The time taken by the ball to hit the ground is 9 seconds in quadratic equation .
What does quartic equation mean?
A fourth-degree equation, also known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.
a) The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.
Differentiating both sides.
δh/δt = -32t + 136
-32t + 136 = 0
or, t = 136/32 = 4.5.
To check whether the value of h is maximum/minimum at t = 4.5, we differentiate
δh/δt = -32t + 136
δh/δt = -32
which is < 0, which that implies, h is maximum at t = 4.5.
the maximum height, by putting in t = 4.5, in the equation, to get:
h = -16(4.5)² + 136(4.5) + 72,
or, h = -16(20.25) + 612 + 72,
or, h = -324 + 684 = 360
Therefore, The maximum height of the ball is 360 feet.
b) the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.
Therefore, it can be written as:
0 = -16t² + 136t + 72.
or, 16t² - 136t - 72 = 0.
Solving this using the quadratic equation, we get
t = - ( -136)± √(-136)² - 4( 16 ) ( -72)/2 * 16
t = 136 ± √18496 + 4608/32
t = 136 ± √23104/32
t = 136 ± 52/32
Therefore, either t = (136+152)/32 = 9,
or, t (136 - 152)/32 = -0.5.
Since t represents time, we won't take the negative value, and hence t = 9.
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On Saturday, the Milleman Family had dinner at a restaurant. They ordered 3 pizzas and 2 cheeseburgers for $41.50. The following weekend, the Anderson Family had dinner at the same restaurant where they ordered 2 pizzas and 5 cheeseburgers for $43.25. Which system of equations can be used to determine the cost of one pizza (p) and one cheeseburger (c)?
Answer: $8.64 and $7.79 respectively.
Step-by-step explanation: To determine the cost of one pizza and one cheeseburger, we can set up the following system of equations:
3p + 2c = 41.50
2p + 5c = 43.25
The first equation represents the total cost of the Milleman Family's meal, where 3p represents the cost of 3 pizzas, 2c represents the cost of 2 cheeseburgers, and 41.50 represents the total cost of the meal. The second equation represents the total cost of the Anderson Family's meal, where 2p represents the cost of 2 pizzas, 5c represents the cost of 5 cheeseburgers, and 43.25 represents the total cost of the meal.
By solving this system of equations, we can determine the cost of one pizza and one cheeseburger. For example, we can use the elimination method to solve the system of equations as follows:
First, we can multiply the first equation by 5 and the second equation by 3 to get the following equations:
15p + 10c = 207.50
6p + 15c = 129.75
Next, we can subtract the second equation from the first equation to eliminate the c terms and find the value of p as follows:
15p + 10c = 207.50
6p + 15c = 129.75
9p = 207.50 - 129.75
9p = 77.75
p = 77.75 / 9
p = 8.64
Finally, we can substitute the value of p that we found into one of the original equations to find the value of c as follows:
3p + 2c = 41.50
3(8.64) + 2c = 41.50
25.92 + 2c = 41.50
2c = 41.50 - 25.92
2c = 15.58
c = 15.58 / 2
c = 7.79
Therefore, the cost of one pizza is $8.64 and the cost of one cheeseburger is $7.79.
Given the definitions of f(x) and g(x) below, find the value of (ƒ o g)(2).
f(x) = -x + 2
g(x) = x² – 5x – 2
Wdym by definition Answer:
Step-by-step explanation:
The perimeter of a rectangle is 54 inches and the length of one of its sides 6 inches. What is the combined length of the other three sides, in feet?
Answer:
4 ft
Step-by-step explanation
the combined length of the other three sides can be found with 54-6 is 48 inches
48 inches can be turned into feet by dividing by 12.
48in / 12=4ft
chris is 5 years older than 4 times arins age. the sum of their ages is less than 40. what is the oldest arin could be?
Answer: 6 years old.
Step-by-step explanation:
Chris: 5+4a
c + a<40
5 + 4a + a < 40
5a<35
a<7
For the oldest, let's assume Arin is 6, because it is the highest number that is less than 7.
Arin can be maximum of 6 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let the Arin's age be x.
So, Chris age is 4x + 5
Now, the sum of their ages is less than 40.
x+ 4x+ 5 < 40
5x < 35
x < 7
Hence, Arin can be maximum of 6 years old.
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John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. Write an inequality to solve for all the possible values of x, the number of pounds of chocolate John could buy.
Use the on-screen keyboard to type the inequality that represents this situation in the box below.
Answer:
Step-by-step explanation:
he could buy 2 pounds of chocolates and save $1.
Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters. Is it a right triangle?
PLSSS HURRY !!!!!!!!!!
For the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters is the right triangle.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that, A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters.
We have to verify whether it is a right-angle triangle or not.
A right-angle triangle must follow the Pythagoras theorem.
The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
If the longest side is the hypotenuse.
h²=p²+b²
LHS
68² = 1424
RHS
60²+25²
3600+625
4225
L.H.S=R.H.S
Thus, the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters in the right triangle.
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Mia is traveling from her house to her sister’s home. She took the bus to the car rental lot and is now driving the rest of the way at a constant rate of speed. What does the -intercept represent in this problem?
the distance (mi) that Mia traveled on the bus to the car rental before she started driving the car
the distance (mi) that Mia traveled from the car rental lot to her sister's home
the amount of time (hr) elapsed for every mile the car travels from the car rental lot
the distance (mi) the car travels from the car rental lot for every 1 hour elapsed
Answer:
The distance (mi) the car travels from the car rental lot for every 1 hour elapsed.
Step-by-step explanation:
find the slope and y-intercept of the line 3x - 5y = 15
The slope of the given line, 3x - 5y = 15, is 3/5 and the y-intercept is -3
Determining the slope and y-intercept of a lineFrom the question, we are to determine the slope and y-intercept of the given line.
The given line is
3x - 5y = 15
To determine the slope, we will write the equation in the slope-intercept form of a line.
The slope-intercept form of a line is given as
y = mx + b
Where m is the slope
and b is the y-intercept
Now, we will express the given equation in this form
3x - 5y = 15
-5y = 15 - 3x
Divide through by - 5
y = -3 + 3/5x
y = 3/5x - 3
By comparing to the slope-intercept form of a line,
m = 3/5
and b = -3
Hence, the slope is 3/5 and the y-intercept is -3
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5. -4h + 3 + Th ≥ 9h - 21
PLEASE ASAP I NEED HELP
Given the inequality 4x ≤ 28, which of the following is a solution that makes the inequality true?
The value of the inequality equation is x ≤ 7
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
4x ≤ 28 be equation (1)
Now , on simplifying the equation , we get
Divide by 4 on both sides of the inequality equation , we get
x ≤ 7
Therefore , the value of x is less than or equal to 7
All the numbers less than or equal to 7 satisfies the condition for x
The value of the equation x ≤ 7 is shown in the graph below
Hence , The value of the inequality equation is x ≤ 7
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Find the area of a Shaded portion
Find the area of a Shaded portion.
D. 68
The ratio of brownies to cookies is 3:5. If there are 75 cookies, how many brownies are there?
Group of answer choices
45
15
60
32
Answer:
15:25 or 15 brownies
Step-by-step explanation:
25 / 5 = 5 (scale factor)
3 * 5 = 15
Given the ratio 8 ounces to 1 cup,how many ounces are in 4 cups?
Answer:
32 oz
Step-by-step explanation:
Given the ratio 8 ounces to 1 cup, how many ounces are in 4 cups?
4 * 8 oz = 32 oz
Algebra
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The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Let's check all the options, then
A) y ≤ (1/4)x - 1
At (-5, -7), we have
-7 ≤ (1/4)(-5) - 1
-7 ≤ -2.25
This is incorrect.
B) x + y ≤ 3
At (-5, -7), we have
-5 + (-7) ≤ 3
-12 ≤ 3
This is correct.
The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.
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What occurs when you are dealing with objects that are round
static friction
sliding friction
rolling friction
nswer the question.
The table shows the amount of fabric needed to make each item of doll clothes. Tamara is making 5 of
Fabric for Doll Clothes
Item Amount of Fabric Needed (feet)
Blouse2/12
Jacket 7/12
Skirt 7/12
How many feet of fabric are needed to make 5 of each item? Move numbers to the boxes to show the answer. If there is no whole number
put a 0 in the first box.
Equation:
5 x (2/12 + 7/12 + 7/12) = f f = amount of fabric needed
Solve:
10/12 + 35/12 + 35/12 = f
80/12 = f
Simplify:
6 8/12
Answer:
Tamara needs 6 ft and 8 inches of fabric to make five of each item.
(3.76x 10-8 )-(2.94 x 10-8)
Write your answer in scientific notation
At as sale, suits were sold for $72 each. This price was 45% of a suits original price. How much did a suit originally cost?
Answer: 1680. The answer is 1680 because 56% of 3000 is 1680 people.
Answer:
The suit orginally costed $160 dollars.
Step-by-step explanation:
write an algebraic expression that marshall can use to determine the total cost of buying a watermelon that weighs w pounds and some tomatoes that weigh t pounds. How much will it cost to buy a watermelon that weighs 18 1/2 pounds and 5 pounds of tomatoes if watermelon cost $0.68 and the tomatoes cost $3.25
Answer: The cost will be a total of $142.05. That is $125.80 for a Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.
Step-by-step explanation:
Given: Watermelons are 0.68 / lb and tomatoes are 3.25 / lb.
Let w = watermelon weight
Let t = tomato weight.
An equation would be:
.68w + 3.25t = Total cost
For 185 lb of Watermelon and 5 lbs of tomatoes:
.68(185) + 3.25(5) =
$125.80 + $16.25 = $142.05
Find the quadratic equation whose parabola has vertex (3, –2) and y-intercept (0, 16). Give your answer in vertex form, and show your work.
Please Help!!
Answer:
y = 2(x-3)^2-2
Step-by-step explanation:
We can find the quadratic equation by using the vertex form. The vertex form of a quadratic equation is:
[tex]y=a(x-h)^2+k[/tex], where x and y are any point on the parabola, a is the constant (indicating whether the parabola opens up or down), and h and k are the coordinates of the vertex.
Since we already have the y-int (an x and y coordinate lying on the parabola) and the vertex, we can plug in both to find a:
[tex]16=a(0-3)^2-2\\16=a(-3)^2-2\\16=9a-2\\18=9a\\2=a[/tex]
Thus, the equation is:
[tex]y=2(x-3)^2-2[/tex]
What is the value of Negative 3 squared + (negative 4 + 7) (2)?
–28
–3
3
15
I am on a unit test hurry please
-3^2+(-4+7)(2)
answer = 15
Answer:
15
Step-by-step explanation:
a negative number squared is positive, so its 9 + (-4 + 7)*2. 7-4 is 3, which we then multiply by 2 to get 6. Now add that to 9 to get 15.
Hope this helps!
Add a term to the expression so that it becomes a perfect square trinomial.
x2-22x +
Answer:
Step-by-step explanation:
is times 43
ILL GIVE BRAINLIESTTTT PLEASE HELP ILL GIVE BRAINLIESTTTT
Answer:
c) Propability of rolling doubles=6
Propability of rolling a sum grrater then or equal to 8 = 15
(Together add up to 21)
d)6 ->(1,1)(1,2)(1,3)(2,1)(2,2)(3,1)
e)9 ->(1,6)(3,4)(5,2)(3,5)(5,3)(3,6)(5,4)(5,5)(5,6)
Isaiah is trying to buy dry-erase markers for his teachers during teacher appreciation week. He
is able to collect 12 markers a day and started off with 15. How many days will it take him to get
to 135 markers? Make an equation to solve the problem using m for markers and d for days.
Answer:
It will take him 10 days to get to 135 markers.
[tex]d=12m+15[/tex]
Step-by-step explanation:
(attached)
Use two different methods to find and explain a formula for the area of a trapezoid
that has parallel sides of length a and b and height h. Consider these ideas or others: (a)
Combine two copies of the trapezoid to make a parallelogram. (b) Subdivide the trapezoid
into two triangles, one with base b and one with base a.
The two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}What is trapezoid?
A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
Area : ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sidesPerimeter : sum of lengths of sides of trapezoidNumber of vertices : 4Number of edges : 4Properties : Convex polygonType : QuadrilateralSum of interior angles : 360°We have a trapezoid.
Now, we can find the area in two ways -
[1] -
A = (1/2) × {a + b} × {h}
[2] -
A = {b x h} - (1/2) x {(b - a} x h}
Therefore, the two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}To solve more questions on trapezoids, visit the link below -
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A cafeteria sold 36 cartons of regular flavored milk. If the ratio of regular milk sold to chocolate milk sold was 9:4, what is the combined amount of chocolate and regular milk sold?
Answer:
The combined amount of chocolate and regular milk sold was 52 cartons.
Step-by-step explanation:
1. Divide
36 ÷ 9 = 4
(This means that the ratio has a unit rate of 4. That means):
2. Second ratio rate
4 x 4 = 16
(Because the unit rate is 4).
3. Add
(Now, we add the original 36 cartons with the 16 cartons we found because the first step was just for finding the unit rate).
36 + 16 = 52 cartons.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
6. Alex says he can find the product for
(3 X 5) X 2 by solving 3 X (5 × 2).
Is Alex correct?
Answer: Yeah
Step-by-step explanation: Multiplication can be done in any order, so using parenthesis to denote which numbers to multiply first should not matter.
Solve for m.
m+15<−123
Responses
m>−11315
m is greater than negative 1 and 13 over 15
m>−1715
m is greater than negative 1 and 7 over 15
m<−1715
m is less than negative 1 and 7 over 15
m<−11315
and show work
The solution to the inequality is m < −1 13/15 . m is less than negative 1 and 7 over 15
How to solve for the inequalityIn this question we have to solve for the inequality that is given as m + 1/5 < -1 2/3
We would have to rewrite the equation using the math tool
[tex]m +\frac{1}{5}\leq 1\frac{2}{3}[/tex]
The mixed fraction can be properly rewritten as improper fraction
[tex]m +\frac{1}{5}\leq \frac{5}{3}[/tex]
subtract 1/5 from 5/3
[tex]m\leq -\frac{5}{3} -\frac{1}{5}[/tex]
we have to carry out the subtraction of the fraction
[tex]m < \frac{-25-3}{15}[/tex]
[tex]m < \frac{-28}{15}[/tex]
This can be written in mixed fraction as
[tex]m < -1\frac{13}{15}[/tex]
Hence the solution of m is D. m < −1 13/15
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Complete question
m + 1/5 < -1 2/3
Responses
A. m > −1 13/15
m is greater than negative 1 and 13 over 15
B. m > −1 7/15
m is greater than negative 1 and 7 over 15
C. m < −1 7/15
m is less than negative 1 and 7 over 15
D. m < −1 13/15
m is less than negative 1 and 7 over 15
describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7
The mean of the given sample data is 210, and the standard deviation is 7.937.
Given size 'n' = 300
The population proportion 'p' = 0.7
Let 'x' be the random variable of the binomial distribution
a) mean of the binomial distribution = n p = 300 × 0.7
μ = 210
b) variance of the binomial distribution
⇒ n p q
⇒ 300 × 0.7 ×0.3
⇒ σ² = 63
The standard deviation of the binomial distribution:
⇒ √n p q = √63 = 7.937
Thus, the mean of the given sample data is 210, and the standard deviation is 7.937.
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The question seems to be incomplete the correct question would be:
describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7 a) Determine the mean of the sampling distributionb) Dtermine the standard deviation of the sampling distribution