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
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your
answers as radicals in simplest form.
Answers
Answer:
x = 10
y = 5
Step-by-step explanation:
Applying Trigonometry ratio
sin∅ = opposite/hypotenuse
cos∅ = Adjacent/hypotenuse
From the diagram,
sin60° = 5√3/x
make x the subject of the equation
x = 5√3/sin60°
But, sin60° = √3/2
x = 5√3/(√3/2)
x = (5√3)(2/√3)
x = 10.
Also, applying
cos60° = y/x
Where x = 10, cos60° = 1/2
y = xcos60°
y = 10(1/2)
y = 5
6.05kg, expressed in kilograms and grams
Answers
Answer:
6.05 kg, 6050 grams
Step-by-step explanation:
The kilograms were already given in your question, so that's one half done.
1 kilogram is equivalent to 1000 grams. If we multiply 6.05 by 1000, then you get 6050, the measurement in grams.
instruction Find m<LMN
Answers
Answer:
∠ LMN = 70°
Step-by-step explanation:
The tangent- secant angle LMN is half the difference of the measures of the intercepted arcs, that is
∠ LMN = [tex]\frac{1}{2}[/tex] (NK - NL) = [tex]\frac{1}{2}[/tex] (210 - 70)° = [tex]\frac{1}{2}[/tex] × 140° = 70°
In a cinema hall a total of 215 tickets were sold. Some were sold at $8 and others at $12. If the total amount collected was 2180, how many $8 tickets were sold
Answers
Answer: 100 tickets.
Step-by-step explanation:
Number of $8 tickets sold = xNumber of $12 tickets sold = ySet up two equations: one representing total amount sold and another representing total dollars earned.
[tex]\left \{ {{x+y=215} \atop {8x+12y=2180}} \right.[/tex]
Rearrange x + y = 215 and find the value of x:
[tex]x+y=215\\x=215-y[/tex]
Substitute it into the other equation and solve for y:
[tex]8x+12y=2180\\8(215-y)+12y=2180\\1720-8y+12y=2180\\4y=2180-1720\\4y=460\\y=\frac{460}{4} =115[/tex]
Substitute in the y-value to the other expression to find x:
[tex]x+y=215\\x+115=215\\x=215-115=100[/tex]
Therefore, they sold 100 of the $8 tickets.
(10^2+8^2+6^2+4^2+2^2)- (9^2+7^2+5^2+3^2+1^2)
Answers
55
you know you can just use a calculator or a search engine for that, right?
Answer:
i got 69 it should be right
Step-by-step explanation:
Fill in each box with the probability of the event that it represents. The following questions can be answered using your area model.
pleeeeaaseee help!!!!
Answers
Answer:
[tex]a. \ \dfrac{1}{36}[/tex]
[tex]b. \ \dfrac{4}{9}[/tex]
[tex]c. \ \dfrac{5}{6}[/tex]
Step-by-step explanation:
The given probabilities are; P(Orange) = 1/3, P(Blue) = 1/6, P(Purple) = 1/2
The probability of rolling any of the six numbers of the six-sided die = 1/6
a. The probability of simultaneously 'rolling a 3' and 'spinning blue', P(3 and Blue) is given as follows;
P(rolling a 3) = 1/6, P(Blue) = 1/6
∴ P(3 and Blue) = (1/6) × (1/6) = 1/36
P(3 and Blue) = 1/36
[tex]P(3 \ and \ Blue) = \dfrac{1}{36}[/tex]
b. The probability of either 'rolling a 1' or 'spinning Orange', P(1 or Orange), is given as follows;
P(rolling a 1) = 1/6, P(Orange) = 1/3
P(1 or Orange) = P(rolling a 1) + P(Orange) - P(1 and Orange)
Where;
P(1 and Orange) = (1/6) × (1/3) = 1/18
∴ P(1 or Orange) = 1/6 + 1/3 - 1/18 = 4/9
P(1 or Orange) = 4/9
[tex]P(1 \ or \ Orange) = \dfrac{4}{9}[/tex]
c. The probability of not spinning a blue, P(not Blue) is given as follows;
P(not Blue) = P(rolling all outcomes of the die) and (The sum of the spin probabilities - P(Blue)
∴ P(not Blue) = 1 × ((1/3 + 1/6 + 1/2) - 1/6) = 1 × (1 - 1/6) = 5/6
P(not Blue) = 5/6
[tex]P(not \ Blue) = \dfrac{5}{6}[/tex]
Analyze the problem and complete the statements.
t-7 = 8
I know this problem is an
because it has an equals sign.
The t is the
The negative sign is the
The 7 and the 8 are both
Answers
Answer:
I know this problem is an
✔ equation
because it has an equals sign.
The t is the
✔ variable
.
The negative sign is the
✔ operation
.
The 7 and the 8 are both
✔ constants
.
Step-by-step explanation: i took the test :( crying cuz im bouta fail
use determinants to find the area of the parallelogram shown below
Answers
Answer:
30
Step-by-step explanation:
To find the determinant of a parallelogram given points (a, b), (c, d), and (e, f), we can use
[tex]\left[\begin{array}{ccc}a&b&1\\c&d&1\\e&f&1\end{array}\right][/tex] and calculate the determinant of that. Three points on the parallelogram are (-1,1), (-1, -5), and (4, 5). Plugging these into the matrix, we get
[tex]\left[\begin{array}{ccc}-1&1&1\\-1&-5&1\\4&5&1\end{array}\right][/tex]. The determinant is equal to
[tex]-1 *det \left[\begin{array}{ccc}-5&1\\5&1\end{array}\right] \\- 1 * det \left[\begin{array}{ccc}-1&1\\4&1\end{array}\right] \\\\+ 1 * det \left[\begin{array}{ccc}-1&-5\\4&5\end{array}\right] \\= -1 * (-5*1 - (1*5))- 1 * (-1 * 1 - (4*1)) + 1 * (-1 * 5 - (-5*4)) \\= -1 *(-5-5) -1 * (-1 - 4) + 1 * (-5 - (-20))\\= -1 * (-10) -1 * (-5) +1 * (15)\\= 10 + 5 + 15\\=30[/tex]
Help help help help help
Answers
Answer: 0 and 4
Step-by-step explanation:
A shipping container is in the shape of a right rectangular prism with a length of 13 feet, a width of 9 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.61 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answers
Answer:
285pound
Step-by-step explanation:
Volume of the container = length * width * height
= 13 * 9 * 4
= 468 cubic feet
Weight of the contents in the container = 468 * 0.61 = 285.48 = 285pound
if the cost of 5 dozen of copies is rupees 60 what is the cost of 33 such copies
Answers
Answer: Rs 33
Step-by-step explanation:
Cost of 5 dozen copies = Rs 60
Total copies in 5 dozen = 5×12
= 60
Cost of each copy = 60/60
= Rs 1 per copy
Cost of 33 copies = 33×1
= Rs 33
Therefore cost of 33 such copies is Rs 33
please click thanks and mark brainliest if you like :)
= 12
So 12 rupees per copy
33x12 = 396 rupees
So the answer is 396 rupees
Write the expression 4^4(4^-7)(4) using a single
exponent.
4^-28
4^-4
4^-3
4^-2
Answers
Answer:
4^(-2)
Step-by-step explanation:
4^4(4^-7)(4)
We know that a^b * a^c = a^(b+c)
4^4(4^-7)(4^1)
4^(4+-7+1)
4^(-2)
HELPPP PYTHAGOREAN THEOREM
Answers
Answer:
60
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2+25^2 = 65^2
a^2 +625 = 4225
a^2 = 4225-625
a^2=3600
Taking the square root of each side
sqrt(a^2) = sqrt(3600)
a = 60
Answer:
Step-by-step explanation:
Hypotenuse: 65
Leg: 25
Let Hypotenuse be c, and leg be a
[tex]a^{2}[/tex] + [tex]b^{2} = c^{2}[/tex]
[tex]a^{2} + 25^{2} = 65^{2}[/tex]
[tex]a^{2} + 625 = 4225\\[/tex]
[tex]a^{2}[/tex] = 4225 - 625
[tex]a^{2}[/tex] = 3600
3600 is the exponential value of a, meaning we need to apply the opposite of squaring to get the value of b. Which is square rooting.
a = [tex]\sqrt{3600\\}[/tex]
a = 60
Therefore a is equal to 60 feet
The mean age of 5 women in an office is 35 years old.
The mean age of 5 men in an office is 24 years old.
What is the mean age (nearest year) of all the people in the office?
Answers
Answer:
29.5
Step-by-step explanation:
(5×35)+(5×24)/10
175+120/10
295/10
=29.5
52
Х
degrees
PLEASEHEHEH
Answers
Answer:
x = 142 degrees
Step-by-step explanation:
52 + 90 + x = 180
142 + x = 180
-142 -142
-------------------
x = 38
180 - 38 = 142
Hope this helped.
nick was scuba diving at -32 1/2 feet if he descends another 8 3/5 feet what is his location ?
Answers
Answer:
-41 1/10
Step-by-step explanation:
subtract the two numbers may i get brainliest plz
This is a really simple fraction problem. All we have to do is realize that, because he is descending, the [tex]8\frac{3}{5}[/tex] is actually negative, so we get [tex]-32\frac{1}{2}-8\frac{3}{5}=-41\frac{1}{10}[/tex] which can also equal -41.1
Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two
Answers
Answer:
The shortest side of the triangle is 18
Step-by-step explanation:
Let the sides the triangle be x, y and z.
From the question, the perimeter of the rectangle is 64, that is
x + y + z = 64 ...... (1)
Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)
The third side, z, is 20 less than the sum of the other two, that is
z + 20 = x + y ...... (3)
Substitute equation (3) into (1)
Then,
z + 20 + z = 64
2z +20 = 64
2z = 64 - 20
2z = 44
z = 44/2 k
z = 22
From equation (3)
z + 20 = x + y
Then, k
22 + 20 = x +y
42 = x + y
x = 42 - y ...... (4)
Substitute this into equation 2
3x = 4y
3(42-y) = 4y
126 - 3y = 4y
4y + 3y = 126
7y = 126
y = 126/7
y = 18
Substitute this into equation (4)
x = 42 - y
x = 42 - 18
x = 24
∴ x = 24, y = 18 and z = 22
Hence, the shortest side of the triangle is 18.
Solve for x.
x = [?]
5x – 16
X + 10
Answers
Answer:
If it is expression than answer 6x-6
If it is an equation 5x-16=x+10 than answer is 13/2
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
[tex]\\ \sf \longmapsto 5x-16=x+10[/tex]
[tex]\\ \sf \longmapsto 5x-x=10+16[/tex]
[tex]\\ \sf \longmapsto 4x=26[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{26}{4}[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{13}{2}[/tex]
find find x in the diagram with angle 56 degree
Answers
Please help, the question is in the picture
Answers
Answer:
per = 18a 7a+2a+7a+2a
area = 14 [tex]a^{2}[/tex] 7a*2a
Step-by-step explanation:
Answer:
(i) 18a
(ii) 14[tex]a^2[/tex]
Step-by-step explanation:
i: 7a+7a+2a+2a
14a+4a
18a
ii: 7a*2a
14a2
I hope this helps!
Find the volume of a cone with radius 10 feet and height of 4 feet.
Answers
Answer:
[tex]\frac{400}{3} \pi[/tex]
Step-by-step explanation:
Formula for Cone: π[tex]r^{2}\frac{h}{3}[/tex]
Since we have all the components, we can find the volume of the cone.
R = 10
H = 4
π[tex]10^{2}\frac{4}{3}[/tex]
10×10 = 100
100π[tex]}\frac{4}{3}[/tex]
[tex]}\frac{4}{3}[/tex]×100
4 100 400
--- × ----- = ------
3 1 3
Answer: [tex]\frac{400}{3} \pi[/tex]
Hope this helped.
Find the volume of a cone with radius 10 feet and height of 4 feet.
Solution :Given Data :
Radius = 10 feet
Height = 4 feet
Formulae :
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \blue{ \underline{ \overline{ \green{ \boxed{ \frak{{ \sf V}olume_{(Cone)} = \pi {r}^{2} \frac{h}{3}}}}}}}[/tex]
Putting the values we get
[tex] \frak{ Volume_{(Cone)} = 3.14 × (10)² × \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 3.14 × 100 × \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 314 \times \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 418.67 \: ft³ }[/tex]
Henceforth, the volume is 418.67 ft³
HELP ASAP!!!!!
thanksssssss
Answers
Answer:
[tex]9(c+5)=9c+45[/tex]
Step-by-step explanation:
Multiply 9 by the variable and the number
Whoever can answer this question gets 100 Points!!!!!!!
question: What is 2 + 2 - 1
Answers
Answer:
3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
-7x + 8, -12x + 12, -17x + 16, . . .
Possible anwers:
-5x + 4
5x + 4
-5x - 4
5x-4
Answers
Answer:
The first one is the answer.
Step-by-step explanation:
It's an arithmetic sequence. It has a common difference.
d = an - a_n-1
an = -12x + 12
a_n-1 = - 7x + 8
d = -12x + 12 - (-7x + 8)
d = -12x + 12 + 7x - 8
d = -5x + 4
Try it. Let's try for the third term
-12x + 12 - 5x + 4
- 17x + 15 which is exactly what the third term is.
Find the interior angle sum for the following polygon
Answers
Answer:
360/ 5 is the answer
Step-by-step explanation:
follow me and please follow me
A ,b,c or d? I need help pls help me
Answers
It depends a lot on where you live. But I would assume the answer is apples. I hope this helps you out and have a nice day! :)
A restaurant is ordering vegetables for the upcoming week. Potatoes are shipped in 30-pound bags and onions are shipped in 5-pound bags. If the restaurant receives 1,800 pounds of potatoes and onions and there are 25 more bags of potatoes than bags of onions, how many pounds of onions are received?
Answers
Answer:
525 pound of onions were recieved
Step-by-step explanation:
1 bag of potatoes: 30 pounds
total pounds of potatoes and onions received= 1800
let the total pounds of onions received be x,
25 bags of potatoes = 25 × 30= 750 pounds
now according to the question,
x + x + 750= 1800
2x = 1800 - 750
x= 1050 ÷ 2
x= 525
Note: plz correct me if I am wrong somewhere
The restaurant receives 150 pounds of onions.
How to determine pounds of onions receivedLet's assume the number of bags of onions is "x". According to the problem, there are 25 more bags of potatoes than bags of onions, which means the number of bags of potatoes is "x + 25".
The weight of each bag of potatoes is 30 pounds, so the total weight of potatoes is 30(x + 25) pounds.
The weight of each bag of onions is 5 pounds, so the total weight of onions is 5x pounds.
According to the problem, the restaurant receives 1,800 pounds of potatoes and onions in total. We can set up the following equation based on this information:
30(x + 25) + 5x = 1800
Simplifying the equation:
30x + 750 + 5x = 1800
35x + 750 = 1800
35x = 1800 - 750
35x = 1050
Dividing both sides by 35:
x = 1050 / 35
x = 30
Therefore, the restaurant receives 30 bags of onions.
To find the weight of onions, we can substitute the value of x into the expression for the weight of onions:
Weight of onions = 5x = 5 * 30 = 150 pounds
Therefore, the restaurant receives 150 pounds of onions.
Learn more about Weight at
https://brainly.com/question/86444
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A survey was taken of students in math classes to find out how many hours per day students spend
on social media. The survey results for the first., second-, and third-period classes are as follows:
First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0
Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3
Which is the best measure of center for second period and why? (5 points)
1. Mean, because there are no outliers that affect the center
2. Median, because there is 1 outlier that affects the center
3. Interquartile range, because there is 1 outlier that affects the center
4. Standard deviation, because there are no outliers that affect the center
Answers
Answer:
1. Mean, because there are no outliers that affect the center
Step-by-step explanation:
Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
The mean = ΣX / n
n = sample size, n = 15
Mean = 34 / 15 = 2.666
The median = 1/2(n+1)th term.
1/2(16)th term = 8th term.
The 8th term = 2
The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.
Both interquartile range and standard deviation are measures of spread and not measures of centre.
Solve for x. Round all answers to the nearest tenth.
Answers
Answer:
4.6
Step-by-step explanation:
tan(75) = 17/x
x = 17/tan(75)
x = 34-17√3
x = 4.6
Answered by GAUTHMATH
Rhonda walked diagonally across a rectangular playground with dimensions 60 m by 45 m. She started at point C. Determine the angle, to the
nearest degree, between her path and the longest side of the playground.
B
45m
D
60 m
Answers
Answer:
37degrees
Step-by-step explanation:
In order to get the required angle, we will use the SOH, CAH, TOA identity.
Let;
Adjacent = 60m
Opposite = 45m
According to TOA:
tan theta = opp/adj
tan theta = 45/60
tan theta = 0.75
theta = arctan 0.75
theta = 36.86
Hence the angle, to the nearest degree, between her path and the longest side of the playground is 37degrees
