An object was dropped off the top of a building. The function f(x)=-16x^2+144f(x)=−16x 2 +144 represents the height of the object above the ground, in feet, xx seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
Answer:
Step-by-step explanation:
Given the height at which an ogject dropped modelled by the function f(x)=-16x^2+144
The height of the body on the ground occurs at when f(x) = 0
0 =-16x^2+144
16x^2 = 144
x^2 = 144/16
x^2 = 9
x = 3
The ball reached the ground after 3 secs
The domain of a function is the input function that will make the function exist. Based on the function given, the function can exist on all given input value of x. Hence the domain of the function will be;
Domain =(-\infty, infty)
The domain of the function is required.
The domain of the function is the set of real numbers
[tex]x\in(-\infty,\infty)[/tex]
The function is
[tex]f(x)=-16x^2+144[/tex]
The y intercept of the function is
[tex]y=-16\times 0+144\\\Rightarrow y=144[/tex]
[tex](0,144)[/tex]
The y intercept is the maximum height here.
The x intercepts are the points where the object is on the ground.
They are
[tex]0=-16x^2+144\\\Rightarrow 16x^2=144\\\Rightarrow x=\pm\sqrt{\dfrac{144}{16}}\\\Rightarrow x=\pm3[/tex]
[tex](3,0),(-3,0)[/tex]
The domain of the function is the set of real numbers
[tex]x\in(-\infty,\infty)[/tex]
The graph of the figure is attached.
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Related Questions
On Friday Simon ate three tenths of a kg of cherries. On Saturday, he ate half of a kg of cherries. What amount of cherries are left now if he had one kg of cherries
Answers
Answer:
1/5 kgStep-by-step explanation:
Initial amount = 1 kgEaten on Friday = 3/10 kgEaten on Saturday = 1/2 kgAmount of cherries left:
1 - (3/10 + 1/2) = 1 - (3/10 + 5/10) = 1 - 8/10 = 2/10 = 1/5 kgI need help asap thxss
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Answer:
Step-by-step explanation:
what is 5(3x+8) answer?
Answers
Answer:
15x + 40
Step-by-step explanation:
5(3x + 8)
Use the distributive property and multiply 5 by 3x and 8
5(3x + 8)
15x + 40
A sporting goods store received a shipment of 500 baseball gloves. 200 were left handed. What is the ratio of right handed gloves to gloves?
WILL RECIEVE BRAINLIST
Answers
Answer:
300:500
Step-by-step explanation:
If there are 200 left handed gloves, then there are 300 right handed gloves.
The total amount of gloves is 500, so its 300:500.
What is the binary number for 24
Answers
Answer:
Here im to lazy to solve so a pic
Step-by-step explanation:
Answer
11000
Explanation
I looked it up
there are 1,920fence posts used in a 12-killometer strech fence how many fence posts are used in one kilometer
Answers
Answer:
160
Step-by-step explanation:
Just divide 1920 into 12
Write a recursive rule for the sequence 10, 18, 26, 34….
Answers
Answer:
42
Step-by-step explanation: It keeps going up by 8
answer all of these please!
Answers
Answer:
1. Given
2. Given
3. Vertical Angles prop
4. SSS
Step-by-step explanation:
Hope this helps ya!
You are lucky I wish our teacher gave us proofs like this!
Factor the algebraic equation
36a+20
Answers
Answer:
4(9a+5)
Step-by-step explanation:
Answer:
4(9a+5)
Step-by-step explanation:
Their common factor is 4 so divide both by 4 and put it in parentheses times 4
The points (20, 80) and (30, 120) form a proportional relationship. What is the slope of the line that passes through these points?
Answers
(120-80)/(30-20)
= (90)/(10) = 9
The slope is 9
Baking flour which costs $4.05/kg is made by combining bleached flour which costs
$5.75/kg with unbleached flour which costs $1.45/kg. Find the number of kg of bleached flour and unbleached flour required to make 17.2 kg of baking flour.
A) 11 kg of bleached flour, 6.2 kg of unbleached flour
B) 13.7 kg of bleached flour, 3.5 kg of unbleached flour
C) 12.7 kg of bleached flour, 4.5 kg of unbleached flour
D) 10.4 kg of bleached flour, 6.8 kg of unbleached flour
Answers
Answer: D) 10.4 kg of bleached flour, 6.8 kg of unbleached flour
Step-by-step explanation:
First find the cost of making a kg of Baking flour.
Assume that x kgs of bleached flour and y kgs of unbleached flour make a kg of Baking flour.
The formulas would be;
x + y = 1
5.75x + 1.45y = 4.05
x = 1 - y
5.75 ( 1 - y) + 1.45y = 4.05
5.75 - 5.75y + 1.45y = 4.05
5.75 - 4.3y = 4.05
4.3y = 5.75 - 4.05
4.3y = 1.7
y = 1.7/4.3
y = 0.395 kg
x = 1 - 0.395
= 0.605kg
To make 1kg of Baking flour, 0.605kg of bleached flour and 0.395kg of unbleached flour is required.
To make 17.2kg of Baking flour;
Bleached flour = 0.605 * 17.2 = 10.4kg
Unbleached flour = 0.395 * 17.2 = 6.8 kg
-12.48-(-2.99)-5.62
-353.92-(-283.56)-131.29
831 106 (92)
(70 points.)
Answers
Answer:
-12164.91462:)
Step-by-step explanation:
Solution of the three expressions;
1). -12.48-(-2.99)-5.62 = -15.11
2). -353.92-(-283.56)-131.29 = -201.65
3). 831 / 106 (92) = 0.0852 (rounded to four decimal places)
What is PEMDAS?When resolving expressions containing several operations, the procedure to follow is denoted by the acronym PEMDAS. "Parenthesis," "exponents," "multiplication," "division," "addition," and "subtraction" are all represented by the letters P through E.
1). -12.48-(-2.99)-5.62
= -12.48 + 2.99 - 5.62 (double negative becomes positive)
= -15.11
Therefore, -12.48-(-2.99)-5.62 equals -15.11.
2). -353.92-(-283.56)-131.29
= -353.92 + 283.56 - 131.29 (double negative becomes positive)
= -70.36 - 131.29
= -201.65
Therefore, -353.92-(-283.56)-131.29 equals -201.65.
3). 831 / 106 (92)
This expression involves multiplication and division, and the order of operations (PEMDAS) tells us to perform the multiplication before the division. So we have:
= 831 / (106 x 92)
= 831 / 9736
= 0.0852 (rounded to four decimal places)
Therefore, 831 / 106 (92) equals 0.0852.
To learn more about the PEMDAS;
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The complete question:
Find the solution to the expressions given below;
1). -12.48-(-2.99)-5.62
2). -353.92-(-283.56)-131.29
3). 831 / 106 (92)
S
You have $18 to spend on lip balm and hand sanitizer. The equation 1.5x + 2.5y = 18 represents this situation, where x is tubes of
lip balm and y is bottles of hand sanitizer. How many tubes of lip balm can you buy when you do not buy any bottles of hand
sanitizer?
Answers
Answer:
(1.5×5) + (2.5×4)
Step-by-step explanation:
if 1.5 + 2.5 is 4.0, and you have $18 and you would see how many times 4 can go into 18 (18÷4) which has four times then you have $2 left so you can get another lip balm so x equals 5 and Y equals 4. I hope this helps! :D
Find the equation of the line through point (−2,3) and parallel to y=x+1. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
Answers
Answer:
y = x + 5
Step-by-step explanation:
The standard form of the slope-intercept is
y = mx + b
where m is the slope
According to this question, the slope is 1 for the given equation
If two lines are parallel, they have equal slopes
So the slope of the line we are trying to get is 1
We can now use the point-slope form to get the equation of the second line
Mathematically, that will be
y-y1 = m(x-x1)
where m is slope and (x1,x2) are the points given
So therefore;
y-3 = 1( x - (-2))
y-3 = x + 2
y = x + 5
How many pounds of turkey?
Answers
Answer:
11.25pounds
Step-by-step explanation:
Each person is eating two, 3/8
so 2x3/8=0.75 or 3/4
then do 3/4 x 15 = 11.25 pounds and for the price you do 11.25 x 1.05$ which is 11.81$ worth of turkey
Pekka tosses a ball out of a window that is 40 feet in the air. Its initial velocity is 15
feet per second. The path of the ball is represented by
h = -16t2 + 15t + 40
How long does it take for the ball to hit the ground (in seconds) rounded to the
nearest hundredth?
Answers
Answer:
2.12 seconds
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 15t + 40[/tex]
Required
Determine how long the ball hits the ground
When the ball hits the ground means that [tex]h(t) = 0[/tex]
So, we have that:
[tex]h(t) = -16t^2 + 15t + 40[/tex] becomes
[tex]0 = -16t^2 + 15t + 40[/tex]
Reorder
[tex]-16t^2 + 15t + 40 = 0[/tex]
Multiply through by -1
[tex]16t^2 - 15t - 40 = 0[/tex]
Solve using quadratic:
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 16[/tex] [tex]b = -15[/tex] [tex]c = -40[/tex]
So, we have:
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]t = \frac{-(-15)\±\sqrt{(-15)^2 - 4*16*-40}}{2*16}[/tex]
[tex]t = \frac{15\±\sqrt{(-15)^2 - 4*16*-40}}{2*16}[/tex]
[tex]t = \frac{15\±\sqrt{225 +2560}}{32}[/tex]
[tex]t = \frac{15\±\sqrt{2785}}{32}[/tex]
[tex]t = \frac{15\±52.77}{32}[/tex]
Split:
[tex]t = \frac{15+52.77}{32}[/tex] or [tex]t = \frac{15-52.77}{32}[/tex]
[tex]t = \frac{67.77}{32}[/tex] or [tex]t = \frac{-37.77}{32}[/tex]
[tex]t = 2.12[/tex] or [tex]t = -1.18[/tex]
But time can't be negative
So:
[tex]t = 2.12[/tex]
Hence, time to hit the ground is 2.12 seconds
Mrs. Kato has 6 bags of dried beans and a 2-pound bag of rice in one shopping bag. In another shopping bag she has a 5-pound bag of flour. The two shopping bags weigh the same amount. What is the weight of each bag of dried beans? Enter the correct answer in the box.
Answers
Given:
Mrs. Kato has 6 bags of dried beans and a 2-pound bag of rice in one shopping bag.
In another shopping bag she has a 5-pound bag of flour.
The two shopping bags weigh the same amount.
To find:
The weight of each bag of dried beans.
Solution:
Let x be the weight of each bag of dried beans.
So, weight of 6 bags of dried beans = 6x.
According to the question,
Weight of first bag = (6x + 2) pounds
Weight of second bag = 5 pounds
The two shopping bags weigh the same amount. So,
[tex]6x+2=5[/tex]
[tex]6x=5-2[/tex]
[tex]6x=3[/tex]
Divide both sides by 6.
[tex]x=\dfrac{3}{6}[/tex]
[tex]x=0.5[/tex]
Therefore, the weight of each bag of dried beans is 0.5 pounds.
The weight of each bag of dried beans is 0.5 pounds.
Given that,
Mrs. Kato has 6 bags of dried beans i.e. 6x and a 2-pound bag of rice in one shopping bag.In another shopping bag she has a 5-pound bag of flour. The two shopping bags weigh the same amount.Based on the above information, the calculation is as follows:
6x + 2 = 5
6x = 5 -2
6x = 3
x = 0.5
Therefore, we can conclude that the weight of each bag of dried beans is 0.5 pounds.
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Find the total surface area of this cuboid,
5 cm
4 cm
6 cm
Answers
Answer:
148
Step-by-step explanation:
Sa=2(lw+lh+wh)
Sa=2(4*5+4*6+5*6)
148=2(4*5+4*6+5*6)
Answer:
100 cm sq
Step-by-step explanation:
The answer is 100 cm sq because the formula would be:
SA= Ph + 2B
Sa= 10 x 6 + 2 x 20 (5 x 4)
SA= 60 + 40
SA= 100 cm sq
Please make me brainliest!!!
help please thank you sm
Answers
15. Which expression has the greatest value?
A. 142-(-172)
B. 1 12+ -1 12
C. -142 - (-14)
D. 142
Answers
Answer:
i think that its D
Step-by-step explanation:
hopes this helps
What is the solution of |x − 1| + 2 = 4? Enter your answers from least to greatest in the boxes
Answers
Answer:
down
Step-by-step explanation:
are there options
2. Similar rectangles have widths of 10 cm and 15 cm respectively. If the smaller rectangle's length is 18, what is the larger rectangle's length?
Answers
Answer:
8
Step-by-step explanation:
10/15=0.66666666666
0.66666666666 times 12 = 8 or the missing length
So the answer is 8 :)
create a function and explain why it is a function using academic vocabulary (input ,output, mapping, vertical line test and function (
Answers
(0,0)(1,2)(7,14)(10,20)
it is a function because each input has only one input.
or
using the vertical line test none of the points are on the same line
Three friends went apple picking and then counted the apples they picked.
Who had the largest red to green apple ratio? Use complete sentences to explain how you got your answer.
Answers
This is because his red to green apple ratio is equal to 1.25.
In order to determine that you take 20 and divide it by 16.
Carmen has the largest red to green apple ratio.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
from the given chart , we get,
the ratio as,
Carmen= 20:12
=1.6
Dylan = 12:10
=1.2
Eli = 16:20
=0.8
now, we have,
Carmen has the largest red to green apple ratio.
This is because his red to green apple ratio is equal to 1.6.
In order to determine that you take 20 and divide it by 12.
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Alto's dove 9 meters below the ocean's surface. She then dove 15 meters deeperShe then rose 19 1/4 meters. What was her position in realtion to the surface of water?
Answers
Answer:
Alto was 4.75 meters under the water, or -4.75.
Step-by-step explanation:
Alto dove 9 meters and then 15 meters. We can add those two which is 24 meters. Then she rose 19 and 1/4, so we have to subtract that from 24.
I hope this helped, and if it did I would appreciate it if you marked me brainliest.
thank you and have a nice day!
A recipe for pasta dough say's use 150 grams of flour per large egg how much flour is needed if 6 larg eggs are used ???
Answers
150 x 6 = 900
(150 is the grams PER egg)
(there is 6 eggs)
calculate the perimeter of a square with vertices on a circle of diameter 4 cm
Answers
Answer:
I dont like sqaures.
Step-by-step explanation: Their pointy.
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
g(x) = 3x – 6
g(x) = 3x + 6
g(x) = 3x – 6
g(x) = 3x + 6
Answers
Answer:
Its A
Step-by-step explanation:
Trust me
Answer:
a
Step-by-step explanation:
Solve for g
8.95 – 5.4g = 3.81 – 9.58 – 8.69
Answers
Answer:
3
Step-by-step explanation:
Answer:
g=4.33
Step-by-step explanation:
8.95 - 5.4g = 3.81 - 9.58 - 8.69
-5.4g = 3.81 -9.58 -8.69 - 8.95
-5.4g = 5.77 - 8.69 - 8.95
-5.4g = -14.46 - 8.95
-5.4g = 23.41
-5.4/-5.4 =23.41/-5.4
g=4.33
what is the answer?
Answers
Answer: 60
Step-by-step explanation:
It’s an equilateral triangle based on the congruent sides.