The equation that models the path of the ball is y = -0.05·x² + 5·x.
Given,
The distance where the football landed from where it was kicked = 100 feet
The maximum height that the football reached = 125 feet
We have to write an equation that models the path of the ball while it was in the air.
The path may be parabola.
So, equation is like:
y = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)
Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;
The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)
We have;
The coordinate of the highest point reached by the ball = (50, 125)
Therefore;
(h, k) = (50, 125)
Substituting the above values in the equation of the parabola gives;
y = a·(x - 50)² + 125
At x = 100, y = 0, which gives;
0 = a·(100 - 50)² + 125 = a·2500 + 125
0 = a·2500 + 125
a = -125/2500 = -0.05
Therefore, we have;
y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125
y = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x
y = -0.05·x² + 5·x
The equation that models the path of the ball is y = -0.05·x² + 5·x.
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evaluate 3(x-4)+2x-x2 for x=5
Answer:-12
Step-by-step explanation:
Im going to assume that x2 means x squared. You can just substitute "x" for 5. 3(5-4)+2(5)-5^2. First parenthesis equals 3(1)+10-5^2. Then it equals 3+10-5^2. So then it would be 13-5^2. 5^2 equals 25. so it would be 13-25. Which equals -12.
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
The height of the base and the perimeter length are respectively; 12 cm and 840 cm
How to find the volume of a Prism?
We are told that;
Volume of Triangular Prism = 1200 m³
Base length = 10 cm
Side length of triangle = 13
Length of box = 20
Now, formula for volume of a triangular prism is;
V = ¹/₄h√(-a⁴ + 2(ab)² + 2(ac)² - b⁴ + 2(bc)² - c⁴)
where;
a is side length of triangle
b is base side length
c is also side length of other triangle
h is length of box
Thus;
Using Pythagoras theorem, we can find the height of the base as;
D = √(13² - 5²)
D = √144
D = 12 cm
B) Formula for perimeter length of triangular prism is;
P = (S1 + S2 + S3)L + BH
P = (13 + 13 + 10)20 + 10(12)
P = 720 + 120
P = 840 cm
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Bashir is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 66, find Bashir's age.
Answer:
15
Step-by-step explanation:
x+x+1+x+2+x+3=66
simplify into 4x+6=66
subtract 6 from both sides to get 4x=60
divide both sides by 4 to get x=15
The age of Bashir is 15 years.
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 consecutive age be x, x+1, x+2 and x+3.
Now, sum of their ages is 66
So, x+ x+1 + x+2 + x+3 = 66
Simplifying for x, we get
4x+6=66
subtract 6 from both sides
4x=60
divide both sides by 4
4x /4 = 60/4
x= 15
Hence, Bashir age is 15 years.
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How do I get the answer
Answer:11
Step-by-step explanation:
Answer:
11 units
Step-by-step explanation:
use the absolute value function to find the difference between A and E
A = - 6 , E = 5 , then
AE = | - 6 - 5 | = | - 11 | = | 11 | = 11
or
AE = | 5 - (- 6) | = | 5 + 6 | = | 11 | = 11
2 tickets cost 11.00 they bought 2 drinks and used a 5.00 off coupon. the total cost was 29.18 how much was 1 drink
After buying tickets and drinks the total cost is 29.18 and using 5.00 off coupon, the cost of one drink is 11.59
As per the question statement, 2 tickets cost 11.00 and they bought 2 drinks and used a 5.00 off coupon. The total cost was 29.18. We are supposed to find out the cost of one drink.
Let the cost of one drink be "x"
Cost of 2 tickets = 11
Off coupon is of 5.00
Cost of two drinks = [tex]2x[/tex]
Total money paid = 29.18
Hence, [tex]11+2x-5=29.18\\2x=29.18+5-11=23.18\\x=\frac{23.18}{2} \\x=11.59[/tex]
Therefore the cost of one drink is [tex]x=11.59[/tex]
This question was a classic example of how to form equations when all the given conditions are in statements.
Algebraic Equation: An equation is when value of something is unknown so we say it as a variable and solve for its value using algebraic operations.To learn more about it, click on the link given below:
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What is the product of −2 1/4 and −4 1/2?
regina has five brothers who are 4, 6, 6, 9, and 15 years of age. the mean age of regina's brothers is .
The calculated mean age of Regina's brothers is 7. This is being attained by using the concept of measure of central tendency i.e. mean.
What is a mean?
Mean is interpreted as the total of all values divided by the total number of values. It is also called a mathematical average. There are three types of mean namely, arithmetic, geometric and harmonic mean.
Calculation of the mean age of Regina's brothers
Total number of Regina's brothers = 5
Sum of their ages = 4 + 6 + 6 + 9 + 10
= 35
Mean age = sum of their ages / total number
= 35 / 5
= 7
Hence, the calculated mean ages of Regina's brothers is 7
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Select the correct product of the exponential expression.
3^5
OA. 3.5
OB. 3.3.3.3.3
OC. 5.5.5
OD. 15
The correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
As given in the question,
Given exponential expression is equal to 3⁵
General form of exponential expression is given by aˣ
a is the base and x is the exponent
This means 'x' times ' a ' is multiplied to ' a '
Compare 3⁵ with general form
3 is base
5 is exponent
This means '5' times ' 3 ' is multiplied to '3'
3⁵ = 3.3.3.3.3
Therefore, the correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
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si tardamos 20 minutos en recorrer una distancia a una velocidad de 40 km/h
1)cuanto tardaremos en recorrer dicha distancia si circulamos a 50 km/h
2) si la velocidad maxima en la zona es de 90 km/h a que porcentaje corresponden los 50 km/h?
porfa necesito el paso a paso :(
ya se q son inversas solo necesito el paso a paso
1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.
2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.
¿Cómo analizar móviles a rapidez constante?
1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.
[(40 km /h) / (50 km / h)] = t / 20 min
4 / 5 = t / 20
t = 80 / 5
t = 14 min
El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.
2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:
r = [(50 km / h) / (90 km / h)] × 100 %
r = 55.556 %
La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.
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Mr. Hazel is a professional plumber. To fix a drain that is clogged, he charges a customer
$50 per hour, plus a fixed fee of $25 for the service call, as represented by the function
f(x)= 50x + 25. In the equation, what is represented by the variable "x"?
Answer:
The x is how much hours the job takes,
You can see that 25 is a fixed fee which is why there is no x attached to it, and 50 is the variable that can change, hope that made sense!
Step-by-step explanation:
^^^
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
"Extend the domain of the trigo functions using the unit circle" Cluster A.
What is unit circle?The following steps can be used to calculate the sine and cosine of any angle thetatheta and allow us to extend the domain of sine and cosine to any real numbers:
Move counterclockwise around the unit circle starting at (1, 0), (1, 0), (1, comma, 0, right parenthesis, until the angle created by your position, the origin, and the positive xxx-axis equals thetatheta.
The yyy-coordinate of your point is equal to sin(theta)sin(theta)sine, and the xxx-coordinate is equal to cos(theta)cos(theta)cos(theta)cosine, left parenthesis, theta, right parenthesis.
There are several references to and issues with in the worlds of calculus, pre-calculus, and trigonometry.
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what is 343250394065834698350968549846÷57547547
Answer: 5.9646399e+21
Solve the following equation
3(1-3x)=2(-4+7)
Answer:
x=-1/3
Step-by-step explanation:
3(1-3x)=2(-4+7)
Use distributive property.
3-9x=-8+14
Combine like terms.
3-9x=6
Subtract 3 from both sides.
-9x=3
Divide -9 from both sides.
x=-1/3
Hope this helps!
Please mark as brainliest if correct!
Answer:
The value of x is -1/3.
Step-by-step explanation:
Given equation,
→ 3(1 - 3x) = 2(-4 + 7)
Now the value of x will be,
→ 3(1 - 3x) = 2(-4 + 7)
→ 3 - 9x = 2 × 3
→ -9x = 6 - 3
→ x = 3/(-9)
→ [ x = -1/3 ]
Hence, the value of x is -1/3.
Brainliest for correct answer
The correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
Graph of functionsFrom the question, we are to determine the correct symbols that complete the given statements
The given statements are
h(0) ___ g(0)
and
h(1) ___ g(1)
To complete the statements, we will find the values of the given functions from the graph
From the graph of h(x), we can observe that
h(0) = 4
and
From the graph of g(x), we can observe that
g(0) = 4
Thus,
The two functions are equal
h(0) = g(0)
Also,
From the graph of h(x),
h(1) = 3
and
From the graph of g(x),
g(1) = 2
That is, h(1) is greater than g(1)
Thus,
h(1) > g(1)
Hence, the correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
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I NEED HELP WITH THIS ANSWER ASAP!!!!!!
A sequence is defined by the formula U(subscript 1)=4/27, u(subscript n+1)=3 x u(subscript n), n>1.
A) Show the sequence is geometric and find the common ratio
From the recursive definition, the next term of a sequence is the previous term multiplied by 3, hence it is a geometric sequence with a common ratio of 3.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The recursive definition of a geometric sequence is:
[tex]a_{n+1} = qa_n[/tex]
In this problem, the sequence is given by:
[tex]u_{n+1} = 3u_n[/tex]
With first term [tex]u_1 = \frac{4}{27}[/tex].
Hence it is a geometric sequence with a common ratio of 3.
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Please help me please help me
Answer: T (4,4)
Step-by-step explanation:
Khadija asked Muhammad, "How many text messages have you sent today?" Is this a statistical question?
Eli, Freda and Geoff were given 800 pounds to share in the ratio of there age. Eli is 9 years old Freda is 13 years old and Geoff is 18 years old. How much should they each have?
a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:
For 450 km, the car need 9.32 liters of gasoline to cover the distance of 450km.
Given,
Car averages 35 miles per gallon of gasoline.
Here we need to find how many liters of gasoline will be needed for a trip of 450 km.
First we have to convert the km into miles in order to solve it.
1 mile = 0.621371 miles
So, 450 km is equal to,
=> 450 x 0.621371 miles
=> 279.617 miles.
Now, we already know that,
1 gallon of gasoline will cover 35 miles.
So, for 279.617 miles, it will need,
Let x be the liters of gasoline will be needed to cover the distance.
So,
=> x = 279.617 / 30
=> x = 9.32
Therefore, we need 9.32 liters of f gasoline will be needed for a trip of 450 km.
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help with explanation!
In a heptagon, the sum of all seven angles is 900 degrees. If you add up the four given angles you will get 600 degrees. In the question it says, "the remaining interior angles are EQUAL" so therefore, the only way to get from 600 to 900 from the remaining three angles is 100. Each remaining angle is 100 degrees
Answer:
Heptagons are known to have seven interior angles that add up to 900°, so we must find the last 3. First, add the first four they gave us.
[tex]160\circ + 130\circ = 290\circ\\= 290\circ + 170\circ + 140\circ\\170\circ + 140\circ = 310\circ\\= 290\circ + 310\circ\\= 600\circ[/tex]
We now know that the remaining angles are all 100°, because the question mentions the rest of the interior angles being equal. The only reasonable 3 equal numbers to add up to 900° would be three 100s in this case.
What’s 8(x + 4) =32? Full answer please
Answer:
x = 0
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x8(x + 4) = 32 Distribute by multiplying 8 to x and 48(x) + 8(4) = 328x + 32 = 32 Subtract 32 from both sides8x = 0 Divide by 8 on both sidesx = 0The value of x should be 0, as any number multiplied by 0 is 0.
find a sequence of rigid motions to take each vertex of triangle ABC onto the corresponding vertex of triangle A’B’C’
Using translation concepts, the sequence of rigid motions to take each vertex of triangle ABC onto the corresponding vertex of triangle A’B’C' are:
Rotation over a vertical line.Shift down and right.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For the motions in this problem, we have that:
There was a rotation over a vertical line, due to the changes in the orientation of A and C.Then, only the position changed, not the orientation, meaning that there was a shift down and right.More can be learned about translations at https://brainly.com/question/4521517
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pls help! marking brainliest
Answer:
296
Step-by-step explanation:
Use long division.
296
21 |6216
-42
201
-189
126
-126
0
Hope this helps!
After a 80% reduction, you purchase a new DVD player on sale for $160. What was the original price of the DVD player?
The original price was $
Answer: $800
Step-by-step explanation: 80% of 800 is 640. So you would do 800-640=160. Hope this helps :)
An angel measures 109 what is the measure of it it’s supplement
Answer:
71°
Step-by-step explanation:
A supplementary angle is the sum of two angles whom are less than 180 degrees, yet the sum will only be 180 degrees. Because we are finding the supplement angle, we must subtract.
[tex]\sf Long\:Subtraction\\9\:doesnt\:go\:into\:10,borrow\:1\\= 10\\= 10 - 9\\= 1\\8\:cant\:go\:into\:0,take\:1\:since\:you\:just\:borrowed\\= 7\\= 7 - 0\\= 7\\1 - 1\\= 0\\\\= \boxed{71}[/tex]
➲ Hope this helps.
So you see...
The question in my math workbook is,
45 ÷ 3 = (30 + ___) ÷ 3
= 30 ÷ 3 + ___ ÷ 3
= 10 + 5
= 15
sorry my brain is broken right now- I have a feeling this problem is really easy to solve, but as I said my brain is broken lol
The blank will be filled with 15.
The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, position of power or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.
The explanation goes like:
45 ÷ 3 = ( 30 + 15 ) ÷ 3
= 30 ÷ 3 + 15 ÷ 3
= 10 + 5
= 15
Hence the answer is 15.
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7 pens cost 84p, how much
would 11 pens cost?
Answer:
132p
Step-by-step explanation:
if 7 pens cost 84 total then you need to find the cost of each to know how much 11 pens would cost in total
84/7=12
now you know it's 12 each so just multiply 12 by 11 and you know how much for 11 total!
12*11=132p
Answer:
132 is correct
Step-by-step explanation:
84÷7=12
12×11= 132
What is the standard deviation of a data set whose values are all the same?
(A) -1
(B) -2
(C) 0
(D) 1
Answer:
C
Step-by-step explanation:
all the values will equal the mean
Directions: Translate equation DO NOT SOLVE!
"four times the difference of a number and 7
is 32"
Number 11:
“ten increased by the quotient of a number and 2 is -15”
Sorry for taking so long :/
Step-by-step explanation:
*Four times the difference of a number and 7 is 32*
Answer-
4(x-7)=32
ten increased by the quotient of a number and 2 is 15-
Answer-
10+(x/2= -15
or
10+x/2=-15
anyone of them
Which statement describes the system of equations?
√x+2y=2
x-2y=-2
O It has infinitely many solutions.
OIt has no solution.
O It has one solution (0, 1).
It has one solution (4, -1).
Mark this and return
For the system of equations √x + 2 y = 2 and x - 2 y = - 2, it has no solutions.
We are given a system of equations:
√x + 2 y = 2 … (1)
x - 2 y = - 2 … (2)
We need to find out which of the given statements if true about this system of equations.
We will do this by first comparing the a₁ / a₂, b₁ / b₂ and c₁ / c₂ with each other.
We have:
a₁ = 1
b₁ = 2
c₁ = 2
a₂ = 1
b₂ = -2
c₂ = -2
Since, b₁ / b₂ = 2 / -2 = -1 and c₁ / c₂ = 2 / - 2 = -1
So,
a₁ / a₂ ≠ b₁ / b₂ = c₁ / c₂
From this, we get that:
It has no solution.
Therefore, for the system of equations √x + 2 y = 2 and x - 2 y = - 2, it has no solutions.
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