Answers
Note that a quadratic function is increasing and decreasing at exactly half between the roots.
The roots are the point on the ground when tossing the ball into the air.
So we need to get the roots of the given equation.
Roots are the values of x when y = 0
[tex]\begin{gathered} y=-x^2+6x \\ 0=-x^2+6x \\ 0=-x(x-6) \\ -x=0\Rightarrow x=0 \\ (x-6)=0\Rightarrow x=6 \end{gathered}[/tex]So the roots are 0 and 6, this will be the x coordinate or the point on the ground.
Since the equation is increasing halfway and decreasing up to the ground, the halfway point is the midpoint between the roots.
Midpoint = (0 + 6)/2 = 3
Therefore, the ball's height is always decreasing at 3 < x < 6
The answer is 3 < x < 6
Related Questions
A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.9 feet from its low point to its high point, and that it returns to its high point every 16 seconds
Answers
Concept
What is a simple harmonic motion ?Repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same
a) y= 1.95ftcos(π/2)
b) v(t)= -0.76sin(π/5t)
Part aSince the buoy oscillates in simple harmonic motion the equation to model this is given by: y= A cos(ωt+θ)
For this case from the info given we know that:
2A= 3.9 , A= 3.9/2= 1.95ft
It returns to its high point every 16 seconds. That means period = 16 , and the angular frequency can be founded like this:
ω=2π/16
= π/8
Assuming that the value for the phase is (θ=0°) our model equation is given by
y= 1.95ftcos(π/2)
Part bFrom definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this,
dy/dt= v(t)= -1.95ft(π/8)sin(π/8t)
v(t)= -0.76sin(π/8t)
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Permutation/combination In how many ways can five people line up to get on a bus? (Hint: all 5 people are lining up)
Answers
We have to calculate in how many ways can five people line up to get on a bus.
This is a permutation of 5 in 5 without repetition, so it can be calculated as:
[tex]P(5,5)=5!=120[/tex]Answer: in 120 ways.
What is the sum of the exterior angles of a polygon with 30 sides a) 180°b) 30°c) 90°d) 360°
Answers
Note that:
The sum of the exterior angles of a polygon does not depend on the number of sides of the polygon
The sum of the exterior angles of a polygon is 360°
Therefore, the correct option is 360°
make a table of values then graph the following quadratic functions, label atleast 5 points
Answers
Given the function below:
[tex]f(x)=\frac{-4(x-3)^2}{9}+4[/tex]Substituting each value of x in the table in the function above, we get
[tex]\begin{gathered} f(0)=\frac{-4(0-3)^2}{9}+4\text{ = }\frac{-4(-3)^2}{9}+4 \\ \\ f(0)=\frac{-4\times9}{9}+4\text{ =-4+4 = 0} \end{gathered}[/tex][tex]f(1)=\frac{-4(1-3)^2}{9}+4\text{ =}\frac{-4\times4}{9}+4=\frac{-16}{9}+4=\frac{20}{9}[/tex][tex]f(6)=\frac{-4(6-3)^2}{9}+4\text{ = }\frac{-4(3^2)}{9}+4\text{ =-4+4 = 0}[/tex]1 B 0 A C If the distance from point A to point C is 7.5 units and O=40°, find the distance from point A to point B to the nearest tenth. (1 Point) a. 8.9 b. 4.7 C. 6.3 d. 2.5
Answers
Answer
Option C is correct.
AB = 6.3 units
Explanation
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
Using trignometric relations, we can see that TOA wil work for this
Tan θ = (Opp/Adj)
θ = 40°
Opp = AB = ?
Adj = AC = 7.5 units
Tan 40° = (Opp/7.5)
Opp = AB = 7.5 (Tan 40°) = 6.3 units
Hope this Helps!!!
Find the surface area Formula: SA= p * h + 2 * B
Answers
Given:
For the given figure,
[tex]h=2ft,w=3ft,l=8ft[/tex]The surface area is calculated as,
[tex]\begin{gathered} S=2lh+2wh+2wl \\ S=2\cdot8\cdot2+2\cdot3\cdot2+2\cdot3\cdot8 \\ S=32+12+48 \\ S=92 \end{gathered}[/tex]Answer: surface area is 92 square ft.
Four friends had dinner at a restaurant. The bill was $45.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?
Answers
Answer:
$13.62
Step-by-step explanation:
To find the tip of 20%, multiply 45.40 by 0.20, and you get 54.48.
Now, since there are 4 friends, divide the amount by 4.
54.48/4=13.62
So each person would pay $13.62.
Hope this helps! :D
Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
Which data display would you use to represent this data?
O Histogram
Scatter plot
O Line graph
O Line plot
Answers
To represent the data, histogram would have been used.
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
In a histogram, a graphical representation of the distribution of data is done. The histogram is represented by a set of rectangles, adjacent to each other and each bar represent a kind of data.
Here the number of chapters can be kept in x axis and the total number of pages can be kept in the y axis.
Therefore, histogram would be used to display the data.
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Expected FrequencyA fair five sided spinner is spun 40 times.a) How many times would it be expectedto land on red?P(Red) = 15It would be expected to land on redItimes.1-5Hint:Set up and solve a proportion.
Answers
It can be observed that sppiner is spun 40 times. So proabaility for red colour must include 40 in denominator. The fraction 1/5 has 5 in denominator which be change to 40 by multiplication of 8 to numerator and denominator.
[tex]\frac{1}{5}\cdot\frac{8}{8}=\frac{8}{40}[/tex]So, it is expected to land 8 times on the red colour.
So answer is,
[tex]\frac{1}{5}=\frac{8}{40}[/tex]and It would be expected to land on red 8 times.
The pie chart below shows the percentage of total revenue that a publisher receives from publications.A) which category accounts for approximately 1/5 of publishers total revenue type in which one (textbooks, cookbooks, magazines, paperbacks,poetry, nonfiction B)Approximately percentage total revenue from paperbacks poetry combined C) if revenue from nonfiction 10% total revenue approximately percentage total comes from poetry
Answers
a) To determine which category represents approximately one-fifth of the publisher's revenue, you can compare the given pie chart with a pie chart divided into 5 parts.
The category that is approximately one-fifth of the revenue, that is, 20% of the total revenue, is textbooks.
To solve parts b and c you can use the following pie chart to compare with the given chart for the publisher's revenue:
b) Looking at the pie charts, the categories "paperback" and "poetry" are approximately 20% of the total revenue.
c) The category "Nonfiction" is 10% of the total revenue, the category "poetry" is approximately half of the size of the category "nonfiction" so you can say that it corresponds to 5% of the total revenue.
Use the pythagorean theorem to find the distance between (2,8) and (-8,2) A. 16.0 B. 4.0 C. 12.3 D. 11.7
Answers
Using the Pythagorean theorem, the distance between two points (x1, y1) and (x2, y2) is gotten as follows:
[tex]\begin{gathered} d^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ \text{Thus:} \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Since we have the two coordinates: (2, 8) and (-8, 2)
where:
(x1, y1)= (2, 8)
(x2, y2) = (-8, 2)
Therefore, the distance between them is:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{((-8)_{}-2_{})^2+(2-8)^2} \\ d=\sqrt[]{((-10_{})^2+(-6)^2} \\ d=\sqrt[]{100+36} \\ d=\sqrt[]{136} \\ d=11.66 \\ d=11.7\text{ (to one decimal place)} \end{gathered}[/tex]Therefore, the distance between the two p is: 11.7
Correct option is: Option D
i need help solving -12=3-2K-3K
Answers
Solve
[tex]\begin{gathered} -12=3-2k-3k \\ \text{Collect like terms} \\ -12-3=-2k-3k \\ \text{Note that when a positive value crosses the equality sign, it becomes negative} \\ \text{Similarly when a negative value crosses the equality sign it becomes positive} \\ \text{Hence, 3 crosses over and becomes negative} \\ -12-3=-2k-3k \\ -15=-5k \\ \text{Divide both sides by -5} \\ \frac{-15}{-5}=\frac{-5k}{-5} \\ 3=k \end{gathered}[/tex]Consider the non-right triangle below.Suppose that m∠CAB=62∘, and that x=35 cm and y=17 cm. What is the area of this triangle? cm^2
Answers
Given that:
x=35 cm and y=17 cm
and angle CAB= 62 degree
[tex]\begin{gathered} A=\frac{1}{2}\times x\times y\times\sin (\angle CAB) \\ A=\frac{1}{2}(35)(17)\sin (62) \\ A=297.5\times\sin (62) \\ A=262.67cm^2 \end{gathered}[/tex]determine whether the given by binomial is a factor of the polynomial p(x) . If so, find the remaining factors of p(x).
Answers
The given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).
What is termed as the factors of polynomial?Factorisation is the process of determining the factors of a given value as well as mathematical expression. Factors are integers which are multiplied together to create the original number.For the given question.
The polynomial is given as; x³ + 2x² -x - 2.
The binomial is given as; (x +2).
The, to get the remainder, divide the polynomial with the binomial.
= (x³ + 2x² - x - 2)/ (x +2)
Taking x² common from the first two terms of the numerator and (-1) from the last two terms.
= x²(x + 2) - (x + 2)/ (x +2)
Taking (x + 2) common from two terms.
= (x + 2)(x² - 1)/(x + 2)
Cancel (x + 2) from both.
= (x² - 1)
Now use the identity to open the square.
(a² + b² ) = (a + b) (a - b)
= (x + 1)(x - 1).
Thus, the given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).
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The correct question is-
Determine whether the given binomial is a factor of the polynomial p(x).
If so, find the remaining factors of p(x).
p(x) = x³ + 2x² -x - 2 ; (x +2)
Answer:
a
Step-by-step explanation:
Laverne created a painting with an area of 72 square inches and a length of 9 inches. They create a second painting with an area of 56 square inches. It has the same width as the first painting. What is the length of the second painting?
Answers
Answer: 7
Step-by-step explanation:
As our first step, we can divide 72 by 9 to discover the width of the first AND second painting. 72÷9=8
Now that we have discovered the width of the second painting, we will now solve the mathematical expression 56÷8.
Because 56 divided by 8 equals 7, the length of the second painting is 7 inches.
7 singles, 13 fives, 4 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
Answers
So,
The probability to obtain one bill of the four, is 1/4.
So, the expected value is:
[tex]\begin{gathered} \frac{1}{4}(7)+\frac{1}{4}(13)+\frac{1}{4}(4)+\frac{1}{4}(3) \\ \\ =6.75 \end{gathered}[/tex]Therefore, the fair price to play this game is 6.75.
State whether the given information is enough to prove that ABCD is a parallelogram.
Answers
From the image given, the data shows that
[tex]\begin{gathered} <1\cong<3 \\ \text{and} \\ AD\cong BC \end{gathered}[/tex]We can observe that
[tex]\begin{gathered} \Delta BDA\cong\Delta DBC\text{ (SAS)} \\ \text{ Reasons:} \\ AD\cong BC\Rightarrow side \\ \measuredangle1\cong\measuredangle3\Rightarrow\text{angle} \\ BD\cong DB(common\text{ sides or reflexive)}\Rightarrow\text{side} \end{gathered}[/tex]Thus, from the above we can say that;
[tex]\begin{gathered} AB\cong DC\text{ (corresponding parts of congruent triangles are congruent)} \\ \text{Therefore, } \\ \measuredangle2\cong\measuredangle4 \end{gathered}[/tex]Hence
Yes, the given information is enough to prove that ABCD is a parallelogram.
11-3x75-1 what is the answer?
Answers
Answer:
Step-by-step explanation:
-215
Answer:
-215
Step-by-step explanation:
the answer to 11-3x75-1 is -215
Real numbersA stock lost 8 and 3/8 on Monday, 1 and 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stocks for these three days?
Answers
Answer: The net gain was 3 stocks for these three days.
Explanation
Given
• Monday: lost 8 and 3/8.
,• Tuesday: lost 1 and 5/8 points.
,• Wednesday: gained 13 points.
Procedure
To calculate the net gain, we have to add all the values we are giving, considering that the stock lost will have a negative sign:
[tex]\text{Net gain}=Gains-losses[/tex]0. Calculating the losses
We have to mixed numbers, for which we can add the whole numbers and the fractions separately.
• Whole numbers
[tex]-8-1=-9[/tex]• Fractions
[tex]-\frac{3}{8}-\frac{5}{8}=-\frac{8}{8}=-1[/tex]At last, we add both results and we get the losses:
[tex]losses=-9-1=-10[/tex]2. Calculating the gains
As we only have one quantity, there is no need for calculations:
[tex]Gains=13[/tex]3. Calculating net gain
Finally, we put both quantities in the formula:
[tex]\text{Net gain}=13-10=3[/tex]Kuta Software Infinie Algebra ? Absolute Value Inequalities Salve each inequality and graph its solution. 61 1 laulsis * -36043 3) m-2/
Answers
Prob 22
7 + | 6v + 7| ≤ 60
then
| 6v + 7| ≤ 53
now eliminate lines ||
6v + 7 ≤ 53
and
6v + 7 ≤ - 53,. 6v ≤ -60
Now solve for x
6v ≤ 47,. v≤ 46/6
also
6v ≥ -47,. v≥ -46/6
Then answer is
-10 ≤ v ≤ -46/6
Graph for problem 22
What is the area of the blue shape?
Answers
In rectangle , 38.5 sq units is the area of the blue shape.
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.We can split the shape into two rectangles.
The small rectangle at the top has an area of 14 sq units (2 * 7).
The middle rectangle has an area of 49 sq units ( 7*7).
Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.
Adding that to 14 sq units will give us 38.5 sq units.
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Assume that 5 cards are drawn from a standard deck of 52 cards. How many ways can I get 3 sevens, 1 six and 1 five?
Answers
Answer
64 ways
Explanation
In a standard deck of 52 cards, there are four 'sevens', four 'sixes' and four 'fives'.
Using Combination formula, the number of ways to pick 3 sevens, 1 six and 1 five is given as
⁴C₃ × ⁴C₁ × ⁴C₁
= 4 × 4 × 4
= 64
Hope this Helps!!!
Find two functions f and g such that (f O g) (x) =h(x) [tex]h(x) = (9x + 7)^{2} [/tex]
Answers
f(x) = x² and g(x) = 9x + 7
Explanation:(fog) (x) = h(x)
h(x) = (9x + 7)²
To get the two functions, we need to understand that the function g(x) will be inserted in function f(x) to get (fog)(x)
g(x) = 9x + 7
This is the function that will be inserted into f(x)
Since we have a square, the function of f(x) will have a square
f(x) = x²
Putting both together, replace x with (9x + 7) in f(x)
(fog)(x) = (9x + 7)²
Hence, f(x) = x² and g(x) = 9x + 7
Factor 9x^4-18x^3+36x^2
Answers
Given the expression:
[tex]9x^4-18x^3+36x^2[/tex]You can factor it by following these steps:
1. Find the Greatest Common Factors (GCF) of the terms:
- The Greatest Common Factor (GCF) of the coefficients can be found by decomposing each coefficient into their Prime Factors:
[tex]\begin{gathered} 9=3\cdot3 \\ 18=2\cdot3\cdot3 \\ 36=2\cdot2\cdot3\cdot3 \end{gathered}[/tex]Notice that all the coefficients have:
[tex]3\cdot3=9[/tex]Therefore, that is the Greatest Common Factor (GCF) of the coefficients.
- The Greatest Common Factor (GCF) of the variables is the variable with the lowest exponent:
[tex]x^2[/tex]Hence:
[tex]GCF=9x^2[/tex]2. Now you can factor it out:
[tex]=9x^2(x^2-2x+4)[/tex]Hence, the answer is:
[tex]9x^2(x^2-2x+4)[/tex]what is a unit rate for meter per second if a car travels 274 m in 17 seconds
Answers
The rate is 274m/17s = 16.1176m/s
9) The temperature outside feels like - 3°C on Thursday. When the temperature is taken, it is actually 16°C. Howmany degrees lower does the temperature feel?
Answers
The temperature feels
[tex]16-(-3)=19[/tex]degrees lower from the actual.
the sum of billiard balls was arranged in an equilateral triangle and 7 balls were extra. Then the same set of billiard balls was arranged into a triangle where each side has one more ball than in the first arrangement but now the new arrangement cannot be completed because there is a shortage of three balls. How many balls are in the set?
Answers
There were 52 billiard balls in the set.
Assume that billiard balls are arranged in rows to form an equilateral triangle, then the first row consists of 1 ball, second row consists of 2 balls, and third row consists of 3 balls, and so on. So there must be n balls in the nth row.
So, the total number of billiard balls that forms the equilateral triangle with n rows is:
1 + 2 + 3 + ... + n = n(n + 1)/2
Let x1 and x2 be the total number of balls in the first and second arrangements respectively.
Then,
x1 = n(n + 1)/2 + 7
It has been said that there were 3 lesser balls in the second arrangement:
x2 = (1 + (n + 1))/2 × (n + 1) - 3
x2 = (n + 1) × (n + 2)/2 - 3
Since x1 = x2,
n(n + 1)/2 + 7 = (n + 1) × (n + 2)/2 - 3
We solve above equation to find the value of n,
multiplying both the sides by 2
n(n + 1) + 14 = (n + 1)(n + 2) - 6
n² + n + 14 = n² + 3n + 2 - 6
n - 3n = -4 - 14
-2n = -18
n = 9
So, x1 = 9(9 + 1)/2 + 7
= 9(5) + 7
= 45 + 7
= 52
Therefore, there were 52 billiard balls in the set.
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I really need help solving thisIt’s from my trig prep bookIt asks to answer (a) and (b)
Answers
The sum in summation notation is:
[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]The expansion is:
[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]Explanation:Given the expression:
[tex](3x^5-\frac{1}{9}x^3)^4[/tex]In summation notation, this can be written as:
[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]The simplified terms of the expression is:
[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= 0.2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012, where x = 0 corresponds to 2003, x = 1to 2004, and so on, and y is in millions of students.(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is millions.(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
In order to find the projected enrollment for 2008, we need to use the value of x equal to 5, because x represents the number of years after 2003.
Then, using the linear model with x = 5, we have:
[tex]\begin{gathered} y=0.2145\cdot5+15.79\\ \\ y=1.0725+15.79\\ \\ y=16.8625 \end{gathered}[/tex]Rounding to the nearest tenth, we have y = 16.9.
160 is what percent of the sum of 100 and 120 and 160
Answers
42.105%
1) Let's first add thosse numbers up: 100 +120+160 =380
2) Now we can write out the following ratio, to find out what percentage is equivalent to 160 out of that 380:
[tex]\begin{gathered} 160----x \\ 380----100 \\ \frac{160}{380}=\frac{x}{100} \\ 380x=16000 \\ \frac{380x}{380}=\frac{16000}{380} \\ x=42.105\% \end{gathered}[/tex]Note that we had to cross multiply that.
3) Hence, the answer is 160 is approximately 42.105% of 380