 cm².
2. Given, The scale factor is in the ratio of 5 : 1.
Therefore, The actual length is 50×5 cm = 250 cm and the width is 180 cm.
3. The area of the actual board is 250×180 = 45000 cm².
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Select the correct answer.
consider this equation.
cos(ф) = \(\frac{8}{9}\)
if ф is an angle in quadrant iv, what is the value of tan(ф)?
Answers
The value of tan(ф) when cos(ф) = 8/9 in quadrant IV is - √17/8
To solve for the value of tan(ф), we need to use the trigonometric identity: tan(ф) = sin(ф)/cos(ф).
Since ф is in quadrant IV, we know that the cosine value is positive (due to cosine being positive in the adjacent side of quadrant IV) and the sine value is negative (due to sine being negative in the opposite side of quadrant IV).
We are given the value of the cosine, which is cos(ф) = 8/9. To find the sine, we can use the Pythagorean identity: sin²(ф) + cos²(ф) = 1.
Plugging in the given value of the cosine, we get: sin²(ф) + (8/9)² = 1. Solving for sin(ф), we get sin(ф) = - √(1 - (64/81)) = - √(17/81) = - √17/9.
Now that we have the values of sin(ф) and cos(ф), we can substitute them into the tan(ф) equation: tan(ф) = sin(ф)/cos(ф) = (- √17/9)/(8/9) = - √17/8.
Therefore, the value of tan(ф) when cos(ф) = 8/9 in quadrant IV is - √17/8.
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Can someone please help me ASAP?? It’s due today!! I will give brainliest If It’s correct.
Answers
The correct option that indicates how Christa sliced the rectangular pyramid is the second option.
Christa sliced the pyramid perpendicular to its base through two edges.
What is a rectangular pyramid?A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.
The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.
The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid
The correct option is therefore the second option;
Christa sliced the pyramid perpendicular to its base through two edges
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Find m<3
mfnfnfmfmf
Answers
Answer:
m∠3 = 92
Step-by-step explanation:
45 + 47 = 92
Check:
180 - 92 = 88
180 - 88 = 92
8. Find the divisor if the dividend is 5x³+x²+3 the quotient is 5x²-14x+42 and the remainder is -123.
Answers
The divisor of the given division is (x+3).
Given that the dividend, quotient and the remainder of a certain division are 5x³+x²+3, 5x²-14x+42 and -123 respectively,
We are asked to find the divisor,
To find the divisor when the dividend, quotient, and remainder are given, we can use the division relation.
The division relation states:
Dividend = Divisor × Quotient + Remainder
Given:
Dividend = 5x³ + x² + 3
Quotient = 5x² - 14x + 42
Remainder = -123
We can plug these values into the division relation and solve for the divisor:
5x³ + x² + 3 = Divisor × (5x² - 14x + 42) + (-123)
Simplifying,
5x³ + x² + 3 + 123 = Divisor × (5x² - 14x + 42)
5x³ + x² + 126 = Divisor × (5x² - 14x + 42)
Divisor = [5x³ + x² + 126] / [5x² - 14x + 42]
Simplifying this we get,
[5x³ + x² + 126] / [5x² - 14x + 42] = x + 3
So,
Divisor = x + 3.
Hence the divisor of the given division is (x+3).
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Which is NOT a partial product for 23 x 54? *
20 x 50
3 x 4
20 x 3
20 x 4
Answers
Answer:
Step-by-step explanation:
Shay makes 24 liters of homemade vegetable stock. She distributes the stock
equally into 8 containers to give to friends and family. How much vegetable stock
is in each container?
Answers
Answer:
3 liters
Step-by-step explanation:
pretty simple first grade question, 24/8
24 divided by 8 is 3 because 8x4 is 32 so subtract 32-8 which gives you 24.
a motorboat capable of 20 mph keeps the bow of the boat pointed straight across a mile- wide river. the current is flowing left to right at 8 mph. find where the boat meets the opposite shore.
Answers
The velocity of the motorboat and the river of 20 mph and 8 mph respectively, indicates that the boat meets the opposite shore at 2/3 miles to the right from the direction the motorboat is pointed.
What is a relative velocity?The relative velocity of an object is the velocity of the object, based on another object or observer.
The speed of the motorboat = 20 mph
The direction of the motorboat = Across the river
The width of the river = 1 mile
The direction of the current = Left to right (downstream)
The speed of the current = 8 mph
The vector components of the velocity of the boat and the river are;
Velocity component of the motorboat = 20·j
Velocity component of the river = 8·i
The resultant direction of the boat, θ, is therefore;
θ = arctan(8/20) ≈ N 21.8° E
The time , t, it takes the boat to cross the river can be found as follows;
t = 1 milke/(12 mph) = 1/12 hours
The distance, d, the river travels in 1/12 hours can be found as follows;
d = (1/12) hours × 8 mph = 8/12 mile = 2/3 milesThe location the boat meets the opposite shore is therefore;
2/3 miles downstream from the point directly facing the starting point on the other side of the shore.
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Can someone explain this to me?
Answers
Answer:
200
Step-by-step explanation:
So its basically you multiply the length by the width which is 15 times 5 which is 75 then you multiply 75 times 4 which is 200 so the answer is 200.
Abcd diagnols= bd and ac bp=2a+4b pd=6b+2 ap=6a+36 find a and b db
Answers
To find the values of variables a and b, as well as the length of diagonal DB, we are given the lengths of various line segments within the quadrilateral ABCD. We can use this information to set up equations and solve for the unknowns.
Let's start by considering the given lengths:
- BP = 2a + 4b
- PD = 6b + 2
- AP = 6a + 36
Since diagonals AC and BD are equal, we can set up the following equation:
AP + PD = BP
Substituting the given expressions, we have:
(6a + 36) + (6b + 2) = 2a + 4b
Simplifying the equation, we get:
6a + 6b + 38 = 2a + 4b
By rearranging terms, we have:
4a + 2b = -38
Now, we have one equation with two variables. To solve for a and b, we need another equation. Unfortunately, we don't have additional information or equations related to a and b, so we cannot determine their specific values or the length of diagonal DB without further information.
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George is entering a speaking contest where he is judged on three topics. Content is worth 50%, appearance is worth 25% and delivery is worth 25% of his total score. What is his weighted score, rounded to the nearest percent, if he earned an 87% on content, 90% on appearance and 85 on delivery
Answers
Answer:
To calculate George's weighted score, we need to first find the weighted value of each topic.
Content: 87% x 0.50 = 43.5%
Appearance: 90% x 0.25 = 22.5%
Delivery: 85% x 0.25 = 21.25%
Now we can find his total weighted score by adding the weighted values together:
43.5% + 22.5% + 21.25% = 87.25%
So George's weighted score, rounded to the nearest percent, is 87%.
Step-by-step explanation:
debra wants to conduct a sex study on individuals who enjoy sadomasochism. she contacts a few of her friends who engage in sadomasochistic behavior. in turn, they contact others whom they know are sadomasochists or attend s/m parties. eventually, a sample of 200 participants is obtained. identify the type of sampling method used in this survey.
Answers
The type of sampling method used in this survey is snowball sampling. Snowball sampling is a type of non-probability sampling approach.
In this technique, the initial group of study participants refers additional participants, and those participants lead to more referrals, and so on, like a snowball rolling down a hill. This technique can be used when the population of interest is unknown or challenging to access.
Debra wants to conduct a sex study on individuals who enjoy sadomasochism. She contacts a few of her friends who engage in sadomasochistic behavior. In turn, they contact others whom they know are sadomasochists or attend s/m parties. Eventually, a sample of 200 participants is obtained.
This technique is used when the population of interest is challenging to access or when the researchers lack information about the population. Here, the initial group of study participants refers additional participants, and those participants lead to more referrals, and so on, like a snowball rolling down a hill.
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I kinda got stuck on this
Answers
Answer:
220 yards
Step-by-step explanation:
15*1760 = 26,400
26,400/120 = 220
A circle has a radius of 13 in. Find the radian measure of the central angle theta that intercepts an arc of length 9 in. (Do not round any intermediate computations, and round your final answer to the nearest tenth).
Answers
The radian measure of the central angle that intercepts an arc of length 9 inches in a circle with a radius of 13 inches is approximately 0.7 radians.
To find the radian measure of the central angle that intercepts an arc of length 9 inches in a circle with a radius of 13 inches, we can use the formula:
θ = s / r
where θ is the radian measure of the central angle, s is the length of the arc, and r is the radius of the circle.
Plugging in the values, we have:
θ = 9 / 13
θ ≈ 0.692
Rounding to the nearest tenth, the radian measure of the central angle is approximately 0.7 radians.
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If quiz grades are normally distributed with a mean of 80. and a standard deviation of 7.0, what is the probability that a student will have a quiz grade of 90. or greater?
Answers
The probability of a student having a quiz grade of 90 or greater is 7.4%.
The probability of a student having a quiz grade of 90 or greater can be calculated using the standard normal distribution. The formula used to calculate this probability is P(x ≥ 90) = 1 - P(x < 90).
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To convert our quiz grade to a z-score, we must subtract the mean (80) from our quiz grade (90) and divide by the standard deviation (7). This gives us a z-score of 1.43.
To calculate the probability of a quiz grade of 90 or greater, we subtract the cumulative probability of a z-score of 1.43 from 1. This can be done using a z-table or a calculator. The result of this calculation is 0.0740 or 7.4%.
In conclusion, the probability of a student having a quiz grade of 90 or greater is 7.4%.
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Https://imgur.com/a/n3PRcMY
Answers
20 = 2x.
That means x = 10
2. Easy now that u have x. Angle 1 is 3x + 10, which means its 3(10) + 10 which is 40
If y=-2 then 2y-1 equals
Answers
Answer:
-5
Step-by-step explanation:
Plug the first equation into the expression
2y-1 = 2(-2) - 1 = -4 - 1 = -5
Answer:
-5
Step-by-step explanation:
2y - 1
2(-2) - 1
-4 - 5
-5
If your original network address with prefix is 172.16.0.0/16, what should your new network address with prefix be if you need 16 subnets?
Answers
172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.
Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.
Here,
Original network address with a prefix = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets = 172.16.0.0/20.
172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.
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Simplifier chacune des expressions suivantes et identifier la nature du nombre obtenu.
= 2 +
2
3
; =
2
5
+ 7; = (√3 + 1)(√3 − 1) ; = (√5 + 1)²
Answers
Answer:its 5
Step-by-step explanation: cuz
Find the solution to - 17 x ( - 21)
Answers
Answer:
Step-by-step explanation:
357x
HELP DUE IN 1 MINUTE 5x^3 + 20x^2-160x
Answers
During a "big air competition, snowboarders launch themselves from a half-pipe, perform tricks in the air, and land back in the half-pipe. The height / (in feet) of a
snowboarder above the bottom of the half-pipe can be modeled by h=-16t^2+24t + 16.4, where t is the time (in seconds) after the snowboarder launches into the air. The snowboard
lands 3.2 feet lower than the height of the launch. About how long is the snowboarder in the air?
Answers
For 2 sec the snowboarder in the air.
We have,
The height (in feet) of a snowboarder above the bottom of the half-pipe can be modeled by h=-16t²+24t + 16.4
So, 3.2 = -16t² + 24t + 16.4
-16t² + 24t + 12.4 = 0
Now, solving the above quadratic equation we get
t = -0.40650, 1.90650
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1 1/3 divided by 4
CAN SOMEONE PLEASE HELP ME I AM STUCK In fraction form
Answers
Answer:
1/3
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
1 1/3 = 4/3 4 = 4/1
4/3 / 4/1 = 4/3 X 1/4 = 4/12 = 1/3
Is the vertical component of velocity ever zero? If so, where?
Answers
The vertical component of velocity can be zero at specific points in the motion of an object.
What is Velocity?
Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.
The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.
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Where can we put parentheses in 60 = 10 x 3 to make it equivalent 2
Answers
Answer:
60= (10x)3
Step-by-step explanation:
I am going to assume that is a variable, not a multiplication sign
60= (10x)3
multiply
60=30x
divide both sides by 30
x=2
help please anybody hmm
Answers
Answer:
94.6-18.8=75.8
75.8 is the answer
Step-by-step explanation:
Hope this helps
May i get braineist pls?
Solve the equation t=r+7kw attempted this problem 4 times. all recorded score is 0%. unlimited attempts remaining
Answers
Answer:
Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.
If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.
To improve your chances of solving the equation successfully, consider the following steps:
Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.
Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.
Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.
Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.
Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.
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Answer:
Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.
If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.
To improve your chances of solving the equation successfully, consider the following steps:
Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.
Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.
Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.
Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.
Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.
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Derek will deposit $5,171.00 per year for 15.00 years into an wecount that earns 12.00% Assumeng the first deposit is: made 400 years from today, how much wit be in the account 31.00 years from foday? AHempts Remaining torfinity Answer fomtat: Currency. Rochd fo 2 decimal ploces What is the value iodiy of teceiving $2.72100 per year forever? Assume the first payment is made next year and the discount rate is 1000%. Atteenpts Remainung infinity Answer format: Curency. Round to 2 decmalplaces. What is the value today of receiving $1,93800 per year forever? Assume the first payment is made 600 years lioen today and the discount rate is 400% Answer format: Curency Round fo: 2 decimat paces. Allewpts Remaning infinity Supcose you itepose 52,70500 inso an account today that earrs 13 b0\% in 21.00 years the account wh be woth Answer format: Cunency found to-2 decimal places
Answers
The amount in the account 31.00 years from today would be approximately $2,990,040.02.
To calculate the future value of annual deposits, you can use the formula for the future value of an ordinary annuity:
Future Value = Payment * [(1 + interest rate)^(number of periods) - 1] / interest rate
Given:
Payment = $5,171.00 per year
Interest rate = 12.00%
Number of periods = 15.00 years
First, let's calculate the future value of the deposits after 15 years:
Future Value = $\(5,171.00 * [(1 + 0.12)^(15) - 1] / 0.12\)
Future Value = $5,171.00 *\((1.12^15 - 1) / 0.12\)
Future Value = $5,171.00 * (4.040609 - 1) / 0.12
Future Value = $5,171.00 * 3.040609 / 0.12
Future Value = $131,525.53
Now, we need to calculate the future value of this amount after an additional 31 years:
Future Value = $131,525.53 * \((1 + 0.12)^(31)\)
Future Value = $131,525.53 * \(1.12^31\)
Future Value = $131,525.53 * 22.737542
Future Value = $2,990,040.02
Therefore, the amount in the account 31.00 years from today would be approximately $2,990,040.02.
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Derek will deposit $5,171.00 per year for 15.00 years into an account that earns 12.00% Assuming the first deposit is: made 400 years from today, how much will it be in the account 31.00 years from today?