Answer:
9
Step-by-step explanation:
Add all numbers together: 36
divide by the amount of numbers in the list: 9
:)
An archer releases an arrow with an initial velocity of 20 feet per second at a height of 12 feet. The path the arrow takes can be modeled using the function f(x)=−16x^2+20x+12, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. What is the maximum height, in feet, reached by the arrow? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.
Answer:
18.25 feetStep-by-step explanation:
The given function is quadratic.
The maximum of the quadratic function is its vertex.
The x-coordinate is determined by x = - b/(2a)
x = - 20/(-16*2) = 5/8Apply the x-value and find the value of f:
f(x) = - 16(5/8)² + 20(5/8) + 12 = 18.25 feetAnswer:
18.25
Step-by-step explanation:
we are given a quadratic function
[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]
where:
f(x) represents the heightx represents the timeTo find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.
Differentiate both sides:
[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]
with sum differentiation rule, we acquire:
[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]
recall that,
differentiation of a constant is equal to 0[tex] \dfrac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]utilizing the rules we acquire:
[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]
now equate f'(x) to 0:
[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]
solving the equation for x yields:
[tex]x _{max}= \dfrac{5}{8} [/tex]
plug in the maximum value of x into the quadratic function:
[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]
simplify:
[tex]f(x )_{max} = 18.25[/tex]
hence,
The maximum height reached by the arrow is 18.25 feet
how to set up definite integral
Answer:
Step-by-step explanation:
First, determine where the quantity inside the absolute value bars is negative and where it is positive for example, So that's 6 times 8 minus 6 times negative 1. Okay and so this will be 48. Minus negative 6 which is 48 plus 6 which is 54 which is the answer.
please answer the following mcqs with proper explanation
Answer:
(iv) b
(v) c
(vi) d
Step-by-step explanation:
The first two questions have to with understanding the meaning of the English words. (It's reading comprehension.)
__
(iv) "no larger than 10" means "less than or equal to 10"
(b) x ≤ 10
__
(v) "at most 1600" means "less than or equal to 1600"
(c) c ≤ 1600
__
(vi) A value of x will be a solution to the inequality if substituting it into the inequality results in a true statement. Here, using x=0 effectively eliminates the x-term from the inequality.
(a) 0 > 0 . . . false
(b) 5 < 0 . . . false
(c) 2 < 0 . . . false
(d) -2 < 0 . . . true
Click on the numbers that fit the description.
(Choose 4)
Answer:
6231
Step-by-step explanation:
Answer:
6,2,30,8 is the common factor of 18 and 30
what is the percentage of this
Answer:
69%
Step-by-step explanation:
10×10 table, 69 cells are orange. Therefore the fraction 69/100 as a percentage is 69%.
write a quadratic function f whose only zero is 11
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here's the solution ~
To write a quadrilatic function, we have to use its roots, like we have to subtract the roots from x and multiply them ~ then we will get our required function !
Since our only root is 11 here, we have to do t double
[tex]\qquad \sf \dashrightarrow \:(x - 11)(x - 11)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 11x - 11x + 121 [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 22x + 121[/tex]
That's our required function ~ I hope you understood the whole thing !
It takes 7 hours and 12 minutes to fly
from Singapore to Tokyo, Japan. You have
to arrive at the airport 45 minutes before
departure. It is a 17 minute taxi ride from
your hotel. By what time would you need
to leave the hotel if the flight lands
at 3:23 p.m.?
The time I would need to leave the hotel if the flight lands at 3:23 p.m is 7 : 09 am
What time should I leave the hotel?The first step is to add the total hours of the flight to the time of the tax ride and the time you need to get to the airport.
7h + 12 min + 45 + 17 = 8 hours 14 minutes
Now subtact 8 hours 14 minutes form 3: 23
(12 + 3:23) - 8 hours 14 minutes =7 : 09 am
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Translate this phrase into an algebraic expression. 73 less than twice Jose's height Use the variable to represent Jose's height.
Answer:
x-73
Step-by-step explanation:
Let x=Jose's height. If it says "less than," then that is subtraction. Since Jose's height is not defined, there is no specific number that can be used to describe "73 less than twice Jose's height," so I use the variable x, and then subtract 73.
The equation w = 20n models the total weight of honey, w, in
pounds that a beekeeper expects to collect from n hives.
a. Graph the relationship modeled by the equation. Include a
title on each axis.
b. How does the graph show the expected rate of pounds of
honey per hive? How is this rate related to the equation?
The graph of the weight function w = 20n is an illustration of linear equations
The expected weight of honey per hive is 20 pounds
The graph of the modelThe equation of the model is given as:
w = 20n
To plot the graph, we use the following representations
n is plotted on the horizontal axisw is plotted on the vertical axisSee attachment for the graph of w = 20n
Interpret the graphThe graph shows that:
As the number of hives increases, the weight of honey increasesThe expected weight of honey per hive is 20 poundsRead more about linear equations at:
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Write the equation in standard form for the circle with center (0, -3) passing through (15/2 , 1)
Check the picture below, so the green line is really the radius of the circle, and we know its center.
[tex]~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad(\stackrel{x_2}{\frac{15}{2}}~,~\stackrel{y_2}{1})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[\frac{15}{2} - 0]^2 + [1 - (-3)]^2}\implies r=\sqrt{\left( \frac{15}{2} \right)^2 + (1+3)^2}\\\\\\r=\sqrt{\left( \frac{15}{2} \right)^2 +4^2}\implies r=\sqrt{\frac{225}{4} + 16}\implies r=\sqrt{\cfrac{289}{4}}\implies r=\cfrac{17}{2}\\\\[-0.35em]\rule{34em}{0.25pt}[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\frac{17}{2}}{ r} \\\\\\\ [x-0]^2~~ + ~~[y-(-3)]^2~~ = ~~\left( \cfrac{17}{2} \right)^2\implies x^2+(y+3)^2 = \cfrac{289}{4}[/tex]
math again. marking as brainliest
Answer:
d po
Step-by-step explanation:
sna maka tulong hheeheh
Our school’s girls volleyball team has 14 players, including a set of
3 triplets: Alicia, Amanda, and Anna. In how many ways can we
choose 6 starters if at most one of the triplets is in the starting lineup? There can't be 2 or more triplets and there can be none.
Answer:
[tex]1,\!848[/tex].
Step-by-step explanation:
There are two disjoint sets of ways to choose a lineup as required:
Include none of Alicia, Amanda, or Anna, orInclude exactly one of Alicia, Amanda, and Anna.Assume that none of Alicia, Amanda, or Anna is to be selected. This lineup of [tex]6[/tex] would then need to be selected from a set of [tex]14 - 3 = 11[/tex] players (which excludes Alicia, Amanda, and Anna.)
The number of ways of selecting (without order) [tex]6[/tex] items out of a set of [tex]11[/tex] (distinct) items is equal to the combination:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 6\end{pmatrix} &= \frac{11!}{(6!)\, (11 - 6)!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].
Assume that Alicia is selected, but neither Amanda nor Anna is selected. The other [tex]6 - 1 = 5[/tex] players in this lineup would then need to be selected from a set of [tex]14 - 1 - 2 = 11[/tex] players. (This set of [tex]11[/tex] excludes Alicia, Amanda, and Anna.)
The number of ways to select [tex]5[/tex] items from a set of [tex]11[/tex] items is:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 5\end{pmatrix} &= \frac{11!}{(5!)\, (11 - 5)!} \\ &= \frac{11!}{5! \times 6!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].
Similarly, there would be another set of [tex](11!) / (6! \times 5!)[/tex] distinct ways to select the lineup if Amanda is selected, but neither Alicia nor Anna is.
Likewise, the number of ways to select the lineup with Anna but neither Amanda nor Alicia would also be [tex](11!) / (6! \times 5!)[/tex].
These sets of configurations for the lineup are pairwise disjoint from one another. Thus, the total number of ways to select this lineup would be:
[tex]\begin{aligned}& \begin{pmatrix}11 \\ 6 \end{pmatrix} + 3 \times \begin{pmatrix}11 \\ 5 \end{pmatrix} \\ =\; & \frac{11!}{6! \times 5!} + 3 \times \frac{11!}{6! \times 5!} \\ =\; & \frac{4 \times 11!}{6! \times 5!} \\ =\; & \frac{4 \times 11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2} \\ =\; & \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 3 \times 2} \\ =\; & 1,\!848\end{aligned}[/tex].
wait hihfedhsdkfsffsdf
Cassie wants to buy carpet to cover her whole living room, except for the tiled floor. The tiled floor is 4
5
6
ft by 2
1
3
ft. Find the area the carpet needs to cover.
Answer:
1456
Step-by-step explanation:
56x2x13
56x26
1456
Find the area. Do you multiply all sides?
Answer:
The area of the Trapezoid is :
h(a+b)/2
3(2+6.2)/2
3(8.2)/2
24.6/2
12.3 m²
Answer:
Step-by-step explanation:
I think you are to assume that this is a trapezoid and that the top right angle symbol is missing.
Area = (b1 + b2 ) * h /2
Givens
b1 = 2
b2 = 6.2
h = 3
Solution
Area = (2 + 6.2)* 3 / 2 Combine what is inside the brackets
Area = 8.2 * 3 / 2 Divide by 2
Area = 4.1 * 3 Combine
Answer: Area = 12.3
A second-degree polynomial is a quadratic polynomial. O A. True O B. False
Answer:
True
Step-by-step explanation:
In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree
Answer:
Step-by-step explanation:
the answer isis truetrue
The area of Sharon's garden is 40
sq ft. List all the possible lengths
and widths of Sharon's garden.
Answer:
1 and 40
2 and 20
4 and 10
5 and 8
Step-by-step explanation:
need to know the factors of 40
factors of are 1, 2, 4, 5, 8, 10, 20 and 40
possible lengths and widths would be
1 and 40
2 and 20
4 and 10
5 and 8
What is the Area of this shape?
Answer:
448 ft ^2
Step-by-step explanation:
[tex]A = \frac{b_{1} + b_{2}}{2} * h\\A = \frac{17 + 39}{2} * 16\\A = \frac{56}{2} * 16\\\\A = 28 * 16\\\\A = 448 ft^{2}[/tex]
Hope this helps,
If best, mark brainliest, if not, hope it helps anyway.
Help picture below problem 10
Answer:
180-52=128
Do mark BRAINLIEST
An angle that measures exactly 180° is known as a/an _____ angle
Answer:
An angle that measures exactly 180° is known as a straight angle
Step-by-step explanation:
A straight angle is basically just a line. It is equal to two right angles (which are 90 degrees) and it is also half of a circle.
I hope this was helpful! If you need any more information on straight angles or any other angles, let me know! Have a lovely day! :)
List the following fractions from least to greatest 1/6 2/3 1/2 1/3
Answer:
1/6 < 1/3 < 1/2 < 2/3
Step-by-step explanation:
We can turn the following to decimal;
1/6 = 0.16666666666
2/3 = 0.66666666666
1/2 = 0.5
1/3 = 0.33333333333
0.16666666666 < 0.33333333333 < 0.5 < 0.66666666666
Thus, from least to greatest is 1/6 < 1/3 < 1/2 < 2/3
~Learn with Lenvy~
A manufacturer created the table below as part of a program aimed to reduce manufacturing costs. The table compares the cost y to the number of hats sold, x. which of the following statements below are supported by the data? select all that apply.
1. The slope is positive.
2. the slope is negative.
3. every additional hat produced results in a cost increase of $.60
4. every additional hat produced results in a cost increase of $6.00
5. before producing any hats, the manufacturing costs are $100.00
6. the cost of producing 75 hats is approximately $136.00
Using linear function concepts, it is found that the correct statements are given by:
1. The slope is positive.
3. every additional hat produced results in a cost increase of $.60.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem:
When the amount increases by 10, the cost increases by $6, hence the slope is of m = 6/10 = 0.6.The y-intercept is the amount of producing 0 hats, which is of b = 105 - 6 = 99.Hence statements 1 and 3 are correct.
More can be learned about linear function concepts at https://brainly.com/question/24808124
Answer:
A. The slope is positive.
C. every additional hat produced results in a cost increase of $.60.Step-by-step explanation:
E. Before producing any hats, the manufacturing costs are about $100.00.
Find the value of X. Round your answer to the nearest tenth please
The value of x from the figure is 17.82 units
SOH CAH TOA identity1) From the first figure.
Opposite side = x
Adjacent = 12
Using the SOH CAH TOA identity
tan53 = opp/adj
tan53 = x/12
x = 12tan53
x = 15.92 units
2) Using the SOH CAH TOA identity
cos27 = adj/hyp
cos27 = x/20
x = 20cos27
x = 17.82units
Hence the value of x from the figure is 17.82 units
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if g = 6x-9 and x = 15 what is g
Answer:
g= 81
Step-by-step explanation:
Replace X with 15
g = 6x -9
g = 6(15) - 9
g = 90 - 9
g = 81
Step-by-step explanation:
g=6x-9
putting the value of x
g=6×15-9
g=81
simplificar la radicacion 18
Answer:
441
Step-by-step explanation:
Find the unit price. 14 ounces of canned corn for $1.96
The unit price of canned corn is $0.14
14 ounces = $1.96
1 ounce = 1.96 / 14
= 0.14
A survey of 2,00 registered voters is used to predict by how many percentage points a candidate is leading. Of the 2,00 people, 1,240 planned to vote for Candidate A. By how many percentage points is Candidate A leading.
This might help cross divide and multiply.
Erica has a rectangular living room that is 9.78 meters long from front to back and 11.85 meters long from side to side. Draw a sketch of Erica's living room, labeling the lengths, and estimate how many square meters of carpet Erica would need to cover her living room floor.
Answer:
-> See attached
115.893 meters²
Step-by-step explanation:
See attached for my sketch.
Area for a rectangle is A = L * W:
9.78 meters * 11.85 meters = 115.893 meters²
Find the missing angles for every point here
In order to find the missing angles, we can see that vertically opposite angles and corresponding angles are equal.
46° + 82° + No. 4 = 180°
No. 4 = 180° - 128° = 52°
Therefore: No. 4 = No. 1 = 52° (vertically opposite angles)
What is angle?In geometry, an angle is actually known to be the figure that is created by two rays that actually meet at an end point that is common to the both rays. It is represented by the symbol: ∠.
So, we can see that:
Line a || Line b and Line c || Line d
46° = 7 (corresponding angles)
So, 46° + 82° + No. 4 = 180°
Thus, No. 4 = 180° - 128° = 52°
Therefore:
No. 4 = No. 1 = 52° (vertically opposite angles)
No. 2 = 180° - 52° = 128° (angles on a straight line)
No. 2 = No. 3 = 128° (vertically opposite angles)
No. 7 = No. 6 = 46° (vertically opposite angles)
No. 8 = 180° - 46° = 134° (angles on a straight line)
No. 8 = No. 5 = 134° (vertically opposite angles).
82° = No. 11 (vertically opposite angles)
No. 9 = 180° - 82° = 98° (angles on a straight line)
No. 9 = No. 10 = 98° (vertically opposite angles)
No. 9 = No. 15 = 98° (alternate angles)
No. 13 = No. 15 = 98° (vertically opposite angles)
No. 12 = No. 14 = 82° (vertically opposite angles)
46°= No. 17 (vertically opposite angles)
No. 18 = 180° - 46° = 134° (angles at a point)
No. 18 = No. 16 = 134° (vertically opposite angles)
No. 19 = 180° - (46° + 82°) = 52° (sum of angles in a triangle)
No. 19 = No. 22 = 52° (vertically opposite angles)
No. 20 = 180° - 52° = 128° (angles on a straight line).
No. 20 = No. 21 = 128° (vertically opposite angles)
No. 25 = No. 2 = 128° (corresponding angles)
No. 25 = No. 24 = 128° (vertically opposite angles)
No. 23 = No. 26° (vertically opposite angles).
So, all the angles are:
1= 52°
2= 128°
3= 128°
4= 52°
5= 134°
6= 46°
7= 46°
8=134°
9= 98°
10= 98°
11= 82°
12= 82°
13= 98°
14= 82°
15= 98°
16= 134°
17= 46°
18= 134°
19= 52°
20= 128°
21= 128°
22= 52°
23= 52°
24= 128°
25= 128°
26= 52°
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A rectangle has a length of 32 yards less than 10 times its width. If the area of the rectangle is 384 square yards, find the length of the rectangle.
The length of the rectangle is 48 yards.
Let's denote the width of the rectangle as "w" yards.
According to the information given, the length of the rectangle is 32 yards less than 10 times its width. So, the length can be represented as: 10w - 32 yards.
The formula for the area of a rectangle is length times width: Area = length × width.
Given that the area of the rectangle is 384 square yards, we can set up an equation:
Area = length × width
384 = (10w - 32) × w
Now, let's solve for the width (w):
384 = 10w² - 32w
0 = 10w² - 32w - 384
Dividing the equation by 2 to simplify:
0 = 5w² - 16w - 192
Now we have a quadratic equation. We can either factor it or use the quadratic formula to solve for "w." Let's use the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
For our equation, a = 5, b = -16, and c = -192. Plugging these values into the formula:
w = (16 ± √((-16)² - 4 × 5 × (-192))) / (2 × 5)
w = (16 ± √(256 + 3840)) / 10
w = (16 ± √4096) / 10
w = (16 ± 64) / 10
This gives us two possible solutions for the width:
w = (16 + 64) / 10 = 8 yards
w = (16 - 64) / 10 = -4.8 yards
Since width can't be negative, we'll ignore the second solution.
So, the width of the rectangle is 8 yards. Now, let's find the length using the earlier expression:
Length = 10w - 32
Length = 10 × 8 - 32
Length = 80 - 32
Length = 48 yards
Therefore, the length of the rectangle is 48 yards.
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