Final answer:
To find the relative minimum of the function, we first calculate its first derivative and set it to zero to find critical points. A single critical point is found at x = -9/2. Using the Second Derivative Test, we conclude that there is a relative minimum at (-9/2, -97/4) since the function's second derivative is positive, indicating the function is concave up at this point.
Explanation:
To find the relative extrema of the function f(x) = x2 + 9x − 4, we first need to determine its critical points. This is done by finding the derivative of f(x) and setting it equal to zero.
The derivative of the function, f'(x), can be calculated as follows:
f'(x) = 2x + 9
Setting the derivative equal to zero gives us:
2x + 9 = 0
x = -9/2
Now, we apply the Second Derivative Test to determine if this critical point is a relative maximum or minimum. The second derivative is:
f''(x) = 2
Since the second derivative is positive, the function is concave up at x = -9/2. Therefore, the function has a relative minimum at this point.
To find the y-coordinate, we substitute x = -9/2 into the original function:
f(-9/2) = (-9/2)2 + 9*(-9/2) − 4
Simplifying this, we get:
y = 81/4 - 81/2 - 4
y = 81/4 - 162/4 - 16/4
y = -97/4
Therefore, the relative minimum is (-9/2, -97/4). There is no relative maximum since the function is a parabola that opens upwards.
What is the value of y in the equation 6.4x 2.8y = 44.4, when x = 3? user: what is the value of x in the equation x ��� y = 30, when y = 15? 4 8 80 200
Jackie has some yellow, red, green, and blue cubes. Exactly 1/6 of the cubes are blue and 1/8 of the cubes are red. What is the number of cubes Jackie might have?
What part of the coordinate plane is equidistant from the points A(-3,2) and B(3,2)? Explain your answer.
Answer;
(0,2)
Step-by-step explanation:
You take out a cash advance of $2,790.00 on a credit card with a 3.5% cash advance fee and a 13.5% APR. What is the amount due by the end of the month?
Answer:
$2,920.14Step-by-step explanation:
cash advance fee: $2,790.00 * 0.035 = $97.65original principal: $2,790.00 + $97.65 = $2,887.651st month interest accrued: ($2,887.65) (0.135)(1/12) = $32.49total due at end of 1st month: $2,887.65 + $32.49 = $2,920.146w-y=2z, Solve for the value of w
What is substitution property of equality?
how many times does 8 go into 64
The scale factor of the blueprint of a garage door to the actual garage door is 0.05. the are of the actual garage door is 220 ft^2.
What is the area of the garage door on the blueprint?
A. 0.55ft^2
B. 5.5ft^2
C. 11ft^2
D. 55ft^2
Answer:
option A
[tex]0.55\ ft^{2}[/tex]
Step-by-step explanation:
Let
x-------> the area of the garage door on the blueprint
y------> the area of the actual garage door
z------> scale factor
we know that
The scale factor squared is equal to the area of the garage door on the blueprint divided by the area of the actual garage door
so
[tex]z^{2}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=0.05, y=220\ ft^{2}[/tex]
substitute the values and solve for x
[tex]0.05^{2}=\frac{x}{220}[/tex]
[tex]x=220(0.05^{2})[/tex]
[tex]x=0.55\ ft^{2}[/tex]
What are the values for the coefficients and constant term of 0 = 2 + 3x2 – 5x?
A=
B=
C=
Keywords:
Polynomial, variable, coefficients, constant term.
For this case, the first thing we must do is rewrite the polynomial in a standard way. For this, we reorder the polynomial coefficients.
The standard form of the polynomial is:
[tex]ax ^ 2 + bx + c[/tex]
Where,
a, b, c: are the coefficients of the polynomial.
x: is the variable
Rewriting the polynomial we have:
[tex]3x ^ 2-5x + 2[/tex]
Comparing with the standard form we have that the values of the coefficients are given by:
[tex]a = 3\\b = -5\\c = 2[/tex]
Answer:
The values for the coefficients and constant term are:
[tex]a = 3\\b = -5\\c = 2[/tex]
Answer:
a= 3 b= -5 c=2
Step-by-step explanation:
i just did it on edge
in a certain class, the ration of passing grades to failing grades is 9 to 3. If 17 grades were failing, how many passing grades were there?
Final answer:
The ratio of passing to failing grades in the class is 3 to 1. With 17 failing grades, we can determine there were 51 passing grades by setting up a proportion and solving for the number of passing grades.
Explanation:
The question relates to the ratio of passing grades to failing grades and asks us to find the number of passing grades if there are 17 failing grades. The ratio given is 9 to 3, which simplifies to 3 to 1 (since both 9 and 3 are divisible by 3). This means for every 3 passing grades, there is 1 failing grade.
Since there are 17 failing grades and the ratio of failing to passing is 1 to 3, we can set up a proportion to find the number of passing grades (p):
1/3 = 17/p
Multiplying both sides by p and then by 3 gives us:
3 × 17 = 1 × p
51 = p
Therefore, there were 51 passing grades.
Estimate 24% of 33.
a) 17
b) 12
c) 8
d) 2
in the drawing six out of every 10 tickets are winning tickets of the winning tickets one out of every three awards is a larger prize what is the probability that a ticket is randomly chosen will award a larger prize
The probability that a randomly chosen ticket will award a larger prize is calculated by multiplying the probability of getting a winning ticket with the probability that the winning ticket is for a larger prize, which results in a 20% chance.
Explanation:The question is seeking to determine the probability that a ticket chosen at random from a raffle will award a larger prize. We are given that 6 out of every 10 tickets are winning tickets, and of those winning tickets, 1 in every 3 is for a larger prize. To find this probability, we need to multiply the probability of a ticket being a winner by the probability of the winning ticket awarding a larger prize:
Probability of a winning ticket = 6/10 or 0.6Probability of a larger prize if it's a winning ticket = 1/3 or approximately 0.333Now, we multiply these probabilities:
Probability of a larger prize = Probability of winning ticket × Probability of a larger prize given a winning ticket
Probability of a larger prize = 0.6 × 0.333
Probability of a larger prize = 0.2 or 20%
Answer: B or 1/5
Step-by-step explanation:
On a certain day the temperature in new york city was -4c and the temperature in austin was 10c. how many degrees lower was the temperature in new york city.
Answer:
14 degress below
Step-by-step explanation:
A class of 28 students. the ratio of girls of 3 girls 4 boys. what is the ratio for the number of boys to total number students in the class?
Joey Chestnut is trying to break his own world record for eating the most hot dogs and buns in 10 minutes. He needs to eat more than 72 hot dogs to break his record. After 1 minute of competition, Joey has eaten 10 hot dogs. Joey wants to know the number of hot dogs per minute that he needs to eat for the next 9 minutes to break his own record.
Joey Chestnut needs to eat more than 6.89 hot dogs per minute for the next 9 minutes to break his record of 72 hot dogs.
Explanation:To find the number of hot dogs per minute Joey Chestnut needs to eat in the remaining 9 minutes to break his record, we need to start by calculating how many more hot dogs he needs to surpass 72 hot dogs. Since he has already eaten 10 hot dogs in the first minute, he needs to eat more than 62 hot dogs in the next 9 minutes to break the record.
We calculate the average number of hot dogs per minute by dividing the remaining number of hot dogs by the number of minutes left. So,
Number of hot dogs needed > 72 hot dogs - 10 hot dogs = 62 hot dogsMinutes remaining = 9 minutesHot dogs per minute needed = Number of hot dogs needed / Minutes remainingHot dogs per minute needed > 62 hot dogs / 9 minutes ≈ 6.89 hot dogs per minuteTo break his record, Joey Chestnut needs to eat more than 6.89 hot dogs per minute for the next 9 minutes.
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Joey needs to eat:
[tex]\[\boxed{7}\][/tex]
hot dogs per minute for the next 9 minutes to break his record.
Joey Chestnut wants to break his record of eating more than 72 hot dogs in 10 minutes. After the first minute, he has already eaten 10 hot dogs. We need to find out how many hot dogs per minute he needs to eat for the remaining 9 minutes to break his record.
First, determine the number of hot dogs Joey needs to eat in total to break the record:
[tex]\[72 + 1 = 73 \text{ hot dogs}\][/tex]
Next, calculate the number of hot dogs he still needs to eat after the first minute:
[tex]\[73 - 10 = 63 \text{ hot dogs}\][/tex]
Since he has 9 minutes remaining, we need to find the number of hot dogs per minute he needs to eat:
[tex]\[\frac{63 \text{ hot dogs}}{9 \text{ minutes}} = 7 \text{ hot dogs per minute}\][/tex]
Therefore, Joey needs to eat:
[tex]\[\boxed{7}\][/tex]
hot dogs per minute for the next 9 minutes to break his record.
express r=2cos(theta)+2sin(theta) as a cartesian function.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?
A. P
B. Q
C. T
D. U
Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?
Answer is A. ∠P
The angle that has the sine ratio, 4/5, is: A. Angle P.
What is the Sine Ratio?Sine ratio is the ratio of the opposite side over the hypotenuse of the right triangle in respect to the given reference angle.
Given, sine ratio of 4/5, then it means:
Opposite side (side directly opposite to the reference angle) = 4
Hypotenuse (longest side) = 5.
Thus, in the image given, using P as the reference angle, the sine ratio of P is:
QR/PQ = 16/20 = 4/5
Therefore, the angle with the sine ratio of 4/5 is: A. P.
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A basket contains 14 white eggs, 15 brown eggs, and 11 lemons. Taylor is in a hurry to make breakfast and picks something from the basket at random.
what is the exact probability that she picks an egg?
Answer: 29/40 (PLATO)
Have a good day!
A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = (x + 7) is written to represent the line. Which equations also represent the line?
List the sample space for rolling two dice and finding the sum of the numbers. How many 8's are there in the sample space? [Assume that rolling a 3 and a 5 is the same as rolling a 5 and a 3.]
Your office manager used 45 paperclips for handouts at his presentation from the 450 paperclips available in the stock room. What percentage of the original number of paperclips did NOT get used?
Answer:
90% of paperclips did not get used.
Step-by-step explanation:
Your office manager used 45 paperclips for handouts at his presentation from the 450 paperclips available in the stock room.
We have to calculate the percentage of the original number of paperclips did not get used.
number of paperclips did not get used = 450 - 45 = 405
the percentage of 405 out of 450 = [tex]\frac{405}{450}[/tex] × 100
= 0.9 × 100
= 90%
Therefore, 90% of paperclips did not get used.
Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the three days Rachel sold 19 books. Create an equation that can be used to find m, the number of books Rachel sold on Monday.
A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?
Two equations are given below:
a – 3b = 28
a = b – 2
What is the solution to the set of equations in the form (a, b)?
(–12, –10)
(–15, –13)
(–17, –15)
(–18, –16)
Sales tax on an item is directly proportional to the cost of the item purchased if the tax on a $600 item is $36 what is the sales tax on a $950 item?
The sales tax on the item costs $950 is $57.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Given that, the cost of the item purchased if the tax on a $600 item is $36.
Now, rate of sales tax =36/600 ×100
= 6%
The sales tax on a $950 item is
6% of 950
= 0.06×950
= $57
Hence, the sales tax on the item costs $950 is $57.
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Evaluate |a + b - c|, given a = 5, b = -3, and c = -2.
-4
4
10
0
Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of the kite from the ground is...
A.20.27 B.61 C.77.27
Answer:
C.77.27
Step-by-step explanation:
For plato users this is correct
A ruler is 12 inches long.what is the length of this ruler in centimeters
find the quotient of 1 1/3 and 5/6..
Can you please show me the steps? thank u ...?
Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b.
What is an equivalent equation solved for h?
h = (– b)÷ r
h = – b ÷ r
h = ÷ r – b
h = ÷ r
Answer:
a
Step-by-step explanation:
Final answer:
The equivalent equation solved for h is h = -b/r. To derive this equation, we can isolate h in the given equation p = 0.7(rh + b) by multiplying both sides by the reciprocal of 0.7, distributing, and simplifying, option n 2 is correct.
Explanation:
The equivalent equation solved for h is h = −b ÷ r.
To derive this equation, we need to isolate h in the given equation p = 0.7(rh + b). We can start by multiplying both sides of the equation by the reciprocal of 0.7, which is 1.4286 (approximately).
Then, we can distribute the 1.4286 to the terms inside the parentheses to get p = 1.4286rh + 1.4286b. Next, we can subtract 1.4286b from both sides of the equation to isolate the 1.4286rh term.
Finally, we can divide both sides of the equation by 1.4286r to solve for h, which gives us the equivalent equation h = −b ÷ r.