The height of a tennis ball tossed into the air is modeled by h(x) = 40x â€" 16x 2, where x is elapsed time in seconds. During what time interval will the tennis ball be at least 15 feet above the ground? x > 0. 5 seconds and x > 2. 04 seconds x > 0. 5 seconds and x ≤ 2. 04 seconds x ≥ 0. 5 seconds and x > 2. 04 seconds x ≥ 0. 5 seconds and x ≤ 2. 04 seconds.
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
PLEASEEEE HELPPPP ASAPPPP
Answer:
x ≈ 7.1
Step-by-step explanation:
Using the cosine ratio in the right triangle.
cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.3}{X}[/tex] ( multiply both sides by x )
x × cos27° = 6.3 ( divide both sides by cos27° )
x = [tex]\frac{6.3}{cos27}[/tex] ≈ 7.1 ( to the nearest tenth )
In 2019, the average full-time worker in the U.S. spent `8.5` hours working each workday. This is an increase on the average of `8.1` hours per workday in 2014. What is the percent change from 2014 to 2019? Round to the nearest tenth of a percent.
Answer 2019 /0.0047 /2014/ 0.493
Step-by-step explanation:
The percent change in average full-time worker in the U.S from 2014 to 2019 is 4.93%.
What is Percent Change?A percentage is a portion of a whole that is stated as a number between 0 and 100 as opposed to being expressed as a fraction.
The percentages of everything are 100%, nothing is 0%, 50% of something is 50%, and nothing is 0%.
Given:
In 2019, the average full-time worker in the U.S. spent `8.5` hours working each workday.
This is an increase on the average of `8.1` hours per workday in 2014.
So, Percent change = (Final value - initial value) / initial value x 100
Percent change = 8.5 - 8.1 / 8.1 x 100
Percent change = 4.93%
Thus, the percent change in average full-time worker in the U.S from 2014 to 2019 is 4.93%.
Learn more about the percent change here:
brainly.com/question/809966
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if you drove 200 miles at an average speed of 55 miles per hour, how long did it take you to drive 200 miles? pls help
Answer:
3 hours 38 minutes is what calculators online say
Step-by-step explanation:
Tell me which option is correct: (0,m) (b,0) (m,0) (0,b) which one of those
Answer:
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Class 11
>>Physics
>>Units and Measurement
>>Errors in Measurement
>>You measure two quantities ...
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You measure two quantities as A=1.0m±0.2m, B=2.0m±0.2m. We should report correct value for
AB
as
Medium
Solution
verified
Verified by Toppr
Correct option is
D
1.4m±0.2m
Here, A=1.0m±0.2m, B=2.0m±0.2m
AB=(1.0m)(2.0m)=2.0m
2
AB
=
2.0m
=1.414m
Rounding off to two significant figures, we get
AB
=1.4m
AB
ΔAB
=
2
1
(
A
ΔA
+
B
ΔB
)=
2
1
(
1.0
0.2
+
2.0
0.2
)=
2
0.3
Δ
AB
=
2
0.3
×
AB
=
2
0.3
×1.414=0.212m
Rounding off to one significant figure, we get
Δ
AB
=0.2m
The correct value for
AB
is 1.4m±0.2m
i need help asap please Question: A dress is on sale for d dollars. The regular price is 3 times as much.
Janine has enough money to buy 2 dresses at the regular price.
How many dresses can Janine buy at the sale price?
Answers i can choose from
A.
1 dress
B.
3 dresses
C.
6 dresses
D.
9 dresses 4th grade work
Answer:
It's C
Step-by-step explanation:
You can just use simple resoning to solve this. If the orginal dress cost three times as much as the dress on sale. Then the dress on sale would cost three times as less as the original dress. Let me know if i'm wrong tho
how to solve 1/2x +8 = 7+ 1/2x
[tex]\frac{1}{2}x +8=7+\frac{1}{2}x <=>\frac{1}{2}x -\frac{1}{2}x =7-8<=>0x=-1[/tex] (no solution)
P/s: [tex]\frac{1}{2}x +8\neq 7+\frac{1}{2}x[/tex]
Ok done. Thank to me :>
Seven tickets for a Broadway show cost $385. How much will only 4 tickets cost?
Answer:
That seems a little hard-
Step-by-step explanation:
Answer:
$220
Step-by-step explanation:
If seven tickets cost 385, then 1 ticket costs one-seventh of that amount, so we divide it by 7 to see how much one ticket costs.
385/7 = 55
One ticket is $55. To find out how much 4 tickets cost, multiply 55, the price of one ticket, by 4.
55 * 4 = 220
$ tickets cost $220
There are 19 men and 31 women on an airplane. What is the ratio of the number of male passengers to the total number of passengers?
Write your answer as a fraction. Use a slash ( / ) to separate the numerator and denominator.
Answer:
19/50
Step-by-step explanation:
19 males and 50 people are in total
Answer:
19/50
Step-by-step explanation:
number of men=19
total passengers = 19+31=50
ratio of men to total people's = 19/50
Identify the equation of the line graphed below. Prove by converting!
A. 2x + y = 4
B. 2x - y = 4
C. x + 2y = 8
D. x - 2y = 8
Are all real numbers either rational or irrational?
Answer:
Yes. All real numbers are either rational or irrational.
Step-by-step explanation:
The set of all irrational numbers is commonly defined as the set of all real numbers that are not rational.
Let [tex]\mathbb{R}[/tex] denote the set of all real numbers. Let [tex]\mathbb{Q}[/tex] denote the set of all rational numbers.
For any given real number [tex]x[/tex] ([tex]x \in \mathbb{R}[/tex],) either [tex]x\![/tex] is rational ([tex]x \in \mathbb{Q}[/tex]) or [tex]x\!\![/tex] isn't rational ([tex]\lnot (x \in \mathbb{Q})[/tex], such that [tex]x \not\in \mathbb{Q}[/tex] and thus [tex]x \in (\mathbb{R} \backslash \mathbb{Q})[/tex].)
Assume that [tex]x[/tex] isn't a rational number. By the definition of rational numbers, since [tex]x\!\![/tex] is a real number but not a rational number ([tex]x \in (\mathbb{R} \backslash \mathbb{Q})[/tex],) [tex]x\![/tex] would be an irrational number.
Therefore, either [tex]x[/tex] is rational or [tex]x\![/tex] is irrational. Every real number would either be rational or irrational.
Write, in slope-intercept-form, the inequality shown in the graph.
Two points which the boundary line intersects are shown?
Answer:
y > 3x - 4
Step-by-step explanation:
lmk if you want an explanation
An inground swimming pool contains 2.3 times 10 Superscript 4 units of water. Which unit of measure was used?
teaspoons
cubic centimeters
fluid ounces
gallonsCassie is measuring the volume of her fish tank to find the amount of water needed to fill it. Which unit of measurement should she use to eliminate the need to write the value in scientific notation? teaspoons inches gallons pounds
Answer:
a) gallons
b) gallons
Step-by-step explanation:
a)1 fluid ounce is about 6 teaspoons or 30 cubic centimeters or 1.8 cubic inches. 2.3×10^4 fluid ounces is less than 1 cubic yard. We suspect the pool is much larger than that, so its volume is probably measured in gallons.
__
b)Of the units listed, only teaspoons and gallons are units of volume. As we saw in the previous problem, a teaspoon is a pretty small volume in relation to the size of most fish tanks. The appropriate unit of measure would be gallons.
Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y=3x+4
y=3x+3
Select the correct answer from the drop-down menu.
Answer:
y=3x+4 I think I am correct hola amigo señorita a person in my class is called adiola adiola adiola hah
Answer:
Its inconsistent
Step-by-step explanation:
If you are doing 5.11 Unit Test: Systems of Equations - Part 1 from K12, this is your answer
The graphs of the lines do not intersect, so the graphs are parallel and there is no solution. Since there are no solutions, its inconsistent.
If it has at least ONE solution, its consistent.
If it has EXACTLY ONE solution, its consistent in dependable
If it has INFINITE AMOUNT of solutions, its consistent dependable
I need the function for the volume of the box for number 1
Answer:
Step-by-step explanation:
The volume of a rectanguiar shape like this one is V = L * W * H, where the letters represent Length, Width and Height. Here L is the longest dimension and is 28 - 2x; W is the width and is 22-2x; and finally, x is the height. Thus, the volume of this box must be
V(x) = (28 - 2x)*(22 - 2x)*x
and we want to maximize V(x).
One way of doing that is to graph V(x) and look for any local maximum of the graph. We'd want to determine the value of x for which V(x) is a maximum.
Another way, for those who know some calculus, is to use the first and second derivatives to identify the value of x at which V is at a maximum.
I have provided the function that you requested. If you'd like for us to go all the way to a solution, please repost your question.
Suppose $\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$. What is the smallest possible value for $x$?
The smallest possible value of x is the value less than 2/3
Given the series [tex]$\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$[/tex]
We need to find the smallest possible value of x as shown:
[tex]\frac{1}{x} > 1\frac{1}{2}\\ \frac{1}{x} > \frac{3}{2}\\[/tex]
Reciprocate both sides
[tex]x < \frac{2}{3}[/tex]
Hence the smallest possible value of x is the value less than 2/3
Learn more on inequality here: https://brainly.com/question/4192645
Answer:x=7
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
C
Step-by-step explanation:
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
(0,6)
(0,–6)
(6,0)
(–6,0)
Answer:
D: (-6,0)
Step-by-step explanation:
Set f(x) equal to 0 and solve for the values of x:
f(x) = (x+6)(x-3)
0 = (x+6)(x-3)
x+6=0 and x-3=0
x=-6 and x=3
Therefore, the x-intercepts are (-6,0) and (3,0). Because only (-6,0) is an option, then option D is correct.
Answer: (-6, 0)
Step-by-step explanation:
got it right on my test
Help please. Been stuck for a few mins now.
Answer:
p = -3v: (4, -1)f: (4, -4)d: y = 2Step-by-step explanation:
The equation ...
(x -h)² = 4p(y -k)
is the equation of a parabola with vertex (h, k) and vertex-focus distance of p. When p is negative (as here), it means the focus is below the vertex, and the parabola opens downward. The directrix is p units on the other side of the vertex from the focus.
The vertex for equation ...
(x -4)² = -12(y +1)
is (h, k) = (4, -1). The value of p is (-12/4) = -3, so the focus is (4, -1-3) = (4, -4), and the directrix is y = -1+3 = 2.
_____
Additional comment
As a check on the graph, you can remember that any point on the parabola is equidistant from the focus and directrix. You will notice the vertex is halfway between the focus and directrix, so you know that relationship is true there.
You will also notice that a horizontal line from the focus to the parabola intersects the same distance away from the focus as from the directrix. Thus the parabola distance relation holds at that point as well.
Systematic bias occurs when the way data are collected and measured is
inaccurate. These flawed data lead to unreliable results.
A. True
B. False
Help!!! Ill give 100 points!
Answer:
7/20
Step-by-step explanation:
Answer: if you calculate math yo7 would get 7/20
Step-by-step explanation:
Convert -439° to radians
Answer:
-439° × π / 180°
= -2.4388888889π rad
= -7.6619954163 rad
Step-by-step explanation:
π rad = 180°
US
Evaluate the following
expression using x = 10:
5x + 31
Answer:
The value is [tex]81[/tex]
Step-by-step explanation:
We need to find value of [tex]5x+31[/tex] when [tex]x=10[/tex]
We have
[tex]5\times10+31=50+31\\\\=81[/tex]
My friend needs your help
Answer:
Excuse me but there doesn't seem to be a question here, please let me know if there is so I can help you
Step-by-step explanation:
Have a great rest of your day
#Nova
Which is a better deal: A can of 3 tennis balls for $3 or a box of 10 balls for $9?
Answer:
a box of 10 balls for $9?
Step-by-step explanation:
because u buy 10 tennis balls for 9 dollars and the first one is not true
becuase u buy 3 balls of tennis with 3 dollars and the last answer is right
becuase you buy 10 balls for 9 that means its 1 dollar less for 10 balls
hope it helps
-x - 11 and the opposite of -11
Answer:
The opposite of -11 is 11, and I dont understand what else you're asking
Step-by-step explanation:
Giving brainiest pls help
Answer:
Ivan: 4
Caleb: 4, 4, 4, 4, 4, 4, 4
Step-by-step explanation:
For every 4 Ivan sees, Caleb sees 28. (4 times 7)
The perimeter of a rectangular piece of paper is 52 inches. The area is 133 square inches. What are the dimensions of the paper?
____inches by ____ inches
Answer:
7 inches by 19 inches
Step-by-step explanation:
We can use a system of equations for this.
x=length
y=width
2x+2y=52 (Perimeter)
xy=133 (Area)
We must find x and y that fit both these equations.
Hope this helps :)
Awnser please jsjshshshdh
Answer:
No
Step-by-step explanation:
A function cannot have two of the same x values (3 and 3)
I hope this helps!
Hannah completed 40 problems in 32 minutes.
I have to put it in a unit rate pls help
Answer: 1.25 problems/min
32 minutes --> 40 problems
1 minute --> 40/32
--> 1.25