The maximum height the football reaches is 147 feet, and it takes 3 seconds for the football to reach that height. To determine when the football is above 122 feet, the equation is set equal to 122 and solved for time t.
To find the maximum height reached by the football, we need to determine the vertex of the parabolic function given by y = -[tex]16t^2[/tex] + 96t + 3. Since the coefficient of [tex]t^2[/tex]is negative, the parabola opens downwards, and the vertex will give us the maximum height.
To find the time at which the maximum height occurs, use the formula t = -b/2a, where a is the coefficient of [tex]t^2[/tex] and b is the coefficient of t.
In this equation, a = -16 and b = 96, so t = -96/(2 x -16) = 3 seconds. Plugging this back into the original equation gives us the maximum height: y = -16[tex](3)^2[/tex] + 96(3) + 3 = 147 feet.
To determine when the football is above 122 feet, we set the equation equal to 122 and solve for t:
122 = -[tex]16t^2[/tex] + 96t + 3. We simplify and solve the quadratic equation, which may yield two possible times, one during the ascent and one during the descent of the football's path.
Carolyn is building a pen for her dog. The perimeter of the pen is 52 ft
a) Explain how you can use a proportion to convert the perimeter into yards and feet.
b) The fencing material is sold by the yard. It costs 10.99 per yard. What is the cost of material before taxes
Carolyn's dog pen with a 52 ft perimeter is approximately 17.33 yards in length. Fencing material costs $10.99 per yard, making the total cost before taxes around $190.44.
Carolyn is constructing a dog pen with a perimeter of 52 feet. To convert the perimeter from feet to yards, we can use the fact that 1 yard equals 3 feet. Since she is purchasing fencing material by the yard, Carolyn needs to know the total length of fencing in yards. This requires setting up a proportion:
1 yard / 3 feet = x yards / 52 feet
Multiplying both sides by 52 gives us x = 52 / 3 yards. Upon calculating, we find that the pen's perimeter is approximately 17.33 yards.
Since the fencing material costs $10.99 per yard, to find the total cost before taxes, we multiply the number of yards needed by the price per yard:
17.33 yards × $10.99/yard = $190.4367
The cost for the fencing materials before taxes is approximately $190.44.
What is the time 23 hours after 8:00 pm
what is 3/20 as a decimal equivalent
The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the first 24 rows?
These are the choices
1,476
2,856
2,952
1,428 ...?
factor the expression. -x^2+3x+40
To factor the expression -x^2 + 3x + 40, use the method of expanding binomials by comparing coefficients.
Explanation:To factor the expression -x^2 + 3x + 40, we need to find two binomials whose product equals the given expression. Let's set up the expression in the form of (a - b)(c - d) and expand it to compare coefficients.
-x^2 + 3x + 40 = (a - b)(c - d)
By comparing coefficients, we can determine that a, b, c, and d are -x, 5, -8, and 8, respectively. Therefore, the factored form of -x^2 + 3x + 40 is (-x + 8)(x + 5).
Learn more about Factoring here:https://brainly.com/question/33624529
#SPJ2
What is the general form of the equation for the given circle?
x2 + y2 − 8x − 8y + 23 = 0
x2 + y2 − 8x − 8y + 32 = 0
x2 + y2 − 4x − 4y + 23 = 0
x2 + y2 + 4x + 4y + 9 = 0
Answer:
A ) x² + y² - 8 x - 8 y + 23 = 0
Step-by-step explanation:
hope i helped
Anne Katz, owner of Katz Sport Shop, loans $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of 8 years with interest compounded semiannually at 8 percent. At the end of 8 years, Anne will receive:
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
y−2=5(x−6)
y+2=5(x+6)
y−6=5(x−2)
y+6=5(x+2)
Answer:
The answer is Y-6=5(x-2)
Two acute triangles are similar. Which of the following must the similar triangles have?
every pair of sides and angles congruent
at least one pair of congruent sides and one pair of congruent angles
congruent corresponding angles and proportional side lengths
a right angle and a hypotenuse
PLEASE HELP BEGGGING YOU
the point Q(9,-1) is reflected across the y axis. Use arrow notation to describe the original point and its reflection
Q(9,-1)----Q(9,1)
Q(9,-1)----Q (-9,1)
Q(9,-1) ------Q(-9,-1)
Q(9,-1) ----Q(9,-1)
Answer:
C is the answer.
Step-by-step explanation:
When you reflect over the y-axis, the y-axis will remain the same and the x-axis will change from either positive to negative, or negative to positive in this case it is positive to negative.
A software company startes with 2 employees. in 6 months, the company has u employees. the number of employees increased at a steady rate. which equation models the relationship between the number of employees n and the number of months m since the company started?
Carla's plant was 10 2/3 inches tall. Yolanda's was 8 3/4 inches tall.
How much taller was Carla's plant than Yolanda's?
A.
1 11/12 in.
B.
2 1/12 in.
C.
2 5/12 in.
D.
2 11/12
Answer: 128/12 > 105/12
Step-by-step explanation:
10 2/3 inches=32/3 inches
8 3/4 inches= 35/4 inches
Find the common denominator, in this case, 12.
128/12 inches is Carla's plant
105/12 inches is Yolanda's plant.
128/12 > 105/12. Therefore, Carla's plant is taller than Yonlanda's
36% of what number is 180?
a magazine costs 3.50 how much can you buy with 100$
A boat moves 60 kilometers east from point A to point B. There, it reverses direction and travels another 45 kilometers toward point A. What are the total distance and total displacement of the boat?
The total displacement of the boat is therefore 15 kilometers east.
The student is asking about calculating the total distance and displacement of a boat after it has traveled in two opposing directions. To find the total distance, we simply add up the lengths of both trips the boat makes. Since the boat moves 60 kilometers east from point A to point B and then reverses direction to travel another 45 kilometers towards point A, the total distance traveled by the boat is the sum of these two trips:
Distance from A to B = 60 kilometersDistance from B to A = 45 kilometersTotal distance = 60 km + 45 km = 105 kilometersThe total displacement, however, is the vector difference between the final and starting positions. Since displacement is directional, we calculate it by subtracting the westward trip from the eastward trip:
Displacement = 60 km (east) - 45 km (west)Since east is the positive direction, the displacement is 60 km - 45 km = 15 km towards the eastThe total displacement of the boat is therefore 15 kilometers east.
Amelia receives a treat bag. the treat bag contains 10 gumballs, 5 pixie sticks, 2 bracelets, and 3 chocolates. If Amelia selects 3 items from her treat bag without looking and gives them to her sister, which could not represent a possible outcome for the items Amelia selects?
F. gumball, gumball, gumball
G. pixie stick, gumball, chocolate
H. bracelet, bracelet, bracelet
J. gumball, gumball, pixie stick
A pack with 6 cans of juice costs 3.48. What it the unit price?
A.0.49 per can B.0.50 per can C.0.58 per can D.0.60 per can**my answer??**
The unit price of one can of juice, when a 6-pack costs $3.48, is $0.58 per can.
The question asks us to calculate the unit price of a juice can when a pack of 6 cans costs $3.48.
To find the unit price, we divide the total cost of the pack by the number of cans in a pack.
In this case, we divide $3.48 by 6, which gives us $0.58.
$3.48 / 6 = $0.58
Therefore, the unit price per can is $0.58.
4x + 5x + 12 = -6 (given)
9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)
Which reason is incorrect?
A) addition
B) given
C) simplify
D) subtraction
Answer:
Addition
Step-by-step explanation:
USA Testprep
The ratio of m∠PQR to m∠PQS is 5:9. What is m∠RQS?
10°
40°
50°
80°
The area of a rectangle painiting is given by the trinomial x^2-9x-36. what are the possible dimensions of the painting ? use factoring
The first term is, x2 its coefficient is 1 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -9 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 3
x2 - 12x + 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
3 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-12)
Which is the desired factorization
900 students attended the school concert. There were twice as many adults as children in the audience. How many children attended the concert? which let statement would you use?
To solve for the number of children at the concert with twice as many adults present in a total of 900 attendees, we let the number of children be x, set up the equation x + 2x = 900, and solve for x to find that there were 300 children.
Explanation:The question pertains to solving a problem involving proportions in a total population. Assuming there are twice as many adults as children at the school concert, we can use a 'let' statement to express the number of children as 'x'. Thus, the number of adults would be '2x' because there are twice as many adults as children. Since the total number of attendees is 900, we can set up the equation: x + 2x = 900.
To find the number of children, we combine like terms to get 3x = 900, and then divide both sides by 3 to find x. Thus, x = 900 / 3, which means x = 300. So, there were 300 children at the concert.
Step-by-Step Solution:Let the number of children be 'x' (let statement).Write the number of adults as '2x' because there are twice as many adults as children.Set up the equation for the total attendees: x + 2x = 900.Combine like terms: 3x = 900.Divide both sides by 3 to solve for x: x = 300.Conclude that there were 300 children at the concert.A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach. A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes.
Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts. Write an inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day.
Answer:
The required inequality is [tex]11x + 8y \leq 600[/tex]
Step-by-step explanation:
Given : A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach.
A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes.
Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts.
To write : An inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day.
Solution :
Time taken to cook the raspberry donuts = [tex]11x[/tex] minutes
Time taken to cook the peach donuts = [tex]8y[/tex] minutes
Donuts produced in 10 hours
1 hours = 60 minutes
10 hours = 60 × 10 = 600 minutes
Total time ≤ 600 minutes
Therefore, the required equation is
→ [tex]11x + 8y \leq 600[/tex]
PTG has side lengths of 18 cm, 14 cm, and 16 cm. which type of triangle is PTG? right, obtuse, acute, isosceles
Final answer:
Triangle PTG is an acute triangle because the sum of the squares of the shorter sides (196 + 256 = 452) is greater than the square of the longest side (324). It is not a right or obtuse triangle, nor is it isosceles.
Explanation:
To determine which type of triangle PTG is, we can use the lengths of its sides (18 cm, 14 cm, 16 cm). A well-known method to identify the type of triangle based on side lengths is by using the Pythagorean theorem, which applies to right triangles.
Specifically, the theorem states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the relationship a2 + b2 = c2 holds true.
First, we can check if PTG is a right triangle by ordering the sides in ascending order and assigning the longest side as 'c'(18 cm), and the other two as 'a'(14 cm) and 'b'(16 cm). If PTG were a right triangle, we would expect to see that 142 + 162 equals 182.
Let's perform the calculations:
142 = 196
162 = 256
182 = 324
Adding together the squares of the shorter sides, we get:
196 + 256 = 452
Since 452 is not equal to 324 (182), the triangle is not a right triangle. Next, we can determine if PTG is an obtuse or acute triangle. For an obtuse triangle, we should have a2 + b2 < c2, and for an acute triangle, we should have a2 + b2 > c2. Since 452 is greater than 324, PTG is an acute triangle.
Factor each completely.
7x^2- 31x-20
5p-p-18 Factor each completely.
7x^2- 31x-20
5p-p-18
If is equal to 0.73, then is equal to ______.
0.73
0.50
0.33
0.27
A copy machine makes 32 copies per minute. How long does it take to make 120 copies?
Greatest common factor of 12, 60, and 68
What two numbers multiply to 80 and add to 28
Final answer:
The task is to find two numbers that multiply to 80 and add to 28. However, after checking possible factors, no such pair of numbers satisfies both conditions. A re-evaluation of the problem may be necessary as the conditions may have been stated incorrectly.
Explanation:
We are looking to find two numbers that when multiplied together equal 80, and when added together equal 28. To solve this problem, we set up a system of equations based on the information given:
By factoring the number 80, we look for factor pairs that also add up to 28. We notice that 16 and 5 are such numbers because:
However, this doesn't meet our second criterion, so we continue searching. Further examination reveals that 20 and 4 are the correct pair because:
In this case, we have not found two numbers meeting both conditions exactly. Therefore, it appears there has been a mistake as no pair of numbers both multiply to 80 and add up to 28. Thus, we either reconsider our pair list or recheck the conditions given.
Which of the following represent x=1/2y written in general form
1/2x-y=0
2x-y=0
x-1/2y=0
Answer:
Option 2 - [tex]2x-y=0[/tex]
Step-by-step explanation:
Given : Expression [tex]x=\frac{1}{2}y[/tex]
To find : Write the given expression in general form?
Solution :
Step 1 - Write the given expression
[tex]x=\frac{1}{2}y[/tex]
Step 2 - Multiply 2 both side,
[tex]2x=\frac{2}{2}y[/tex]
Step 3 - Solve the expression
[tex]2x=y[/tex]
[tex]2x-y=0[/tex]
Therefore, The general form of given expression is [tex]2x-y=0[/tex]
Hence, Option 2 is correct.
The length of a rectangle is 3 meters more than twice its width. the length of this rectangle is 10 meters. write an equation to solve the perimeter of this rectangle