The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.
Given that,
The height of a tennis ball tossed into the air is modeled by,
[tex]\rm h(x) = 40x - 16x^2[/tex]
Where x is elapsed time in seconds.
We have to determine,
During what time interval will the tennis ball be at least 15 feet above the ground?
According to the question,
The height of a tennis ball tossed into the air is modeled by,
[tex]\rm h(x) = 40x - 16x^2[/tex]
Where x is elapsed time in seconds.
Then,
When the tennis ball be at least 15 feet above the ground,
[tex]h(x) = 15[/tex]
Substitute the value of h(x) in the equation,
[tex]\rm h(x) = 40x - 16x^2\\\\ 15 = 40x - 16x^2\\\\ 16x^2-40x+15=0[/tex]
Factorize the equation for finding the time interval will the tennis ball be at least 15 feet above the ground is,
[tex]\rm 16x^2-40x+15= 0\\\\x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2-4 \times 16 \times 15}}{2 \times 16}\\\\x = \dfrac{-(-40)\pm \sqrt{1600- 960}}{32}\\\\x = \dfrac{40\pm \sqrt{640}}{32}\\\\x = \dfrac{40 + 25.29}{32} \\\\x = \dfrac{40 + 25.29}{32} \ and \ x = \dfrac{40 - 25.29}{32}\\\\x = \dfrac{65.29}{32} \ and \ x = \dfrac{14.71}{32}\\\\x = 2.04 \ and \ x = 0.45[/tex]
Hence, The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.
For more details about Inequality refer to the link given below.
https://brainly.com/question/17177510
(repost) Please help! It involves inequalities! Also please include a number line.
Answer:
-5 ≤ x
Step-by-step explanation:
2(x -3) -5x ≤ 9 . . . . . given
2x -6 -5x ≤ 9 . . . . . . eliminate parentheses
-3x -6 ≤ 9 . . . . . . . . combine like terms
-6 ≤ 9 +3x . . . . . . . add 3x
-15 ≤ 3x . . . . . . . . subtract 9
-5 ≤ x . . . . . . . . . divide by 3
__
The point x=-5 is included in the solution set, so there is a sold dot at that point. The rest of the solution set is values of x that are greater than that value, so the number line is shaded to the right of that point. Your number line should show an arrow at the right end of the graph to indicate it extends that direction indefinitely. (My graphing program doesn't draw arrows easily.)
_____
Additional comment
Perhaps the most straightforward way to solve this would have been to add 6 instead of 3x. That would give ...
-3x ≤ 15
Then dividing by -3 would give x. That operation would reverse the inequality symbol (because the divisor is negative). Then you would have ...
x ≥ -5
Either way works. We judge it to be less confusing when we don't have to change the direction of the inequality symbol.
A=6,500(1.0175)^4t
How long would the person need to leave their money in the bank until it reaches $20,100? Round the nearest whole number!
The time it will take the pereson to leave their money in the bank until it reaches $20,100 is 3 years
Given the exponential equation expressed as:
[tex]A=6500(1.0175)^{4t}\\[/tex]
Given that A = 20100, Substituting into the expression will give;'
20100 = 6500(1.0175)^4t
20100/6500 = (1.0175)^4t
3.0923 = (1.0175)^4t
Taking the ln of both sides
ln3.0923 = 4tln(1.1075)
4t = ln3.0923 /ln(1.1075)
4t = 1.12891/0.1021
4t = 11.05690
t = 11.05690/4
t = 2.76
t ≈ 3 years
Hence the time it will take the pereson to leave their money in the bank until it reaches $20,100 is 3 years
Learn more on compound interest here: https://brainly.com/question/24274034
Three men can build a wall in 8 days. How long will it take them if they have the help of 2 boys? Assume that each boy works half as fast as each man.
(with explanation pls)
Answer:
6 days
Step-by-step explanation:
2 boys that each work half as fast as the men is equivalent to having one extra man. So instead of 3 men we have 4. 4/3 the manpower means 3/4 the time. 3/4 of 8 is 6.
Answer:
6 days.
Step-by-step explanation:
The 3 men can build 1/8 of a wall in 1 day.
So 1 man can build 1/24 wall in 1 day.
So 1 boy can build 1/48 in 1 day and 2 boys can build 1/24 wall in 1 day.
So we have the equivalent of 4 men working and they can build 4 * 1/24
= 1/6 of a wall per day
So the answer is 6 days.
the area of a triangle with vertices at (-3,-2),(3,-2),(1,2) is
please provide small explanation
Answer:
12
Step-by-step explanation:
First, you have to graph (which I sadly cannot provide an image of)
Then look at the vertical height which is 4, the how long it is which is 6.
So A=1/2*6*4=12
the smallest number that is divisible by each one of 9,12 and 15 is
(a) 60. (b) 90. (c) 120 (d) 180
Given the graph below, find the slope.
A. -3/2
B.3/2
C -2/3
D. 2/3
HELP PLEASE WILL GIVE BRAINLIEST
Answer:
In attachment
Step-by-step explanation:
See the attachment. They are much easier to solve if you set up a spreadsheet template and then copy that template for each problem. The inputs would be the two given points for each graph. Problem 3's slope is undefined, since it is a vertical line and the run is 0, no change in x. Since slope is "Rise/Run," this is dividing by zero, a No-No for mathematicians, as well as us chemists and other mortals.
whats the equation? for the problem
Answer: YOU DONT GIVE THE PROBLEM
Step-by-step explanation:
Work out the percentage change to 2 decimal places when a price of £60 is increased to £89.99.
Answer:
49.98%
Step-by-step explanation:
Original price: £60
New price: £89.99
The difference in prices: £89.99 - £60 = £29.99
£60 - 100% (the original price)
£29.99 - x (the % that we want to calculate)
29.99 × 100 = 2999
2999 ÷ 60 = 49,9833333
Can someone help me out?
Answer:
d
Step-by-step explanation:
2. You have 7 folders and you want to put the same number of pages in each folder.
a. If you have a total of p pages, how many pages will be in each folder?
b. Evaluate your expression to calculate the number of pages in each folder if you have 147 pages or
245 pages.
Answer:
a. p/7
b. 21; 35
Step-by-step explanation:
To find the number of pages in each folder, divide the number of pages by the number of folders.
a. There will be p/7 pages in each folder.
b. 147 pages will result in 147/7 = 21 pages in each folder
245 pages will result in 245/7 = 35 pages in each folder
what are all the roots of the function f(x)= x^3+3x^2-x-3
Answer:
\mathrm{Domain\:of\:}\:x^3+3x^2-x-3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}
Step-by-step explanation:
Juno is taking a taxi. The table represents a linear function and shows the amount she owed after various numbers of miles traveled. Is the rate of change 2. 25? Amount Juno Owed for a Taxi Miles Amount Owed (dollars) 1 2. 5 2 2004. 75 3 7 4 9. 25 5 11. 5 Yes, because the amount owed changes by 1 every time the miles change by 2. 25. Yes, because the amount owed changes by 2. 25 every time the miles change by 1. No, because the amount owed does not change by 1 every time the miles change by 2. 25. No, because the amount owed does not change by 2. 25 every time the miles change by 1.
Linear functions are represented by constant rates.
The true statement is (d) No, because the amount owed does not change by 2.25 every time the miles change by 1.
From the table, we can see that:
As the number of miles increase by 1, the amount owed increases, but it does not increase at a constant rate of 2.25.
This means that, the table does not represent a linear function.
Represent the linear functions at:
https://brainly.com/question/15602982
(-3x+4)+(x-9) help please.
Answer:
- 1 · (2×±5)Step-by-step explanation:
Answer:
−2−5
Step-by-step explanation:
(-3x+4)+(x-9)
−3x+4+x−9
Subtract
−3x+4+x−9
-3−5+
Combine terms
−3x−5+x
−2−5
Last month, Korey’s Comics had $4,350 in net sales with a gross profit of $3,320 and a net income of $1,850. Calculate Korey’s net profit margin. A. 42. 5% b. 55. 7% c. 76. 3% d. 179. 5%.
Korey's net profit margin is 42.5%.
Net profit margin is the ratio of net income to net sales. It is a profitability ratio. Profitability ratios measure the efficiency with which a company generates profit from its asset.
Net profit margin = net income / net sales
Net profit margin = $1850 / $4350 = 0.425 = 42.5%
A similar question was answered here: https://brainly.com/question/5990973
Answer:
A. 42.5%edge⬇️
1/ 99 to 4 significant figures
Answer:
0.01010
Step-by-step explanation:
The decimal equivalent is ...
[tex]\dfrac{1}{99}=0.\overline{01}[/tex]
Rounded to 4 significant figures, it is ...
0.01010
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
Answer:
Below.
Step-by-step explanation:
Part A.
m < RPB = 180 - 115 = 65 degrees.
So the m < x = 180 - 65 - 62
= 53 degrees.
Part B.
First line of Part A:
M < RPB + m < PRD = 180 degrees ( Internal angle between 2 parallel lines are equal).
Second line:
The 3 angles x, 62 and 65 degrees are all on the same straight line (AB), so they sum to 180 degrees.
ax + b = c solve for x
smiplify 3^2 x 3^4 x 3^6
PLEASE ANSWER QUICKLY
[tex] {3}^{2} \times {3}^{4} \times {3}^{6} [/tex]
[tex] = {3}^{2 + 4 + 6} [/tex]
[tex] = {3}^{2 + 10} [/tex]
[tex] = {3}^{12} [/tex]
6 A clothing store paid $30 for a jacket, and sold the jacket for $48.
What was the percent increase?
Answer:
60%
Step-by-step explanation:
% increase = Increase ÷ Original Number × 100
Answer:
60%
Step-by-step explanation:
Total increase in cost = $(48 - 30) = $18
Now,
% increase = Increase/Original amount × 100
=> 18/30 × 100
=> 18/3 × 10
=> 6 × 10
=> 60%
Question 1 of 51 Which of the following is not a Pythagorean triple O A. (5, 12, 13) O B. (7,8,9) O C. (3,4,5) D. (9,12,15)
Answer:
B
--------
Because:-
5, 12, 13 is a Pythagorean triple
3, 4, 5 is a Pythagorean triple
9, 12, 15 is a Pythagorean triple
7, 8, 9 is not a Pythagorean triple
use this rule:-
[tex]a^{2} +b^{2}=c^{2}[/tex]
Help help help help
Answer:
C = 18
Step-by-step explanation:
Put the numbers in place of their symbols and do the arithmetic. The diagram is showing you r = 3.
C = 2πr
C = 2(3)(3) . . . . . using 3 for π, as directed
C = 18
[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]
Here we've been provided with the information given that radius (r) = 3.
And we have to find the circumference (c) of circle. And we have been provided with the formula i.e C = 2πr.
Placing (π = 3) in the above equation,
[tex]:\implies\tt{c = 2\pi r}[/tex]
[tex]:\implies\tt{c = 2 \times 3 \times 3}[/tex]
[tex]:\implies\tt{c = 6 \times 3}[/tex]
[tex]:\implies\tt{c = 18}[/tex]
The circumference of circle is 18cm.In A Fraction What Is The Number On Top Called
Answer: numerator
Step-by-step explanation the bottom is the denominator
Hopes this helps✊
[tex]15yx^{2} -34y-16[/tex]
Answer:
15yx^2-34y-16
Step-by-step explanation:
Solve and show your work for each question...
[tex]0.\overline{36} = \dfrac{36-0}{99} = \dfrac{36}{99} = \dfrac{4}{11}\\\\\\0.3\overline{6}= \dfrac{36-3}{90} = \dfrac{33}{90} = \dfrac{11}{30}\\\\\\0.36 = \dfrac{36}{100} = \dfrac{9}{25}[/tex]
this is an area in which objects will interact with a magnet
the area of a square whose length is 4.5 m
area of a square = length × length
a=4.5×4.5
2x/5=9/15 what does x equal
Answer:
2x/5=9/15
2x=9/3
x=1.5
a water tank can hold up 80 gallons of water. if it is 40% full now. how many gallons of water does the tank contain?
Answer:
32 gallons of water
Step-by-step explanation:
If the total tank can hold up to 80 gallons of water, it is considered full when it contains 80 gallons. When the tank is 40% full, it has 40% of 80 gallons in the tank. 40% of 80 is 40/100*80=8*4=32 gallons of water.
F(x)=log2(x+3)+5 what's the x and y int.
Answer:
x int (-3), y it. (5)
Step-by-step explanation:
x+3=0, just subtract 3 and x = 3
Number to the right of parenthesis is always y int. for this sort of problem
