It will take the ball 4.0625secs to stay in the air
The maximum height of the ball is 264.0625m
Given the function representing the height reached by the golf expressed as;
h(t) = -16t^2 + 130t
The velocity function is expressed as:
v(t) = -32t + 130
At maximum height, the velocity of the ball will be zero, i.e v(t) = 0
0 = -32t + 130
32t = 130
t = 130/32
t = 4.0625
Hence it will take the ball 4.0625secs to stay in the air
b) Substitute t = 4.0625 into the height function to have:
h(t) = -16t^2 + 130t
h(t) = -16(4.0625)^2 + 130(4.0625)
h(4.0625) = -264.0625 + 528.125
h(t) = 264.0625m
Hence the maximum height of the ball is 264.0625m
Learn more on velocity function here: https://brainly.com/question/10962624
Five tickets numbered 1, 2, 3, 4, and 5 are placed in a box, and three are selected at random. Determine the probability of obtaining a 1 or a 2 or both.
Answer:
the probability is 1 and 2
Tarik filled his tank with 11 gallons of
premium gasoline. He paid $38.76. How
much did Tarik pay per gallon?
The hypotenuse of a 30°-60°-90º triangle is 8 units and one leg is 4 units. What is the length of the other leg?
Answer:
The length of the other leg is [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
There are 2 ways to solve this.
1) Pythagorean theorem (the harder way)
A 30-60-90 triangle is a right triangle, and therefore you can use the pythagorean theorem to calculate the measure of 1 side given the 2 others.
[tex]a^2+b^2=c^2\\a^2+4^2=8^2\\a^2+16=64\\a^2=48\\a=\sqrt{48}\\a=6.9282...[/tex]
That's one solution, but its not a very nice number or the exact answer you probably want. Instead, you can simplify the root.
First, you need to factor 48:
[tex]2*24=48\\2*12=24\\2*6=12\\2*3=6[/tex]
The prime factors of 48 are:
[tex]2*2*2*2*3=48[/tex]
Then, you need to find perfect squares:
[tex](2*2)*(2*2)*3=48\\2^2*2^2*3=48[/tex]
And finally, you can remove those like this:
[tex]\sqrt{48} =\sqrt{2^2*2^2*3} \\\sqrt{48} =2\sqrt{2^2*3} \\\sqrt{48} =2*2\sqrt{3} \\\sqrt{48} =4\sqrt{3}[/tex]
The length of the other leg is [tex]4\sqrt{3}[/tex]
2) 30-60-90 triangle relationships (the easier way)
There are 4 simple rules here:
Short leg × 2 = hypotenuseShort leg × √3 = long legLong leg ÷ √3 = short legHypotenuse ÷ 2 = short legThey're actually pretty easy to remember. You can multiply the short leg by 2 or √3, and 2 is greater than √3 (check a calculator). The hypotenuse of course is also longer than the long leg, so you have to multiply by 2 to get it. Then for the long leg, the only option is to multiply by √3. The same works in reverse for both of those.
Here, we have the short leg. You can check that with the pythagorean theorem again to be sure:
[tex]a^2+4^2=8^2\\a^2+16=64[/tex]
Because 16 is less than half of 64, a has to be the longer leg. Using the rules above, multiply the short leg by √3 to get the answer:
[tex]4 * \sqrt{3} \\4\sqrt{3}[/tex]
Same answer as the previous method.
What is the expanded form of 14.702
Answer:
The expanded form for 14.702 is
fourteen and seven hundred two thousandths
What is sin 60°?
WA :)
an
2
90
30
5
A. I
оо
B.
-IS
o
C. 1
D.
O
E. 5
o
OF
PREVIOUS
Answer:
F
Step-by-step explanation:
If you look at that triangle and do trigonometry with sin, you would have to do opposite/hypotenuse. This would be (square root of 3)/2
The sum of two numbers is 17 and their product is 66 what are the two numbers.
Answer:
11 and 6
Step-by-step explanation:
Let the numbers be X and Y
Then their sum: X+Y=17 equation 1
Product: X×Y=66 equation 2
X+Y=17. X =17-Y
XY=66.
(17-Y)Y=66 -Y²+17Y-66=0
Y=6 or 11
X=17-Y. X=17–6=11 or X=17–11=6
Therefore you can conclude that the numbers are 11&6
Answer:
11 and 6
Step-by-step explanation:
x + y = 17
x × y = 66
First, solve for y
x + y = 17
x + y - x = 17 - x
y = 17 - x
Then substitute y to x × y = 66
x × y = 66
x(17 - x) = 66
17x - [tex]x^{2}[/tex] - 66 = 66 - 66
- [tex]x^{2}[/tex] + 17x - 66 = 0
(- [tex]x^{2}[/tex] + 17x - 66) = 0
(-x + 6)(x - 11) = 0
-x + 6 = 0
-x + x +6 = 0 + x
6 = x or x = 6
x - 11 = 0
x - 11 +11 = 0 + 11
x = 11
Then the numbers are 11 and 6
Trayvon enters a competition to guess how many balls are in a barrel.
Trayvon’s guess is 63 balls.
The actual number of balls is 60.
What is the percent error of Trayvon’s guess?
5% error
Step-by-step explanation:
% error = (estimation - actual value)/actual value * 100%
Trayvon's estimation is 63 and the actual value is 60, so our expression is:
(63 - 60)/60 * 100
63 - 60 = 3, so we get:
3/60 * 100
And 3/60 = 0.05, so now we have:
0.05 * 100 = 5
The percent error of Trayvon’s guess is 5%
What is the absolute error?"It is the absolute difference between an observed value and the actual value."
What is the relative error?"It is the ratio of the absolute error of the measurement to the actual value."
What is the percent error?"It is the relative error multiplied by 100."
For given example.
Trayvon’s guess is 63 balls.
[tex]V_o=63[/tex]
The actual number of balls is 60.
[tex]V_A=60[/tex]
The absolute error is,
[tex]\Rightarrow A=|V_o-V_A|\\\\\Rightarrow A=|63-60|\\\\\Rightarrow A=3[/tex]
The relative error is,
[tex]\Rightarrow R=\frac{A}{V_A} \\\\\Rightarrow R=\frac{3}{60}\\\\ \Rightarrow R=0.05[/tex]
The percent error is,
[tex]\Rightarrow P=R\times 100\\\\\Rightarrow P=0.05\times 100\\\\\Rightarrow P=5\%[/tex]
Therefore, the percent error of Trayvon’s guess is 5%
Learn more about the percent error here:
https://brainly.com/question/3670306
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URGENT, WILL GIVE BRAINLIEST!!
In △ABC, A=27∘, a=27 and c=24. Which of these statements best describes angle C?
C must be acute.
C must be obtuse.
C can be either acute or obtuse.
△ABC cannot be constructed.
Answer:
C must be acute, and ABC cannot be constructed
Step-by-step explanation:
24 degrees is under 90 degrees making angle c an acute angle.
ABC cannot be contructed because a triangle makes up of 180 degrees, and ABC does not make up 180 degrees.
Have a great day friend! :D
Answer:
C must be acute.
Step-by-step explanation:
The smaller the length of the side, the smaller is the angle opposite it, so C must be < 27.
How do you find the answer for 30=6x+20
Answer:
5/4Step-by-step explanation:
How do you find the answer for 30=6x+20?
solve for x30 = 6x + 20
10 = 6x
x = 10/6
semplify5/4
------------------ check
30 = 6 * 10/6 + 20
30 = 10 + 20
30 = 30
the answer is good
Marsha Hansen, the manager of the Flint Plant of the Michigan Company is responsible for all of the plant's costs except her own salary. There are two operating departments within the plant, Departments A and B. Each department has its own manager. There is also a maintenance department that provides services equally to the two operating departments. The following information is available. (on the picture) Departments managers are responsible for the wages and supplies in their department. They are not responsible for their own salary. Building rents, utilities, and maintenance are allocated to each department based on square footage. Required: Complete the responsibility accounting performance reports below that list costs controllable by the manager of Department A, the manager of Department B, and the manager of the Flint plant.
I will post the template too
Part 1:
Answer:
Hello
Step-by-step explanation:
If it takes you 2 1/2 hours to assemble one unit, how many units will you complete in 15 hours? (Change 2 1/2 to improper fraction first)
Answer:37.5
Step-by-step explanation:
2 1/2 as an improper fraction is 5/2
If i'm wrong tell me please i hope this helped you
If $20,000 is invested at 7% for 15 years, find the future value if the interest is compounded daily(365 days)
(2, 7); m = -3
(Write an equation in point-slope form of the line that passes through the given point and has the given slope)
Answer:
Step-by-step explanation:
y - 7 = -3(x - 2)
y - 7 = -3x + 6
y = -3x + 13
answerrrrrrrrrrrr plssssssssssssssssssssssssssssssss
Charlie saves $2 for every $9 he earns. Melody saves $4 for
every $12'she earns. Is Charlie's ratio of money saved to money
earned equivalent to Melody's ratio of money saved to money
earned?
no they are not equivalent
Step-by-step explanation:
due that when you subtract 12 from 4 =8
but when you subtract 9-2=7 and that when Charlie will be losing a dollar and that Melody will have a dollar more
2 paisa per 2 rupees per month
Answer:
2 paisa per rupees per month
So rate= 2%
Explain how you can write 4.1 as a/b
Answer:
ax + by
Step-by-step explanation:
i hope its correct
if its wrong then im sorry :)
Which of the following statements are correct?
Please help
Answer:
True A. angles one and five are corresponding angles.
True B. angles three and six are alternate interior angles.
False C. angles two and seven are alternate interior angles.
Angles two and seven are alternate exterior angles.
False D. angles five and eight are alternate exterior angles.
Angles five and Eight are verticle angles.
False E. angles two and four are same-sided consecutive angles.
Angles two and four are supplementary angles
True F. angles four and six are same side consecutive angles.
True G. angles one and eight are alternate exterior angles.
What is the sum of the two expressions? (3/7x+4)+(1/7x-2)
Combine the like terms:
3/7x + 1/7x = 4/7x
4 + -2 = 4-2 = 2
Answer: 4/7x + 2
what is the trend of the graph of the equation y = 3x + 10
Answer:
3x+y-10
Step-by-step explanation:
please Mark my answer in brainlist
HELP ME OUT PLEASE
Use the data to create a scatter plot.
Answer: i dont know if this will be correct but, the 2 goes on the bottom count 5 up so you will get the first one done, bottom 3 and count up 8, bottom 4 and count up to 13, its the same for all of them.
Step-by-step explanation:
5. What does the following addition equal?
3 and 7 eights + 6 and 5 eights
3 7/8 + 6 5/8 =
9 12/8 = 10 4/8
10 4/8 = 10 1/2
The answer is 10 1/2
If you are not looking for a mixed fraction it should be..
21/2
Use the graph to determine the
solution (solutions) of the equation
f(x) = 0.
Please help, with explanation
Answer:
-3, 1
Step-by-step explanation:
The vertical scale of the graph is f(x). So, f(x) = 0 is the x-axis. Where the graph crosses the x-axis, the value of f(x) is 0.
The x-axis is labeled on alternate lines. Those labels are sufficient to tell you that each grid line represents one unit. The curve intersects the x-axis 3 units to the left of the vertical axis, at x = -3, at 1 unit to the right of the vertical axis, at x = 1.
The values of x where f(x) = 0 are -3 and 1.
Find the slope of the line that passes through:
(6,7) and (4,2)
Answer:
5/2
Step-by-step explanation:
Slope = Change in y/Change in x
Slope = 2 - 7/4 - 6
Slope = -5/-2
Slope = 5/2
-Chetan K
Simplify the following expression
3x + 2(x +6) -4 -2x
A. 3x + 2
B. 7x + 8
C. 3x + 8
D.7x + 10
Answer:
C
Step-by-step explanation:
3x+2(x+6)-4-2x.
First, we do the parenthesis.
This gives us: 3x+2x+12-4-2x.
Then, we reorder so like terms are together.
This gives us: 3x+2x-2x+12-4.
Then, we combine like terms.
This gives us: 3x+8, which is C.
1) The temperature in Chicago is 42°F and the temperature in
Dayton is 19° cooler. What is the temperature in Dayton?
A. 25°F B. 61°F C. 23°F D. 58°F
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
[tex]\huge{\underline{\underline{\boxed{\sf{\purple{Answer}}}}}}[/tex]
Since column 3 of the given matrix consists of numbers which are all constant multiples of each other, there is a theorem which states that the determinant of this matrix is 0 .However, I will prove it from calculation just to verify and show how you would calculate such determinants should you not be aware of the theorems of linear matrix algebra.Use co-factor expansion along any row or column of your choice.This involves adding the products of the entries in each row with their co-factors[tex] { - 1}^({i + j} )[/tex]for an entry in row I and column j, multiplied by the minor of the entry, formed by evaluating the resulting determinant when you delete row I and column j.In this case, since the given matrix is 3x3 indimension, it will result in three 2×2 determinants which we can find from definition[tex] \binom{a \: b}{c \: d} [/tex] = ad-bc
I will take co-factor expansion along row 1 as an example to find the determinant of the given matrix as :
∆=[tex] 1( - 1) {}^{1 + 1} {} \binom{56}{8 \: 9} + 2( - 1) {}^{1 + 2} \binom{4 \: 6}{7 \: 9} + 3( - 1) {}^{1 + 3} \binom{4 \: 5}{7 \: 8} \\ = 1(45 - 48) +( - 2)(36 - 42) + 3(32 - 35) \\ = - 3 + 12 - 9 \\ = 0 [/tex]
Solve
-16 - 8
A. 24
B. 8
C. -8
D. -24
Answer:
D. 24
Step-by-step explanation:
This can be rewritten as
-16 + -8
This is equal to -24
Answer:
D= -24
Step-by-step explanation:
coz I used the table method so I also found it's correct
Given the system of equations presented here:
4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?
Multiply the first equation by −4 to get −16x − 4y = −16.
Multiply the second equation by −4 to get −8x − 24y = −96.
Multiply the first equation by −2 to get −8x − 2y = −8.
Multiply the second equation by −2 to get −4x − 12y = −48.
Answer:
yep its D
Step-by-step explanation:
Answer:
D Multiply the second equation by −2 to get −4x − 12y = −48.
Step-by-step explanation:
Answer:
Multiply the second equation by −2 to get −4x − 12y = −48.
Step-by-step explanation:
Given:
4x + y = 4 (1)
2x + 6y = 24 (2)
Multiply the second equation by −2 to get −4x − 12y = −48.
4x + y = 4 (1)
−4x − 12y = −48 (3)
Variable x can be eliminated by adding the equations
4x + (-4x) + y + (-12y) = 4 + (-48)
4x - 4x + y - 12y = 4 - 48
0 - 11y = -44
-11y = -44
Divide both sides by -11
y = -44/-11
= 4
y = 4
1. The method of substitution is likely the best method for which system?
−8x−2y=18x−2y=5
2x+y=103x+2y=5
5x−2y=32x+2y=1
−3x+2y=93x−5y=4
2. Solve the system of equations using the substitution method.
5x−4y=−15x−3y=−3
(3, 0)
(0, -4)
(-3, 0)
(0, -3)
Answer:
2.) x=−3 and y=0
Step-by-step explanation:
im still tryna figure out answer to number 1. sorry