Answers
Answer:
[tex]h(t)=-6(t-2)^2+24[/tex]
Step-by-step explanation:
Given function:
[tex]h(t)=-6t^2+24t[/tex]
where:
h = height (in feet)t = times (in seconds)Rewrite in the form [tex]h(t)=a(t-h)^2+k[/tex]
The quickest way to do this is to expand [tex]h(t)=a(t-h)^2+k[/tex] and compare coefficients with the original function.
[tex]\begin{aligned}h(t)& =a(t-h)^2+k\\ & = at^2-2aht+ah^2+k\end{aligned}[/tex]
Comparing coefficients with [tex]h(t)=-6t^2+24t[/tex]
[tex]\begin{aligned}\implies at^2& =-6t^2\\ a &=-6\end{aligned}[/tex]
[tex]\begin{aligned}\implies -2aht & =24t\\ -2(-6)ht& =24t\\ 12ht & = 24t\\ 12h & = 24\\ h & = 2\end{aligned}[/tex]
[tex]\begin{aligned}\implies ah^2+k & = 0\\(-6)(2)^2+k &=0\\ -24+k & =0\\ k &=24 \end{aligned}[/tex]
Therefore, substituting the found values into the equation:
[tex]h(t)=-6(t-2)^2+24[/tex]
Related Questions
Helen bought 5 pounds of oranges. She sliced
2 pounds of oranges to bring to a party. How
many pounds of oranges does Helen have left?
Answers
Answer:
3 oranges
Step-by-step explanation:
Helen has 5 pounds of oranges
2 pounds of oranges are brought to a party, so they are gone
5-2 = 3
Helen will only have 3 oranges left.
If x^2 - 6xy = z - 9y^2, make x the subject of the formula
Answers
[tex]~~~~x^2-6xy=z-9y^2\\\\\implies x^2- 2\cdot x\cdot 3y + (3y)^2 - (3y)^2 = z-9y^2\\ \\\implies (x-3y)^2 -9y^2 = z-9y^2\\\\\implies (x-3y)^2 = z\\\\\implies x - 3y =\pm\sqrt z\\\\\implies x = 3y\pm\sqrt z[/tex]
Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005. The table gives the number of tickets sold for each
concert. Select the points that represent this data.
Year
Tickets Sold
(thousands)
10
2000
2001
10
2002
20
2003
40
2004
55
2005
70
90
80
70
(so
Answers
The points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on graph.
How to read the data from the table?Table is a way to represent the data of the two or more variable. To read the data from the table, look for the value of one variable, and get the resultant value of other variable from the corresponding block.
Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005.
The table gives the number of tickets sold for each concert. Select the points that represent this data.
Tickets Sold (thousands) Year 10 200010 200120 200240 200355 200470 2005The graph which represent the data in the data is attached below year wise.
For the first point, select the value 10 on graph vertically at year 2000. Similarly, select all the points on the graph for the table.
Thus, the points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on the graph.
Learn more about the data table here;
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please help ??????????
Answers
5•2/3
[tex]\bold{EXPLANATIONS:}[/tex]
Rationalise the denominator of 5/√(3-√5)
Pls send the answer by today
Answers
Answer:
[tex]\dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]
[tex]\textsf{or}\quad \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]
Step-by-step explanation:
[tex]\textsf{Given expression}:\dfrac{5}{\sqrt{3-\sqrt{5}}}[/tex]
Method 1
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}:[/tex]
[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}=\dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}[/tex]
Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{a} =a[/tex]:
[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})=3-\sqrt{5}[/tex]
Therefore:
[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}= \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}}[/tex]
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{3+\sqrt{5}}{3+\sqrt{5}}:[/tex]
[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}} \times \dfrac{3+\sqrt{5}}{3+\sqrt{5}}=\dfrac{5\sqrt{3-\sqrt{5}}(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}[/tex]
Simplify the denominator:
[tex]\implies (3-\sqrt{5})(3+\sqrt{5})=9+3\sqrt{5}-3\sqrt{5}-5=4[/tex]
Therefore:
[tex]\implies \dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]
Method 2
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}:[/tex]
[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}=\dfrac{5\sqrt{3+\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})}[/tex]
Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{b} =\sqrt{ab}[/tex]:
[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})=\sqrt{(3-\sqrt{5})(3+\sqrt{5})[/tex]
[tex]\implies\sqrt{(3-\sqrt{5})(3+\sqrt{5})}=\sqrt{9-5}=\sqrt{4}=2[/tex]
Therefore:
[tex]\implies \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]
[tex]\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}[/tex]
To rationalise:-
[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } [/tex]
There is a formula in math if there is root in denominator
for example
[tex] \frac{1}{ \sqrt{a - b} } [/tex]
we can say rationalize by multiplying √(a-b) in numerator and denominator both
[tex] \frac{1}{ \sqrt{a - b} } \times \frac{ \sqrt{a - b} }{ \sqrt{a - b} } \\ \frac{ \sqrt{a - b} }{a - b} [/tex]
In here
[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } \times \frac{ \sqrt{3 - \sqrt{5} } }{ \sqrt{3 - { \sqrt{5} } } } \\ \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } [/tex]
but still here is root to remove this we have to multiply
3 + √5 in numerator and denominator.
[tex] \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5} ) }{ {3}^{2} - { (\sqrt{5} )}^{2} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5}) }{9 - 5} \\ \frac{5( \sqrt{3 - \sqrt{5} } )(3 + \sqrt{5}) }{4} [/tex]
Jill Barley obtained a 25-year, $145,117 mortgage loan from University Savings and Loan Association. The
interest rate is 6 percent. The monthly payment is $1,800.00. For the first payment, what is he interest?
Answers
Answer:
175,424.02
Step-by-step explanation:
multiply 145,117 by 106%
multiply 1800 by 12 (months in a year)
add 21600 to 153,824.02
can someone please help me with this!!!!
Answers
PLEASE HELP! WILL GIVE BRAINLIEST
Answers
Answer:
See below ~
Step-by-step explanation:
The equation which represents 1/12 :
1 ÷ 12 = ___The division equation which represents 1/14 :
1 ÷ 14 = ___Answer:
Question 3:
C) 1 divided by 12 _
Question 4:
A) 1 divided by 14 _
please help fast I dont know the answer
Answers
hope this helps
SOMEONE PLEASE HELP ME WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER
IMAGE BELOW
Answers
Answer:
[tex]\sqrt{51[/tex]
Step-by-step explanation:
6^2 + 8^2 = y^2 (Pythag)
100 = y^2
10 = y
7^2 + x^2= 10^2
49+ x^2 = 10^2
x^2 = 51
A cone has a base with a diameter of
12 inches and a height of 15 inches. What
is the volume of the cone in
cubic inches
using 3.14 for 77?
Answers
Answer:
452.16 in^3
Step-by-step explanation:
Volume of a cone = 1/3 pi r^2 h
= 1/3 (3.14)(6^2) (12)
Evita is solving the system of equations shown using the elimination method. first equation: 3x+8y=20 second equation: 5x−2y=4 what operation will eliminate one of the variables?
a. multiply the first equation by 2
b. multiply the first equation by 4
c and multiply the second equation by 2
d. multiply the second equation by 4
Answers
Answer:
d. multiply the second equation by 4
What is the slope of a trend line that passes through the points (5, 80) and (7, 65)?
a.) -15/2
b.) -2/15
c.) 2/15
d.) 15/2
Answers
Answer:
65 - 80 = -15
7 - 5 = 2
which is -15/2
which is A
In the context of the least squares procedure, any data point that does not fall on the regression line is the result of
Answers
In the context of the least squares procedure, any data point that does not fall on the regression line is the result of multicollinearity.
What is least square regression?A least square regression simply shows the linear relationship that exist between two variables.
Here, in the context of the least squares procedure, any data point that does not fall on the regression line is the result of multicollinearity.
Learn more about least sqaure on:
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A man invests $8 000 at 12% simple interest for 3 years. If he invests the same amount of money for the same time period at 12% compound interest, what is the difference between the two investments?
Answers
Answer:
$359.42
Step-by-step explanation:
The difference in the investment values can be computed by making use of the formulas for the account balance in each case.
compound interest: A = P(1 +r)^t . . . . interest at rate r compounded annually
simple interst: A = P(1 +rt) . . . . simple interest at rate r
__
The account earning simple interest will have a balance of ...
A = $8000(1 +0.12×3) = $10,880
The account earning compound interest will have a balance of ...
A = $8000(1 +0.12)^3 ≈ $11,239.42
The difference between the two investments is ...
$11,239.42 -10,880 = $359.42
:)
Mariam sells tires for $90 each and a service plan for $50. One customer
pays $410 for some tires and the service plan. Which equation represents
how many tires, t, the customer purchased?
A 410 = 50 + 90t
B 410 = 90 + 50t
© 410 = 50t + 90
D 410 = 90(4t) + 50
Answers
Answer:
the answer is A
Step-by-step explanation:
410 is the total amount paid
so 50 dollars was a base fee for the service charge
and 90 was per tire. Because we dont know how many tires she bought 90 x number of tires(t) = 90t
so 410 dollars = 50 dollars(service fee) + 90 dollars ( multilied by number of tires "t")
PLEASE HELP ASAP!!!! WILL GIVE BRAINIEST TO BEST ANSWER!
Answers
Answer:
63√6 cm
Explanation:
Perimeter is the total measure of all sides.
Solve:
15√6 + 12√54 + 6√24
factorize
15√6 + 12√6(9) + 6√6(4)
apply radical rule: √ab = √a √b
15√6 + 12√6 √9 + 6√6 √4
simplify
15√6 + 12(3)√6 + 6(2)√6
multiply
15√6 + 36√6 + 12√6
add similar terms
63√6
Answer:
63√6 cmStep-by-step explanation:
Perimeter : Sum of the sides
15√6 cm is already in simplest form6√24 = 6√(4 × 6) = 6 x 2 x √6 = 12√6 cm12√54 = 12√(9 x 6) = 12 x 3 x √6 = 36√6 cmPerimeter
15√6 + 12√6 + 36√627√6 + 36√663√6 cmCan someone help me with this problem?
Answers
Answer:
yes
Step-by-step explanation:
4:8 and 3:6 when simplified gives the same result which is 1:2
Answer:
A.) Yes, they do catch fish at the same rate.
Daniel:
4 : 8
Lester:
3 : 6
Both of these ratios have a rate of 1 catfish for every 2 trout. Daniel has just caught 1 more catfish and 2 more trout.
4 - 1 = 3
8 - 2 = 6
Both have a rate of catching 1 catfish for every 2 trout.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
if a type of salami at the deli costs 1.59 per 100 g how much will you pay for 350 g? pls help and explain how to do it
Answers
Answer:
[tex]\huge\boxed{\sf 350\ g\ salami = 5.565}[/tex]
Step-by-step explanation:
From the question:
100 g salami = 1.59
Divide 100 to both sides
1 g salami = 1.59/100
1 g salami = 0.0159
Multiply both sides by 350
350 g salami = 0.0159 × 350
350 g salami = 5.565
[tex]\rule[225]{225}{2}[/tex]
Pls help I’m in a rush (find the pattern)
Answers
se va sumando de 5 en 5
Answer:
y=x+12, add 12
Step-by-step explanation:
To get from each x to y you have to add 12
so the equation is:
y=x+12
A committee of four is chosen at random from a group of 8 women and 5 men. Find the probability that the committee contains at least one man. Answer:
Answers
Explanation:
Using the key word ‘probability’, eliminate the usage of permutation and combination formula.
Probability = favorable/total
total = 8 women + 5 men
= 13 people
favorable = 5 men
P(1 man) = 5/13
What is 800divided by the a times the 9 3 times?
Answers
Answer:
21600/a
Step-by-step explanation:
800/a *9
7200/a
21600/a
First, times 800 divided by a by 9.
Then, we get 7200/a.
Lastly, times it by 3.
The answer is 21600/a
Sussy mcsuser
Poop noobs
What is the square root of 144?
Answers
Answer:
12
Step-by-step explanation:
When you multiply 12 by itself its 144.
I hope it helps! Have a great day!
pan~
Answer:
12
Step-by-step explanation:
Divide 144 by 2 and it’s 12.
Or you could guess and check b dividing each number by itself until you get 144.
I hope it helps! Have a great day!
Muffin °-°
Which function is modeled in this table
X
f(x)
1
1000
2
800
3
640
4
512
Answers
Answer:
[tex]f(x)=1250*(\frac{4}{5})^x[/tex]
Step-by-step explanation:
Calculate the perimeter of the shape below. Show ur work! TYSM!!
Answers
Answer:
1,001
Step-by-step explanation:
13ft X 11ft X 7ft = 1,001
Not sure if its correct but im glad to help atleast
Answer:
68 is the perimeter.
Step-by-step explanation:
You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.
Which is the equation in slope-intercept form for the line that passes through (−1, 5) and is parallel to 3x + 2y = 4? y=−32x+72 y=23x+72 y=−23x+72 y=32x−72
Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?
y=32x+18
y=32x−12
y=23x+18
y=−32x+18
Which best describes the relationship between the lines?
2x – y = −1
4x – 2y = 6
parallel
same line
neither
perpendicular
Answers
1. The equation in slope-intercept form is: y = -3/2x + 7/2
2. y = -3/2x - 18
3. Both lines have the same slope, they are therefore parallel.
What is the Equation in Slope-intercept Form for Parallel Lines?Two lines that are parallel will have the same slope (m), and is represented by the equation in slope-intercept form as, y = mx + b.
1. Rewrite 3x + 2y = 4 in slope-intercept form:
2y = -3x + 4
y = -3x/2 + 4/2
y = -3/2x + 2
The slope is -3/2. Therefore, the slope (m) of the line that passes through (-1, 5) would be -3/2.
Substitute m = -3/2, and (a, b) = (-1, 5) into y - b = m(x - a):
y - 5 = -3/2(x - (-1))
y - 5 = -3/2(x + 1)
Rewrite in slope-intercept form:
2(y - 5) = -3(x + 1)
2y - 10 = -3x - 3
2y = -3x - 3 + 10
2y = -3x + 7
y = -3x/2 + 7/2
y = -3/2x + 7/2
2. The slopes of perpendicular lines are negative reciprocal to each other.
Rewrite 2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
The slope of the ine that passes (-2, 15) would be -3/2.
Substitute (a, b) = (-2, 15), and m = -3/2 into y - b = m(x - a):
y - 15 = -3/2(x - (-2))
y - 15 = -3/2x - 3
y = -3/2x - 3 - 15
y = -3/2x - 18
Therefore, the equation in slope-intercept form of the line that passes through (-2, 15) is: y = -3/2x - 18.
3. Given the equations, 2x – y = −1 and 4x – 2y = 6:
Rewrite in slope-intercept form and find their slope
2x - y = -1
-y = -2x - 1
y = 2x + 1 (slope if 2)
4x - 2y = 6
-2y = -4x + 6
y = -4x/-2 + 6/-2
y = 2x - 3 (slope is 2)
Both lines are therefore, parallel.
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10. Which of the following could be the perimeters of the three squares below?
A. 12 11 10 ft and 20 ft
B. 20 ft, 16 f1 and 24 ft
C. Both A and B
D. Neither A or B
Answers
Answer:
A, 12ft, 16ft, 20ft.
Step-by-step explanation:
3,4,5 Triangles are right triangles, Answer A on the Paper says 12:16:20 which is proportinate to said ratio, hence the answer is A
the Paper says 12:16:20 which is proportinate
to said ratio, hence the answer is A
last year the hiking club had 19 members. this year there are 37 members in the club. estimate the percetnage change in the number of club members
Answers
I hope that answers your question
nearest whole number of
3÷80.81
Answers
Answer:
0.04
Step-by-step explanation:
3÷80.81= 0.037
to the nearest whole number = 0.04
6 1/2 + 5 7/8 what is the answer?
Answers
Answer:
12 3/8
Step-by-step explanation:
6 1/2 + 5 7/8 =
= 6 4/8 + 5 7/8
= 11 11/8
= 11 + 8/8 + 3/8
= 11 + 1 + 3/8
= 12 3/8