Answers
Given the model for the height of a ball:
[tex]h(t)=-16t^2+5t+15[/tex]To hit the ground, the height must be h(t) = 0. Then:
[tex]\begin{gathered} -16t^2+5t+15=0 \\ \Rightarrow16t^2-5t-15=0 \end{gathered}[/tex]We use the general solution for a quadratic equation:
[tex]ax^2+bx+c=0\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=16 \\ b=-5 \\ c=-15 \end{gathered}[/tex]Using the formula:
[tex]\begin{gathered} t=\frac{5\pm\sqrt{25+4\cdot15\cdot16}}{2\cdot16}=\frac{5\pm\sqrt{985}}{32} \\ \\ \Rightarrow t_1=1.137 \\ \Rightarrow t_2=-0.825 \end{gathered}[/tex]We only take the positive value (because the time is always positive!). Then, the answer is:
[tex]1.137\text{ seconds}[/tex]Related Questions
What will the new demensions of the rectangle below be after a dilation within scale factor of 9\4
Answers
Answer
The new dimensions of the rectangle after dilation by scale factor of (9/4) include
New length = 72 feet
New width = 18 feet
Explanation
The relationship between new length, original length and scale factor of dilation is given as
New length = (Original length) × (Scale factor)
For this question,
Scale factor = (9/4)
Original length = 32 feet
New length = (Original length) × (Scale factor)
New length = 32 × (9/4) = 72 feet
New width = (Original width) × (Scale factor)
Original width = 8 feet
Scale factor = (9/4)
New width = (Original width) × (Scale factor)
New width = 8 × (9/4) = 18 feet
Hope this Helps!!!
Find the probability of winning a new tvFind the odds against the team winning its next match
Answers
a)
[tex]\frac{2}{7}[/tex]b)
[tex]\frac{12}{11}[/tex]ExplanationThe probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring, the probability is givenby:
[tex]P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}[/tex]so
Step 1
we can find the odds in favor by using the expression:
[tex]Odds\text{ in favor=}\frac{P(A)}{1-P(A)}[/tex]so
let
[tex]\begin{gathered} P(A)=unknown \\ odds\text{ in favor=}\frac{2}{5} \end{gathered}[/tex]now, replace and solve for P(A)
[tex]\begin{gathered} Odds\text{ in favor=}\frac{P(A)}{1-P(A)} \\ \frac{2}{5}=\frac{P(A)}{1-P(A)} \\ cross\text{ multiply } \\ 2(1-P(A))=5*P(A) \\ 2-2P(A)=5P(A) \\ add\text{ 2P\lparen A\rparen in both sides} \\ 2-2P(A)+2P(A)=5P(A)+2P(A) \\ 2=7P(A) \\ divide\text{ both sides by 7} \\ \frac{2}{7}=\frac{7P(A)}{7} \\ \frac{2}{7}=P(A) \end{gathered}[/tex]therefore, the probabilyt of winning a new TV is
[tex]\frac{2}{7}[/tex]Step 2
now, to find the odds against we need to use the formula:
[tex]odds\text{ agains=}\frac{1-P(A)}{P(A)}[/tex]so
let
[tex]P(B)=\frac{11}{23}[/tex]now, replace in the formula and calculate
[tex]\begin{gathered} odds\text{ against=}\frac{1-P(A)}{P(A)} \\ odds\text{ against=}\frac{1-\frac{11}{23}}{\frac{11}{23}} \\ odds\text{ against=}\frac{\frac{12}{23}}{\frac{11}{23}}=\frac{12*23}{11*23}=\frac{12}{11} \\ odds\text{ against=}\frac{12}{11} \end{gathered}[/tex]therefore, the odds against are
[tex]\frac{12}{11}[/tex]I hope this helps you
3 What is the area of the parallelogram? Show your work.
0.36 m
0.09 m
Answers
Answer:
0.0324
Step-by-step explanation:
0.36x0.09=0.0324
Determine whether the following system of linear equations has no solution, only one solution, or infinitely many solutions. If the system has only one solution, find that solution.
Answers
You have the following system of equations:
3x - 3y + 3z = 0 (1)
2x - y - 3z = 2 (2)
-7x + 6y - 2z = -2 (3)
In order to determine if the previous system has solution or not, proceed as follow:
Add equation (1) and (2):
3x - 3y + 3z = 0
2x - y - 3z = 2
5x - 4y = 2 (5)
Multiply the equation (3) by -3 and the equation (2) by 2:
(-7x + 6y - 2z = -2)(-3)
21x - 18y + 6z = 6
(2x - y - 3z = 2)(2)
4x -2y - 6z = 4
Add the previous results:
21x - 18y + 6z = 6
4x -2y -6z = 4
25x - 20y = 10 (6)
You can notice that equation (6) is five times equation (5). It means that there is no way of getting a solution for x or y with equations (5) and (6).
the previous situation also means that there is no solution to the system of equations.
Evaluate the expression uv^2 + 5uv + u^2 for u = 3 and v = 4.1171128496
Answers
Answer:
117 (1st option)
Explanation:
Given:
[tex]uv^2+5uv+u^2[/tex]To find:
the value of the expression when u = 3 and v = 4
To determine the value, we will substitute for u and v in the expression
[tex]\begin{gathered} uv^2+5uv+u^2\text{ = 3\lparen4}^2)\text{ + 5\lparen3\rparen\lparen4\rparen + 3}^2 \\ \\ =\text{ 3\lparen16\rparen + 60 + 9} \\ \\ =\text{ 48 + 69} \\ \\ =\text{ 117 \lparen1st option\rparen} \end{gathered}[/tex]
Jessica was 44 inches at the beginning of 6th grade. At the end of 8th grade she was 62 inches. What was her
percent increase?
Answers
Answer:
40.91%
Step-by-step explanation:
62 - 44 = 18
18/44 = 0.4091
0.4091*100 = 40.91%
Then the increase percent is:
40.91%
Emerson wants to fence in a rectangle play area for his dog. He decides to make the length 2 feet longer than the width. He has 32 feet of fencing to use for this project and will use it all. What will the dimensions of the dog’s play area be?
Answers
If Emerson wants to fence a rectangular play area for his dog where he decides to make the length of the fence, 2feet more than the width, and he uses the complete 32feet fencing he had with himself, for this project, then the dimensions of the play area are 9ft in length and 7ft in width.
As per the question statement, Emerson wants to fence a rectangular play area for his dog and he decides to make the length of the fence, 2feet more than the width, for which, he uses the complete 32feet fencing he had with himself.
We are required to calculate the dimensions the play area from the above-mentioned data.
To solve this question, we need to know the formula to calculate the perimeter of rectangle which goes as [p = 2(l + b)]
Where, "p" is the perimeter of the rectangle, "l" is the length and "b" is the breadth of the rectangle.
Here given that, length of the fence will be 2feet more than width of the same. So, let us assume that width of the fence is "x" ft, and the length of the fence should be (x + 2)ft.
Also since, Emerson uses the complete 32feet fencing he had with himself, the perimeter of the play-area will be 32ft.
Substituting our assumptions in the above mentioned formula to calculate the perimeter of rectangle, we get, [32 = 2{x + (x + 2)}], which is a linear equation. Therefore, solving this equation for x, we will obtain our desired answer.
[32 = 2{x + (x + 2)}]
Or, [32 = 2(x + x + 2)]
Or, [32 = 2(2x + 2)]
Or, (32 = 4x + 4)
Or (4x = 32 - 4)
Or, (4x = 28)
Or, [x = (28/4)]
Or, (x = 7).
Therefore, (x + 2) = (7 + 2) = 9ft.
Rectangle: Any four-sided, closed polygon (quadrilateral) having right angles at all four interior angles, and two pairs of equal and parallel opposite sides, is known as a rectangle.To learn more about Perimeter of rectangles, click on the link below.
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2. What is the solution point for the system below?
Answers
Answer
The point of intersection is the solution point for the system equation
The point of intersection is the solution
The final answer
x = 4
y= -3
[tex](x,y)=(4,-3)[/tex].Which expression is equivalent to 45 ÷ (2 - x)?
A
45
2-X
B (2-x) = 45
C 45+ (x - 2)
D
2-x
45
Answers
The equivalent expression to 45÷(2-x) is 45/(2-x).
According to the question,
We have the following expression:
45÷(2-x)
Or in other words, it can be said that 45 is divided by (2-x).
Now, when we are finding the equivalent expression of any expression for that matter then the final expression after solving any expression should be equal to the original one.
For example, the equivalent expression for 3/5 is 6/10 because when we divide the second fraction by we will get 3/5.
Now, in this case, the equivalent expression will be:
45/(2-x)
Because the fraction also means division.
Hence, the correct option is A.
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Can you please help me my friend says it’s not $6.17 but I think it is what is the right answer please give an explanation cuz my friend wants why it’s $6.17 lol she think it’s $3.25
Answers
1.
In order to calculate how much is 5% of the original value, let's use the following rule of three:
[tex]\begin{gathered} 6.50\to100\text{\%} \\ x\to5\text{\%} \\ \\ \frac{6.5}{x}=\frac{1}{0.05} \\ x=0.05\cdot6.5 \\ x=0.325 \end{gathered}[/tex]So the amount taken off is $0.32.
2.
Subtracting this amount from the original price, we have:
[tex]6.50-0.32=6.18[/tex]So the final value is $6.18.
3.
A solution in a sentence would be:
The final value after the discount is 0.95 * 6.5 = $6.18.
Write the equation of the line, y = -2/3x + 4 y = 2/3x + 4 y = 3/2x + 4 y = -3/2% 4 4
Answers
Given data:
The given graph is shown.
The first point on the graph is (0, 4), and the second point on the graph is (2, 1).
The equation of the line passing through these points is,
[tex]\begin{gathered} y-4=\frac{1-4}{2-0}(x-0) \\ y-4=-\frac{3}{2}x \\ y=\text{ -}\frac{3}{2}x+4 \end{gathered}[/tex]ХBased on the table, which best predicts the end behaviorof the graph of f(x)?f(x)-6-20-5-4-3-2-101As xoo, fx) - 00, and as x, f(x) – 00.As X-oo, f(x) - oo, and as X - -co, f(x) – 4.O As X - co, f(x) – oo, and as X - oo, f(x) - 09.As x - 00, f(x) ---, and as Xoo, f(x) = -0.440-2.-6-1023
Answers
Given the table:
x f(x)
-5 -6
-4 -2
-3 0
-2 4
-1 4
0 0
1 -2
2 -6
3 -10
Let's find the best behaviour if the graph.
From the table, as the values of x increases, the values of f(x) decreases and as the values of y decreases, the values of f(x) decreases.
From the table of values, we can see that as x approaches negative infinity, f(x) approaches negative infinity.
Also, as x approaches infinity, f(x) approaches negative infinity.
Thus, we have the statement that best predicts the behaiour of the graph f(x):
As x ==> ∞, f(x) ==> -∞, and as x ==> -∞, f(x) ==> -∞
ANSWER:
The point A (-1,1) is reflected over the point (3,-1) and it's image is point B. What are the coordinates of point B?
Answers
B (7,-3)
1) Let's visualize this
Point A (-1,1) is reflected over the point (3,-1)
When point A(-1,1) is reflected over the point (-3,1) it goes 4 units to the right and 2 units down, so after the
2) So point B is (7,-3)
Lex had b pounds of apples. She gave away 1/10 of the apples. Which of the following expressions represents the weight of apples she gave away?
A. B + 1/10
B. B x 1/10
C. B - 1/10
D. B divided by 1/10
PLS HELP
Answers
Answer:
B. B x 1/10
Step-by-step explanation:
Lex had b pounds of apples. She gave away 1/10 of the apples. Which of the following expressions represents the weight of apples she gave away?
A. B + 1/10 this would be giving away more than the apples she has
B. B x 1/10, correct
C. B - 1/10 this would be giving 9/10 lb apples away. This represents the apples she kept.
D. B divided by 1/10 Lex does not have this many to give away
How many kilometers is 2,400,000 meters?
Answers
Answer:
2,400 km
Step-by-step explanation:
1 km = 1000 m or 1 m = 10^-3 km
so 2,400,000 x 10^-3 = 2,400 km
The graph of a function is shown in the figure.30110X-101What is the value of the function for =2?
Answers
The function's value for x = 2 is the point (y-coordinate) on the graph corresponding to x = 2.
If you go to x = 2, then go to the function, it is located at y = -2.
Hence, the value of the function for x = 2, is:
-21 shown. If the diameter of a circle is of an inch, what 4 is its radius? 1 What is the radius r of a circle with a diameter of 4 a r in (Simplify your answer. Type an integer or a fraction.) Enter your answer in the answer box е e Save for ater
Answers
Given
d = 1/4 inch
d = diameter
Procedure
[tex]\begin{gathered} r=\frac{1}{2}d \\ r=\frac{1}{2}\cdot\frac{1}{4} \\ r=\frac{1}{8}\text{ inch} \end{gathered}[/tex]
Frazer is buying paint to paint one of his walls. The wall measures 3 feet bu 5 feet. A por of paint will cover 20 square feet. Will it be enoigh to cover his wall?
Answers
Yes, It will be enough to cover the wall.
What is the perimeter?A perimeter is the length of a two-dimensional shape's boundary. It is sometimes described as the total length of the object's sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides. For the various geometric shapes, we have formulas.
Area: 3×5=15 square feet [s=length-width]
Perimeter: (3+5) × 2 = 16 feet
∵ 15 square feet <20 square feet
∴ It will be enough
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Factor 2x2 + 8x − 90 completely.
Answers
we have the expression
[tex]2x^2+8x-90[/tex]step 1
Factor 2
[tex]2(x^2+4x-45)[/tex]step 2
Simplify
[tex]2(x^2+4x-45)=2(x+9)(x-5)[/tex]g3-h²+8, when g = 3, h = 5
Answers
I think it's 8- I did this before
An equation is shown below:6(2x − 11) + 15 = 3x + 12Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)Part B: What value of x makes the equation true? (4 points)Can you answer part a and part b in written form please?
Answers
Given:
[tex]6(2x-11)+15=3x+12[/tex]Required:
To write the steps to solve the given equation and to find the value of x.
Explanation:
(A)
Consider
[tex]6(2x-11)+15=3x+12[/tex]First multiply 6,
[tex]12x-66+15=3x+12[/tex]Next subtract 15 from 61, we get
[tex]12x-51=3x+12[/tex]Add 51 to the above equation
[tex]\begin{gathered} 12x-51+51=3x+12+51 \\ 12x=3x+63 \end{gathered}[/tex]Subtract 3x we get
[tex]\begin{gathered} 12x-3x=3x-3x+63 \\ 9x=63 \end{gathered}[/tex]Divide 9 on both side, we get
[tex]\begin{gathered} \frac{9x}{9}=\frac{63}{9} \\ \\ x=7 \end{gathered}[/tex](B)
[tex]\begin{gathered} 6(2x-11)+15=3x+12 \\ 12x-66+15=3x+12 \\ 12x-3x=12-15+66 \\ 9x=63 \\ x=\frac{63}{9} \\ x=7 \end{gathered}[/tex]x = 7 makes the equation true.
Final Answer:
The value of x = 7 makes the equation true.
I need some help please
Answers
Then
4 | x + 1| + 2 > 6
Substract 2 , at left and right
4 |x+1 | > 6-2 = 4
Now divide by 4
(4 |x + 1| )/4 > 4/4
Then
| x + 1| > 1
Now solve this equation, by way of 2 equations
x + 1 > 1
and
- (x + 1) < 1
Solution for first iis
x > 1 - 1
x > 0
And solution for second inequality is
- x - 1 < 1
x < -1 - 1
x < -2
THEN ANSWER interval for this is
(-OO, -2) U (0, OO)
ANSWER IS OPTION B)
Interval notation is
x > 0 ( 0, infinite)
x < -2 ( - infinite, -2)
Karen's furniture store advertised a table at 23% discount. The original selling price was $123, and the sale price was $100. What is the sales price?
Answers
Using the original selling price calculate the real sales price that it should be if there is a discount of 23%
[tex]\begin{gathered} SalesPrice=OrigalPrice\cdot(1-0.23) \\ SalesPrice=123\cdot(0.77) \\ SalesPrice=94.71 \end{gathered}[/tex]The sales price is higher than it should be.
Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Which of the following combinations will satisfy these constraints?
20 paintings and 65 bracelets
25 paintings and 60 bracelets
26 paintings and 61 bracelets
14 paintings and 45 bracelets
Answers
If Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Then 20 paintings and 65 bracelets will satisfy the given constraints.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Marissa is selling paintings for $15 each and bracelets for $7 each.
Let x represents paintings and y represents bracelets
7x+15y≥800...(1)
Marissa must sell at least 60 bracelets.
y ≥ 60..... (2)
Now substitute 60 in 1
7x+15(60)≥800
7x+900≥800
7x≥-100
x≤20
Hence of the following combinations 20 paintings and 65 bracelets will satisfy these constraints
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Answer:
26 paintings and 61 bracelets
Step-by-step explanation:
if you do 26x15=390 and 61x7=427 390+427=817
so the answer is 26 paintings and 61 bracelets
also i took the test so i know this is right
help meeeeeeeeeeeeeeeeeee please
Answers
Answer: 539.9
Step-by-step explanation: Since 2004 is our starting year, 9 years have passed since 2004 and 2013. 9 would be the “x” in the equation.
y = 20.1(9) + 359
y = 180.9 + 359
y = 539.9
Density is a unit rate measured in units of mass per unit of volume. The mass of a garnet is 5.7 grams. The volume is 1.5 cubic centimeters (cm3). What is the density of the garnet?
Answers
The density of the garnet is 3.8
Mass of the garnet = 5.7 grams
Volume = 1.5 cm^3
Since each element and compound has a distinct density, DENSITY is a physical attribute of matter. In a qualitative sense, density is the quantification of the relative "heaviness" of things with a constant volume.
A crumpled piece of paper of the same size is visibly less dense than a rock. A ceramic cup is denser than a styrofoam cup. Use the styrofoam vs. ceramic cup comparison to illustrate how closely "packed" or "busy" the material appears to be.
The density of the garnet =. Mass/Volume
= 5.7/1.5
= 3.8
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Mr. Perkins has \$ 120$120 in a savings account. The interest rate is 5 \%5% per year and is simple interest. How much will he have in 2 years?
Answers
Answer:
$12
Step-by-step explanation:
Simple interest calculation is
I = Prt
where P is the principal, r is the rate of interest as a decimal and t the number of years
Given
P = 120, r = 5% = 5/100 = 0.05 and t = 2 years
the simple interest
= 120 x 0.05 x 2 = $12
==============================================
Work Shown:
i = P*r*t
i = 120*0.05*2
i = 12
Mr. Perkins earns $12 in simple interest over the two year period. His account balance will be 120+12 = 132 dollars
------------
Slight shortcut:
A = P*(1+r*t)
A = 120*(1+0.05*2)
A = 132
Jamie runs a math-tutoring program. For each student, she charges an enrollment fee of $63.00 plus $18.00 per hour of tutoring. If h representsthe number of hours a student participates in tutoring, which inequality symbolizes when a student's average cost per hour of tutoring is nomore than $22.207
Answers
Hence, the inequality which symbolizes when a student's average cost of tutoring is no more than $22.207 is:
[tex]\frac{63}{h}+18\leq22.207[/tex]
How many ways can 5 students be assigned a seat in a classroom if there are 9 seats in a row?
a) 45
b) 14
c) 362,880
d) 15,120
e) 126
f) None of the above.
Answers
Answer: I believe it is D! hope this helps
Step-by-step explanation:
find the standard deviation for the following set of numbers 29,31,37,42
I’m
not too sure on the next steps and very confused
Answers
The standard deviation for the following set of numbers 29,31,37,42 is 34.75.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard deviation:
= (29 + 31 +37 + 42 )/ 4
= 34.75
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