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
i13(12)-2give answer
Answers
2. Estimate the square root of the following
(i) 99
(ii) 572
(iii) 11437
(4) 476
(5) 9027
(6) 512375
Answers
Answer:
1..9.9
2....23.9
3...106.9
4....21.8
Step-by-step explanation:
1-9.9
2-23.9
3-106.9
4-21.8
5-95.01
6-715.8
10 pointssss!!!!!:))
write the formula of the function y whose graph is shown.
a).
[tex]y = \frac{2}{x} [/tex]
b).
[tex]y = \frac{1}{ x } + 2[/tex]
c).
[tex]y = \frac{1}{x - 2} [/tex]
plss, I need helpp!!!!
Answers
9514 1404 393
Answer:
(a) y = 2/x
Step-by-step explanation:
The vertical and horizontal asymptotes are the axes, so there is neither a vertical nor a horizontal offset to the parent function y = 1/x. There is a vertical stretch by a factor of 2, so the describing function is ...
y = 2/x
help and I'll follow you
Answers
Answer:
12 nickels and 9 dimes
Step-by-step explanation:
1/ We have: n + d = 21 <=> d = 21 - n or opposite (n = 21 - d)
2/ We have: 0.05n + 0.10d = 1.50 and then we will put 1/ into 2/
=> 0.05n + 0.10(21 - n) = 1.50
=> 0.05n + 2.1 - 0.1n = 1.5
=> -0.05n = -0.6
=> n = 12
Nevertheless, d = 21 - n = 21 - 12 = 9
1.Una granja tiene gallinas y vacas. En total hay 58 cabezas y 168 patas. ¿Cuántos gallinas y cuantas vacas hay?
Answers
Answer:
no c
Step-by-step explanation:
What is the value of x?
[tex] \frac{4}{5} x - \frac{1}{10} = \frac{3}{10} [/tex]
Answers
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{5}[/tex] x - [tex]\frac{1}{10}[/tex] = [tex]\frac{3}{10}[/tex]
Multiply through by 10 ( the LCM of 5 and 10 ) to clear the fractions
8x - 1 = 3 ( add 1 to both sides )
8x = 4 ( divide both sides by 8 )
x = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
225 students appeared at an examination. Among them, the ratio of the number of students who passed in the first and in the second division were 4.5. If 25 students passed in the third division and 29 students failed in the examination, find (i) the number of students who passed in the first and in the second division (ii) The ratio of the number of students who passed in the first second and in the third division.
Answers
(i) the number of students who passed in the first and in the second division
76+95=171 students
(ii) The ratio of the number of students who passed in the first second and in the third division.
RATIO is 4:5:(25/19) or 4:5: 1.3157894…….
225-29=196 (29students failed)
196-25=171. (Subtract 25 students from the 3rd division)
4x+5x= 171 (171 students from 1st and second division)
9x=171
X=19
4x19=76 5x19= 95 1.31578.....x19= 25
Which of the following expressions is equal to - x^2 - 36 ?
O A. (-x-6)(x-61)
B. (x +61)(x-6)
C. (-x+6)(x-61)
D. (-X-61)(x+61)
Answers
Answer:
I think the answer is option C
PLEASE HELP THIS IS MY LAST QUESTIONNNN
- The electric company charges Dalton a monthly service fee of $30 plus $0.15 per kilowatt-hour of electricity used. This month, Dalton's bill is $105.
- How many kilowatt-hours of electricity did Dalton use?
Answers
Answer:
500 kilowatt-hours.
Step-by-step explanation:
Let k = number of kilowatt-hours.
[tex]0.15k+30=105\\0.15k=75\\k=500[/tex]
Therefore, Dalton used 500 kilowatt-hours of electricity.
Can someone help me with this math homework please!
Answers
Answer:
1. [tex]x=2[/tex]
2. Simplify by combining like terms
3. [tex]x=1[/tex]
4. [tex]k=0.5[/tex]
5. [tex]y=3[/tex]
Step-by-step explanation:
1. [tex]2.5(6x-4)=10+4(1.5+0.5x)[/tex]
Distribute within the parenthesis
[tex]15x-10=10+6+2x[/tex]
Combine like terms
[tex]15x-10=16+2x[/tex]
Isolate the variable expression by using the addition/subtraction properties of equality
[tex]13x=26[/tex]
Isolate the variable by using the division/multiplication properties of equality
[tex]x=2[/tex]
2. Like terms are always combined as soon as possible but never before the distributive property is applied.
3. You can find the solution by comparing the tables.
4. [tex]6k+10.5=3k+12[/tex]
Apply the addition/subtraction properties of equality
[tex]3k=1.5[/tex]
Apply the division/multiplication properties of inequality
[tex]k=0.5[/tex]
5. [tex]y+3=-y+9[/tex]
Addition/subtraction properties
[tex]2y=6[/tex]
Division/Multiplication properties
[tex]y=3[/tex]
helpppp and explain///////////////////////////
Answers
Answer:
A
Step-by-step explanation:
The first thing we have to do here is to subtract g(x) from f(x)
We have this as;
2x + 4 -(3x-7)
= 2x + 4-3x + 7
= -x + 11
Now, we substitute the value of x for 5
We have -5+ 11 = 6
PLEASE HELP ASAP! Worth 15 points!!
Which graph represents a function with direct variation?
Answers
Answer:
The bottom right photo
Step-by-step explanation:
A direct variation is an equation in the form y = kx, where k is the constant of variation. Since it is in this form, the equation will pass through the origin (0, 0)
What conversion ratio was skipped in this multiple-step conversion?
Answers
Answer:
B
Step-by-step explanation:
B was missed. You have to convert this from hours into minutes before you can deal with seconds.
Which inverse trig function could I use to solve this problem?
Answers
Answer:
Inverse sine
Step-by-step explanation:
Recall the three common trig ratios
Remember SohCahToa
Sine = Opposite over Hypotenuse (SOH)
Cosine = Adjacent over Hypotenuse (CAH)
Tangent = Opposite over Adjacent (TOA)
Now let's look back at the question
It asks us which inverse function would we use to solve for angle Z
Looking at angle Z, we are given it's opposite side length and the hypotenuse ( longest side ).
When dealing with the opposite side length and hypotenuse we use trig function sine.
When trying to find the angle we use inverse so we would use inverse sine to find the measure of angle A
A 4 metre ladder is placed against a vertical wall.
The base of the ladder is 1.5 metres from the base of the wall.
Answers
Answer:
Original position: base is 1.5 meters away from the wall and the vertical distance from the top end to the ground let it be y and length of the ladder be L.
Step-by-step explanation:
By pythagorean theorem, L^2=y^2+(1.5)^2=y^2+2.25 Eq1.
Final position: base is 2 meters away, and the vertical distance from top end to the ground is y - 0.25 because it falls down the wall 0.25 meters and length of the ladder is also L.
By pythagorean theorem, L^2=(y -0.25)^2+(2)^2=y^2–0.5y+ 0.0625+4=y^2–0.5y+4.0625 Eq 2.
Equating both Eq 1 and Eq 2: y^2+2.25=y^2–0.5y+4.0625
y^2-y^2+0.5y+2.25–4.0625=0
0.5y- 1.8125=0
0.5y=1.8125
y=1.8125/0.5= 3.625
Using Eq 1: L^2=(3.625)^2+2.25=15.390625, L=(15.390625)^1/2= 3.92 meters length of ladder
Using Eq 2: L^2=(3.625)^2–0.5(3.625)+4.0625
L^2=13.140625–0.90625+4.0615=15.390625
L= (15.390625)^1/2= 3.92 meters length of ladder
hope it helps...
correct me if I'm wrong...
Evalute f (3) if(x) = -4x+5
Answers
Answer: f(3)=-7
Step-by-step explanation:
To evaluate f(3), we want to plug in x=3 into f(x)=-4x+5.
f(3)=-4(3)+5 [multiply]
f(3)=-12+5 [add]
f(3)=-7
Now, we know that f(3)=-7.
Rudy rode a bike at the speed of 32 2/3 miles per 3 1/2 minutes. What is his speed in terms of miles per hours?
HELPPP
Answers
Answer:
[tex]32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour[/tex]
560 miles per hourWhich of the following is a geometric sequence
Answers
Answer:
B.
Step-by-step explanation:
A geometric sequence is where a number is multiplied or divided by same number
in option be all number ar the power of 2 so the correct answer would be B
someone help me please with this algebra problem
Answers
Answer:
60
Step-by-step explanation:
5x + 10y = 800
y = 50
5x + 10(50) = 800
5x + 500 = 800
5x = 300
x = 60
Answer: 60
Step-by-step explanation:
If x = small vehicles and if y = large vehicles and y = 50, then substitute and solve for x. So,
5x + 10(50) = 800
5x + 500 = 800
5x = 300
x = 60
So, the number of small vehicles is 60.
i've been stuck on this question for 3 days ;< halp meh ples
Calculate the average time for each vehicle.
What was the average time for the Big Car? Show your work.
What was the average time for the Small Car? Show your work.
Calculate the average speed for each vehicle. Use the average time for this calculation.
What was the average speed for the Big Car? Show your work.
What was the average speed for the Small Car? Show your work.
Answers
Answer:
1.
avg time = total time/ 3
for big car :-
= 4.46/ 3
= 1.48
for small car :-
= 5.14/ 3
= 1.71
2.
avg speed = total distance/ total time
for big car:-
= 2/ 4.46
= 0.45
for small car :-
= 2/ 5.14
= 0.4
A rhino can run 28 miles per hour. What is that speed in feet per second, to the nearest whole number?
Answers
Answer:
A rhino runs at a speed of about 28 miles per hour.
We need to determine the speed in feet per second.
Converting miles to feet:
The miles can be converted to feet by multiplying 5280 with 28 miles per hour.
Thus, we have;
28 x 5280 = 14784028 × 5280 = 147840
Thus, the speed of the rhino in feet per hour is 147840
Converting hours to seconds:
The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)
Thus, we get;
Speed=\frac{147840}{3600}Speed=
3600
147840
Speed = 41.066667Speed=41.066667
Rounding off to the nearest whole number, we get;
Speed = 41
Therefore, the speed of the rhino is 41 feet per second.
In the diagram, ABC is an equilateral triangle, BCFG is a square and CDEF is a rectangle. The perimeter of the whole diagram is 65cm, find the length of GE
Answers
Answer:
22 cm
Step-by-step explanation:
the perimeter = AB+BG+GF+FE+ED+DC+CA
= 65 cm
7+7+7+FE+7+DC+7=65 => FE = CD
35+ 2FE = 65
2FE = 65-35
= 30
FE = 30/2 = 15
so, GE = GF + FE
= 7+15 = 22 cm
you have some marbles. when you make a shape of an equilateral triangle, you either have 5 extra, or you need 10 more to complete the shape, how many marbles do you have? how long is one side of your triangle?
I'm giving brainliest to correct answer!
Answers
Answer:
110 marbles
side 14
Step-by-step explanation:
Draw triangles using marbles as the sides.
If the side is 2 marbles long, the triangle uses 3 marbles. 1 + 2 = 3
If the side is 3 marbles long, the triangle uses 6 marbles. 1 + 2 + 3 = 6
If the side is 4 marbles long, the triangle uses 10 marbles. 1 + 2 + 3 + 4 = 10
If the side is n marbles long, the triangle uses n(n + 1)/2 marbles.
These numbers are called triangular numbers.
We are looking for the side, n.
n(n + 1)/2 + 5 = (n + 1)(n + 2)/2 - 10
n^2 + n + 10 = n^2 + 3n + 2 - 20
n + 10 = 3n - 18
-n = -14
n = 14
For n = 14
n(n + 1)/2 =
= 14(15)/2
= 105
For n = 15
n(n + 1)/2 =
= 15(16)/2
= 120
105 + 5 = 120 - 10
You have 110 marbles. If you had 5 fewer, 105, you'd have a triangle with sides 14. If you had 10 more, 120, you'd have a triangle with sides 15. Since you have 110, you have 5 too many for side 14 and 10 too few for side 15.
The sides of the triangle is 14.
Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = 3721
Write the formula to calculate the height, h.
Answers
Answer:
V=1/3(pi)*r^2*h
Step-by-step explanation:
Think about a cylinder. If you combine 3 cones, you get a cylinder. Find the volume of a cylinder
Answer:
Step-by-step explanation:
V = 1/3 r^2 * π * h
3V = r^2 *π * h
3V/π = r^2 * h
h = 3V/(r^2 * π)
i need help.
A. 145
B. 35
C. 55
D. 75
Answers
Explanation:
Angles 4 and 8 are corresponding angles since they are both in the southwest corner of their respective 4 corner configuration.
Corresponding angles are congruent when we have parallel lines like this.
Set the expressions equal to each other and solve for x
angle 4 = angle 8
x+20 = 2x+5
x-2x = 5-20
-x = -15
x = 15
Use this x value to find the two angles to help confirm we have the correct x value, and to finish up to answer the question.
angle 4 = x+20 = 15+20 = 35angle 8 = 2x+5 = 2(15)+5 = 30+5 = 35So that's why the answer is B) 35 degrees
I need help ASAP !!!
Answers
Radius 5
Diameter 10
Area 25 π
Circumference 10 π
I need some help with this one. Please give it a go! Thank you for your time!
Answers
Answer:
A) [tex]3x^{2} - x - 4[/tex]
B) [tex]-3x^{2} -4x -5[/tex]
Step-by-step explanation:
Bella leans a 20-foot ladder against a wall so that it forms an angle of 76° with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.
Answers
Answer:
4.8 feet
Step-by-step explanation:
Use the cosine ratio, since we are given the length of the hypotenuse (the ladder) and are asked to find the horizontal distance between it and the ground.
Let x represent the horizontal distance (the adjacent leg)
cosine θ = adjacent / hypotenuse
cosine 76° = x / 20
(20)(cosine 76°) = x
4.8 = x
So, the horizontal distance is approximately 4.8 feet
Convert the following 4.5 hours Into Second- ( Soin 24
Answers
Answer: 16,200 Seconds
Step-by-step explanation:
Data: 4.5 hours(h)=x seconds(s)
Step One, Convert Hours Into Minutes
4.5h=4h and 30 minutes(m)
1h=60mx4=240m+30=270m
Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.
Step two, Convert Minutes Into Seconds
1m=60s
270mx60=16,200s
Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.
I hope this helps!
(-9g5+ 9) + (4g5- 5)
Answers
−9g5+9+4g5−5
−9g5+4g5+9−5
−5g5+9−5
Answer: −5g5+4
