Answers
Answer:
h(t) = -5*t^2 + 20*t + 2
Step-by-step explanation:
First, we know that the motion equation of the ball will be quadratic, so we write the equation:
h(t) = a*t^2 + b*t + c
Now we need to work with the data in the table.
h(1) = 17
h(3) = 17
h(1) = h(2) = 17
Then we have a symmetry around:
(3 - 1)/2 + 1 = 2
Remember that the symmetry is around the vertex of the parabola, then we can conclude that the vertex of the parabola is the point:
(2, h(2)) = (2, 22)
Remember that for a quadratic equation:
y = a*x^2 + b*x + c
with a vertex (h, k)
we can rewrite our function as:
y = a*(x - h)^2 + k
So in this case, we can rewrite our function as:
h(t) = a*(t - 2)^2 + 22
To find the value of a, notice the first point in the table:
(0, 2)
then we have:
h(0) = 2 = a*(0 - 2)^2 + 22
= 2 = a*(-2)^2 + 22
2 = a*(4) + 22
2 - 22 = a*(4)
-20/4 = -5 = a
Then our function is:
h(t) = -5*(t - 2)^2 + 22
Now we just expand it:
h(t) = -5*(t^2 - 4*t + 4) + 22
h(t) = -5*t^2 + 20*t + 2
The correct option is the first one.
Related Questions
find the measure of the complementary angles that satisfy each case. the measure of the first angle is 30 greater than the measure of the second angle
Answers
Answer:
First angle: 60°
Second angle: 30°
Step-by-step explanation:
Let the two angles be signified by the variables x & y.
Let the first angle = x, and the second angle = y.
It is given that:
"The measure[ments] of the complementary angles...": x + y = 90°
"The measure of the first angle is 30 greater than the measure of the second angle": x = y + 30°
Use the system of equations. Plug in y + 30 for x in the first equation:
(y + 30) + y = 90
Combine like terms:
(y + y) + 30 = 90
2y + 30 = 90
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 30 from both sides of the equation:
2y + 30 (-30) = 90 (-30)
2y = 90 - 30
2y = 60
Next, divide 2 from both sides of the equation:
(2y)/2 = (60)/2
y = 60/2
y = 30°
Plug in 30 for y in one of the equations:
x = y + 30
x = (30) + 30
x = 60°
Your answers:
First angle: 60°
Second angle: 30°
Tahmar knows the formula for simple interest is I = Prt, where I represents the simple interest on an amount of money, P, for t years at r rate. She transforms the equation to isolate P : P = P : P equals Start Fraction I Over r t End Fraction.. Using this formula, what is the amount of money, P, that will generate $20 at a 5% interest rate over 5 years?
Answers
Answer:
P = $80
Step-by-step explanation:
I = P*r*t
P = I/rt
Where,
simple interest, I = $20
Interest rate, r = 5%
Time, t = 5 years
P = I / rt
= 20 / 5% * 5
= 20 / 0.05 * 5
= 20 / 0.25
= 80
P = $80
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
15.4
Step-by-step explanation:
sin 17° = 4.5 /x
x = 4.5 / sin 17° = 4.5 /0.2924
= 15.4
The value of the variable 'x' using the sine formula will be 15.4 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of 'x' is given by the sine of the angle ∠GIH. And the sine of an angle is the ratio of the normal and hypotenuse of the right-angle triangle. Then we have
sin 17° = 4.5 / x
x = 15.4
The value of the variable 'x' using the sine formula will be 15.4 units.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ7
solve the equatiuon =
Answers
Help please... What is the measurement of arc AC?
Answers
Answer:
D) 88 degrees
Step-by-step explanation:
Angle ABC is 1/2Arc AC (Inscribed angle theorem)
How would the domain and range of the function y = one-fourth x minus 6 be determined? Explain.
Answers
Answer:
Domain = ( -∞ , ∞ )
Range = ( ∞ , ∞ )
Step-by-step explanation:
A function is given to us and we need to find the domain and range of the given function .
The function :-
[tex]\rm \implies y = \dfrac{1}{4}x - 6 [/tex]
Definitions :-
Range :- The range is the set of all valid y values .Domain :- All real numbers except where the expression is undefined.In this case, there is no real number that makes the expression undefined. Therefore the domain will be :-
Domain :-
[tex]\rm Domain = ( -\infty , \infty ) [/tex]
or
[tex]\rm Domain = \{ x | x \in \mathbb{R} \}[/tex]
Range :-
[tex]\rm Range = ( -\infty , \infty ) [/tex]
or
[tex]\rm Range = \{ y | y \in \mathbb{R}\} [/tex]
Answer:
Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers.
Step-by-step explanation:
Heather wants to start a business. She has two products to sell, and knows it takes her a
different amount of time to make each. It takes her 1.5 hours to make each frame (f),
and 2.25 hours to make each canvas (c). She is planning to work for 40 hours on these
projects this week. Write the equation that represents this relationship.
Answers
Answer: 1.5f + 2.25c = 40
Step-by-step explanation:
You'd need to multiply the variables of unknown value (how many she'd make in 40 hours) by the time it takes to make one. This would mean multiplying 1.5 by f and 2.25 by c. you'd add this as together they equal the 40 hours she'd be working for the week.
A pipe 11/15 liters of tub in 22/45 minutes what is its flow rate in terms of liters per minute
Answers
Answer:
3/2 liters/minute
Step-by-step explanation:
Divide 11/15 liters by 22/45 minutes:
11
------
15
-----------
22
-----
45
This is equivalent to:
11 45
----- * ----- = 3/2 (liters/min)
15 22
The flow rate of the pipe is 3/2 (or 1.5) litres per minute.
To calculate the flow rate of the pipe, we divide the volume of water (in litres) by the time taken (in minutes).
Given:
Volume of water = 11/15 liters
Time taken = 22/45 minutes
Flow rate = Volume / Time
Flow rate = (11/15) liters / (22/45) minutes
To divide by a fraction, we multiply by its reciprocal:
Flow rate = (11/15) x (45/22) liters/minutes
Simplifying the expression:
Flow rate = 495/330 litres/minutes
The fraction can be simplified further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 165 in this case:
Flow rate = (495/165) / (330/165) litres/minutes
Flow rate = 3/2 liters/minutes
Therefore, the flow rate of the pipe is 3/2 (or 1.5) litres per minute.
To know more about expression follow
https://brainly.com/question/29115565
#SPJ2
Six pounds of grapefruit costs $3.00. 5 pounds of apples costs 2.65.
What is the cost per pound for each fruit?
Answers
Answer:
1 grapefruit cost $0.50 and 1 apple cost $0.53
Step-by-step explanation:
To find the unit cost of 1 fruit, divide the cost by the amount of fruit.
Grapefruit = 3.00 ÷ 6 = $0.50
Apple = 2.65 ÷ 5 = $0.53
The equation of line a is y=12x−1, and it passes through point (6,2).
Line b is perpendicular to line a, and it passes through point (−6,2).
A: What is the slope of line b?
B: What is the y-intercept of line b?
Answers
Answer:
A). slope = -1/12 y-intercept = 3/2
Step-by-step explanation:
y = -1/12x + b
2 = -1/12(-6) + b
2 = 1/2 + b
3/2 = b
y = -1/12x + 3/2
In a carnival game called Spot the Spot, the player has to drop five disks onto a red circle. The disks must cover it completely for the player to win. The probability that a skilled player can drop one of the disks onto the exact place on the red circle that it must occupy is about 1/3. What is the probability that such a player will be able to drop
Answers
Answer:
See explanation
Step-by-step explanation:
Given
[tex]n=5[/tex] --- disks
[tex]p = \frac{1}{3}[/tex] --- success probability
Required
The question is incomplete, as the required probability is not stated.
However, the question follows binomial distribution and the probability is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
Assume the question requires that we calculate the probability that he's able to drop 2 disks, the probability will be:
[tex]P(x = 2) = ^5C_2 * (\frac{1}{3})^2 * (1 - \frac{1}{3})^{5-2}[/tex]
[tex]P(x = 2) = ^5C_2 * (\frac{1}{3})^2 * (\frac{2}{3})^{3}[/tex]
[tex]P(x = 2) = 10 * \frac{1}{9}* \frac{8}{27}[/tex]
[tex]P(x = 2) = \frac{80}{243}[/tex]
Apply the formula to the complete question
resolver:
[5+(-3+6)+(-2)]-[(-4+10)+(-3)-(-5)]
Answers
Just be careful of signs
[ 5 + (3) -2] - [ (6)-3+5]
[6] - [8]
6 - 8
= -2
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10-
(7.2)
- 10
(0,0)
10
- 10 -
A. y 1x
B. y = 7x
C. y = 2x
D. y = -7x
E. y= ²x
F. y= -2x
Answers
Answer:
[tex]y = \frac{2}{7} x[/tex]
Step-by-step explanation:
The slope is
[tex]slope = \frac{rise}{run} = \frac{2}{7} [/tex]
The y-intercept is 0
The equation of line between the points is y = ( 2/7 )x
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 7 , 2 )
Let the second point be Q ( 0 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2/7 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 0 = ( 2/7 ) ( x - 0 )
y = ( 2/7 )x
Hence , the equation of line is y = ( 2/7 )x
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ7
Write a compound interest function to model the following situation. Then, find the balance after the
given number of years.
$13,700 invested at a rate of 2% compounded quarterly; 6 years
Answers
Answer:
The balance after the 6 years of investment will be $ 15,442.08.
Step-by-step explanation:
Given that $ 13,700 was invested at a rate of 2% compounded quarterly during 6 years, to determine the final result of the investment, the following calculation must be performed:
13,700 x (1 + 0.02 / 4) ^ 4x6 = X
13,700 x (1 + 0.005) ^ 24 = X
13,700 x 1,005 ^ 24 = X
13,700 x 1.1271 = X
15,442.08 = X
Therefore, the balance after the 6 years of investment will be $ 15,442.08.
Find the measure of the indicated angle
Answers
Answer:
x = 52
Step-by-step explanation:
The triangle is isosceles. The markings tell us that.
The 76 is not opposite either one of the equal sides. Let the angle values opposite the equal sides be x
x + x + 76 = 180 All triangles = 180
2x + 76 = 180 Subtract 76 from both sides.
2x = 180 - 76
2x = 104 Divide both sides by 2
x = 104/2
x = 52
So x = 52
Using f(x) = 4x + 6 with a domain of{-1, 0, 2 }, find the range.
1. {10, 6, 15}
2. {2, 14}
3. {-4, 0,8}
4. {2, 6, 14}
Answers
Answer:
{2,6,14}
Step-by-step explanation:
The range are the f(x) values
the domain are the x values
So we have it that;
f(-1) = 4(-1) + 6 = 2
f(0) = 4(0) + 6 = 6
f(2) = 4(2) + 6 = 14
so we have the range as;
{2,6,14}
Find the quotient: 63/-9
Answers
Answer:
-7
Step-by-step explanation:
63/9 but there is an odd number of negative numbers so negative answer
help asap no wrong answers pls
Answers
Answer:
- 1.4
Step-by-step explanation:
The average rate of g(x) in the closed interval [ a, b ] is
[tex]\frac{g(b)-g(a)}{b-a}[/tex]
Here [ a, b ] = [ - 4, 1 ] , then
g(b) = g(1) = - 3 ( value of g(t) when t = 1 ]
g(a) = g(- 4) = 4 ( value of g(t) when t = - 4 )
average rate of change = [tex]\frac{-3-4}{1-(-4)}[/tex] = [tex]\frac{-7}{5}[/tex] = - 1.4
What are the side of triangle PQR
Answers
Can someone help me with this math homework please!
Answers
Answer:
During that time, math symbols (like the division and multiplication sign) and numbers weren't invented yet, so they used words because that was the only choice either than verbally speaking.
Step-by-step explanation:
This is open-ended question, so you can write something similar to the answer I wrote or add on to it :-)
I searched online for the answer and found it on Brainly just to let you know because I was unsure about it loll
Credit: Edufirst
Hope it helps (●'◡'●)
ABCD is a rectangle. Find the length of segment AC
Answers
Answer:
52
Step-by-step explanation:
First, find x. As BE and DE will have the same measurements, you can set your formula up as
5x+11=3x+17
5x=3x+17-11
5x-2x=6
2x=6
x=6/2
x=3
CE and AE will also have the same value, now substitute 3 in place of x to get the value of segment BE
5x+11
5*3+11 = 26
This also means that CE = 26 and AE = 26
AC = CE + AE
AC = 52
How do relational databases work mathematically?
Answers
Answer:
A relational database stores data in a series of tables so that the data models a mathematical theory of relations. The model allows for queries based on projection, selection, and join, among other operations, and connects the data in the tables by way of keys.
Answer:
Well, I guess in a formal sense you could call relational algebra a type of logic, which puts it into the realm of ‘math’, though I don’t think most mathematicians would look at it as being a very significant area, more ‘applied logic’ than anything else.
That being said, relational algebra DOES present some formalisms in the shape of relations, tuples, normalizations, and denormalization, etc. There is also a model of sequential operations and thus the underpinnings of the ACID database concept.
Since the overwhelming primary use of RA has been as a way to structure our ideas about SQL RDBMSes there isn’t really a lot of deep theory there. I don’t think anyone has really built any other models of RA beyond an RDBMS. There have been limited non-SQL RDBMS implementations, but AFAIK none of them are really actively maintained today.
If a semi circle has a diameter of 5 m what is the area?
Answers
Answer:
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Step-by-step explanation:
Semi circle formula: 1/2 * 4/3 * pi * r^3
r = 2.5
1/2 * 4/3 * pi * 2.5^3
2/3 * pi * 2.5^3
2/3 * pi * 15.625
10.416..... * pi
Exact answer = 10.417pi
We can estimate pi as 3.14
So, 10.417 * 3.14 = 32.70938
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Pls help plz help pls plz help plz plz help
Answers
Answer:
The first choice, Equation A and equation C.
Step-by-step explanation:
The lines A and C are intersecting in the point (0,8). That is the solution for those lines.
What is the following sum?
Answers
Answer:
[tex]D. 7x^{2}(\sqrt[3]{x^{2}y} )[/tex]
Step-by-step explanation:
is this edge?
If it is, my friend had the same question i think. I didn't tho
A mixture contains nothing biet water and are tone in a ratio of stof 1.2. After 2oom of water is added to the mixture, the ratio of water to acetone He is 2:3. The original volume of the mixture is
Answers
Answer:
Step-by-step explanation:
Find the missing part.
Answers
Answer:
[tex]y=\frac{15\sqrt{3}}{4}[/tex]
Step-by-step explanation:
We are given that
[tex]\theta_1=60^{\circ}[/tex]
[tex]\theta_2=30^{\circ}[/tex]
We have to find the missing part.
[tex]\frac{x}{15}=cos\theta_1=cos60^{\circ}[/tex]
Using the formula
[tex]\frac{base}{hypotenuse}=cos\theta[/tex]
[tex]x=15cos60^{\circ}=\frac{15}{2}[/tex]
[tex]\frac{z}{15}=sin60^{\circ}[/tex]
Using the formula
[tex]\frac{Perpendicular\;arm}{hypotenuse}=sin\theta[/tex]
[tex]z=15\times \frac{\sqrt{3}}{2}=\frac{15\sqrt{3}}{2}[/tex]
Now,
[tex]\frac{a}{x}=cos60^{\circ}[/tex]
[tex]\frac{a}{\frac{15}{2}}=\frac{1}{2}[/tex]
[tex]a=\frac{1}{2}\times 15/2=\frac{15}{4}[/tex]
[tex]y=x sin60^{\circ}[/tex]
[tex]y=\frac{15}{2}\times \frac{\sqrt{3}}{2}[/tex]
[tex]y=\frac{15\sqrt{3}}{4}[/tex]
What is the slope of the line? What is the y-intercept of the line? y = 1
Answers
Answer:
m = 0
y intercept = 1
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 1[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 0 [/tex]
[tex]\implies y - intercept= 1[/tex]
Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1
y intercept of the line is y = 1.
Answered by GAUTHMATH
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be
Answers
Step-by-step explanatiosorry don't understand question be more specific
If < A and < B are vertical angles, and < A = 5x - 1 degrees, and < B = 4x + 4 degrees, find x.
Select one:
a. 5 / 9
b. - 3
c. 5
d. 11
Answers
Answer:
c
Step-by-step explanation:
vertical angles are congruent, so
5x - 1 = 4x + 4 ( subtract 4x from both sides )
x - 1 = 4 ( add 1 to both sides )
x = 5 → c
The value of x is c. 5
Given that,
If < A and < B are vertical angles, and < A = 5x - 1 degrees, and < B = 4x + 4 degreesBased on the above information, the calculation is as follows:
5x - 1 = 4x + 4
5x -4x = 4 + 1
x = 5
Learn more: brainly.com/question/17429689