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.
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What is 2 rounded to the nearest whole number?
Answer:
2
Step-by-step explanation:
I NEED HELP PLEASE will give crown
Answer:
hey. use cymath. its easier and youll me able to answer more questions like this. it also shows you the whole process. here look:
Step-by-step explanation:
Please Help
Factor the polynomial: x^3 + 3x - 2x - 6
Answer:
(x^2-2)(x+3)
Step-by-step explanation:
x^3 + 3x^2 - 2x - 6
x^2(x+3)-2(x+3)
(x^2-2)(x+3)
Need help ASAP! Directions in picture ;)
Answer:
Simplifying
X + 59 + 84 + X + 51 = 180
Reorder the terms:
59 + 84 + 51 + X + X = 180
Combine like terms: 59 + 84 = 143
143 + 51 + X + X = 180
Combine like terms: 143 + 51 = 194
194 + X + X = 180
Combine like terms: X + X = 2X
194 + 2X = 180
Solving
194 + 2X = 180
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-194' to each side of the equation.
194 + -194 + 2X = 180 + -194
Combine like terms: 194 + -194 = 0
0 + 2X = 180 + -194
2X = 180 + -194
Combine like terms: 180 + -194 = -14
2X = -14
Divide each side by '2'.
X = -7
Simplifying
X = -7
A movie screen has an area of 162 square meters and a perimeter of 54 meters. What are the dimensions of the screen?
____meters by ___ meters
Answer:
18 meters by 9 meters (or 9 meters by 18 meters)
Step-by-step explanation:
lets say the dimensions are x and y. we have x*y=162, and 2x+2y=54. from the second equation we have x+y=27 so y=27-x. plug this into the first equation to get x(27-x)=162 or -x^2 + 27x = 162. x^2 - 27x + 162 = 0. simplify to get (x-18)(x-9)=0. so x=18 or x=9. when x=18, y=9, when x=9, y=18 so the dimensions are 18 by 9 meters
Which of the following are equivalent to the expression 9/4 ( 1.75 - 2 1/4)? Select all that apply.
A. -9/8
B. 1.6875
C. -2 1/4
D. 1 1/8
E. 7/4
F. -1.125
Answer:
9/4 (1.75 - 21/4)
=9/4 (1.75 - 5.25)
=2.25 -3.5
= -1.25
I think your f answer is wrong
there should be -1.25
Write the integer from least to greatest. 4, 12, -12, -11
Answer:
-12, -11, 4, 12
Step-by-step explanation:
A negative number is less the higher it is, and a positive number is more the higher it is
A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories.
(a) Determine how many calories 6 brownies would have.
(c) Determine how many calories 14 brownies would have. Round to the nearest calorie.
(b) Determine how many calories 21 brownies would have.
(d) If c represents the number of calories and b represents the number of brownies, write a proportional relationship involving c and b and solve it for c.
(e) Graph the proportional relationship you found
in part (d) on the grid shown. 300
200 100
(f) Using the graph, what is the smallest whole number of brownies a person would need to eat in order to consume 125 calories? Illustrate on your graph.
(g) Algebraicallydeterminethenumberofbrownies a person would need to eat in order to consume 300 calories.
Answer:
Step-by-step explanation:
R
The number of calories in 14 brownies is 233 calories.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories.
The first step is to determine the average calorie in 1 brownie.
Average calorie = 50 calories / 3 = 16.667 calories
In order to determine the number of calories in 14 brownies, multiply the average calorie by 14 brownies.
Total calories = 16.67 x 14 = 233 calories
Hence, The number of calories in 14 brownies is 233 calories.
learn more on multiplication click:
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f(x) = -4(x+2) what is f(4)
Answer:
-24
Step-by-step explanation:
f(4)= -4(x+2)
f(4)= -4(6)
f(4)= -24
Answer:
F(x)=-4(x+2)
0=-4-8
4x=-8
X=-2
So,-2×2
-4
Step-by-step explanation:
Have a great day!
What is the common ratio for the geometric sequence?
18,12,8, ...
16/3
Enter your answer in the box.
Answer:
Answer below
Step-by-step explanation:
basically, what should we multiply each term by to get next term
18 times what=12
what=12/18=2/3
12 times what=8
what=8/12=2/3
common ratio is 2/3
_____________________________________________________
(hope this helps can I pls have brainlist (crown)☺️)
(Uhm....This is a question out of maths) How many floors are 78 steps
Lily needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3.5 hours and charged her $159 for parts. The total was $456.50. Write and solve an equation which can be used to determine x x, the cost of the labor per hour.
The equation to represent the problem is written as
$456.50 = 3.5x + $159
the cost of the labor per hour is $85.
How to determine the cost of the labor per hourLet x be the cost of the labor per hour.
The technician worked on the computer for 3.5 hours, so the labor cost would be 3.5x.
The total cost, including the labor and parts, was $456.50.
So, we can set up an equation to represent the total cost:
Total cost = Labor cost + Parts cost
$456.50 = 3.5x + $159
Solving for x:
Subtract $159 from both sides:
$456.50 - $159 = 3.5x
$297.50 = 3.5x
Finally, divide both sides by 3.5 to find the value of x:
x = $297.50 / 3.5
x = $85
Therefore, the cost of the labor per hour is $85.
Learn more about writing equation
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Find the area of the circle. Use 3.14 for pi *
87.9
614.5
153.8
43.9
Answer:
614.5
Step-by-step explanation:
Hope this helps!
Answer:
87.9
Step-by-step explanation:
The formula for the area of a circle is pi times r to the power of two, written as πr^2. so we input our values.
πr^2
(3.14)(14^2)
(3.14)(196) ≈ 87.9
Find the diameter of a circle with a circumference of 443 feet. Use 3.14 for pi
143
21
7
5
and if you can go answer my other questions????? plzzz
What forms of the following equation in?
y=5x−3
Triangle UVW is dilated by a scale factor of 3 to form triangle UVW. Side VW
measures 54. What is the measure of side VW?
Answer:
162
Step-by-step explanation:
In geometry, dialation is increasing the size of a shape on a plane. Since the porblem you have givine isn't requiring the triangle to be centered around a point, this is fairly easy. If you are increasing UVW by a scale factor of 3, you are multiplying each side by 3. So, if side VW is 54, after dilation VW' will have a length of 162. (54 × 3 = 162)
Hope that helped!
please please help for brainlist !!!!!!!!
f(x) is linear.
g(x) is exponential.
F(x) is linear! Remember, linear functions have a set amount of rate of change, in this case it’s 2! G(x) is a exponential function because instead of going down by a certain amount, it’s simply going down by half.
Hope this helps!
slopeeeeeeeeeee please help me someone no bots
Answer:
5) -2
6) 1
7) -4/3
8) I'm not sure for this one
9) 8
10) 9/5 i think
1) A
2) D or A
3) C
4) A
Step-by-step explanation:
Slope intercept form: y = mx + b, and m is the slope, and b is the y-intercept
What two numbers add to -6 and multiple to 6
9. The perimeter of the rectangle below is 65 inches.
2x
a. What is the value of x?
32x + 1
b. What are the dimensions of the rectangle?
65*2x=_________
32x+1=_________
x=65*2x=32x+1
`this is the solution `
Which congruence criteria is met in the following scenario?
AAS
ASA
SAS
None, because the sides of one triangle are NOT congruent to the sides of the other triangle.
SSS
A commercial airplane is flying at an elevation of 15,000 feet and ascends to an elevation of 20000 feet at a rate of 1250 feet per minute. How many minutes does this ascent take?
Answer:
4 minutes
Step-by-step explanation:
Put it into an equation
20000 = 1250x + 15000
Subtract 15000 from both sides
5000 = 1250x
Divide both sides by 1250
4 = x
When looking at a graph, explain how you would know two variables were not proportional.
Answer:
a straight line that does not go through the origin.
HELPPP EASY MATH IM IN 5 GRADE
Answer:
What's the question of the problem
Simplify each expression by filling in the box.
Answer:
1. (2^3)^3 = 2^x x=9
2. 4^x x = 6 5^y y= 9
3. 3^6/3^3 = 3^x x = 3
Five times the difference of a number and 8 is 19.
3. Write the equation of the altitude from B for A(-7,-5) B(-5,5), C(2, 1).
Answer:
y -5 = -3/2(x +5)
Step-by-step explanation:
The altitude from B is perpendicular to segment AC. The slope of segment AC is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-5))/(2 -(-7)) = 6/9 = 2/3
The slope of the altitude line will be the opposite reciprocal of this, so is ...
-1/m = -1/(2/3) = -3/2
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -5 = -3/2(x +5) . . . . . line with slope -3/2 through B(-5, 5)
_____
Additional comment
The equation can be put in other forms, as you may wish. Solving for y gives the slope-intercept form.
y = -3/2x -5/2 . . . . . slope-intercept form
3x +2y = -5 . . . . . . . standard form
In ΔJKL, j = 74 cm, k = 14 cm and l=80 cm. Find the measure of ∠J to the nearest degree.
Answer:
∠J = 60°
Step-by-step explanation:
The Law of Cosines tells you ...
j² = k² +l² -2kl·cos(J)
Solving for J gives ...
J = arccos((k² +l² -j²)/(2kl))
J = arccos((14² +80² -74²)/(2·14·80)) = arccos(1120/2240) = arccos(1/2)
J = 60°
_____
Additional comment
It is pretty rare to find a set of integer side lengths that result in one of the angles of the triangle being a rational number of degrees.
Answer:
60
Step-by-step explanation:
please help me to get the answers please its important
Answer:
Q16a: 432 cm³
Q16b: sides: 20 m, 6 m; height: 13 m.
Step-by-step explanation:
Q16aEach cube will have a volume ...
V = s³
V = (6 cm)³ = 216 cm³
The two cubes together will have a volume that is twice that.
The cuboid volume is 432 cm³.
__
Q16bLet h represent the height of the trapezium. Then its area is ...
A = 1/2(b1 +b2)h
169 = 1/2((h +7) +(h -7))h = 1/2(2h²) = h²
h = √169 = 13 . . . . . distance between the parallel sides
The side lengths are h+7 = 20 m and h-7 = 6 m. The distance between them is 13 m.
Manuel has 4
4 gallons of diesel in his tractor. If the tractor holds 7 gallons of diesel
many more gallons does he need to add to completely fill the tractor's fuel tank
Answer:
3
Step-by-step explanation:
7-4=3
Answer:
He has three!
Step-by-step explanation:
7-4=3 so manuel needs three more gallons! Hope this helps! :)