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
Mrs. Purple bought 3.5 yards of yellow fabric. She used ⅔ of the fabric to make a chicken costume. Then she used the remaining fabric to make plush banana toys for her seven dogs. How much fabric was used to make each banana?
Answers
Answer:
[tex]0.17\ \text{yards}[/tex]
Step-by-step explanation:
Total length of yellow fabric = 3.5 yards
[tex]\dfrac{2}{3}[/tex] of the yellow fabric was made to make a chicken costume.
So, the fraction of the yellow fabric used to make toys for her 7 dogs is
[tex]1-\dfrac{2}{3}=\dfrac{1}{3}[/tex]
The amount of fabric to make the 7 toys is
[tex]\dfrac{1}{3}\times 3.5=1.17\ \text{yards}[/tex]
Assuming that equal amount of fabric was used for 1 toy for 7 of her dogs each.
The amount of fabric used for 1 dog's toy is
[tex]\dfrac{1}{7}\times 1.17=0.17\ \text{yards}[/tex]
The amount of fabric used to make each banana is [tex]0.17\ \text{yards}[/tex].
It takes Taylor hour to make of a batch of cookies. About how long will it take him to make 8 batches?
B.
3.6 hours
C.
5.4 hours
D.
7.2 hours
Answers
Answer:
it would be 8 hours.....
Step-by-step explanation:
im am a bit confused, why is that not an answer choice
The sum of 4 consecutive even numbers is 364 A. 91 B. 65 C. 89.5 D. 182
Answers
Answer:
91
Step-by-step explanation:
Sum of the middle two numbers is ''182'' for 4 consecutive even number.
What is Addition?The process of combining or adding two or more numbers is called the Addition.
We have to given that;
Sum of 4 consecutive even numbers = 364
Let 4 consecutive even numbers are,
⇒ (x - 2), x, (x + 2), (x + 4)
So, We can formulate;
⇒ (x - 2) + x + (x + 2) + (x + 4) = 364
Solve for x;
⇒ 4x + 4 = 364
⇒ 4x = 364 - 4
⇒ 4x = 360
⇒ x = 90
Hence, The two middle numbers are,
⇒ (x) = 90
⇒ (x + 2) = 90 + 2
= 92
So, Sum of two middle numbers = 90 + 92
= 182
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The complete question is this,
The sum of 4 consecutive even numbers is 364. What is the sum of the middle two numbers?
the sum of three times a number x and nine"
Answers
Answer:
3x+9
Step-by-step explanation:
you are multiplying 3 and x because it says "three times a number x" which means 3x and you are adding it to 9 which is 3x+9.
What is the length of side A in centimeters?
Answers
Answer:
6
Step-by-step explanation:
Answer:
10 cm
Step-by-step explanation:
6. Consider the inequality 12<-3 (x + 4). Which value of xis part of the solution set of this inequality?
Answers
Answer:
x < -8
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define inequality
12 < -3(x + 4)
Step 2: Solve for x
Distribute -3: 12 < -3x - 12Add 12 to both sides: 24 < -3xDivide -3 on both sides: -8 > xRewrite: x < -8Here we see that any value x that is smaller than -8 would work.
Temperatures have been falling steadily at 5°F each day. Which number
sentence shows how to find the change in temperature 7 days from today's
A)5 + 7 = 12°F
B)none of these
C)-5* 7 = -35°F
D)O 7-5 = 2°F
Answers
answer: none of these
T−7×−5 = Tn
Let T equal the present temperature
7 = the number of days
-5= the drop each day
Let Tn = the new temperature
cuales son las soluciones (o raices) de la ecuacion x^2 + 6x - 16 = 0?
Answers
Answer:
x = 2,-8
Step-by-step explanation:
Simplify 2 x × − 3 x × − x
Answers
Answer:
[tex]\huge\boxed{2x^x-3x^x-x=-x^x-x}[/tex]
Step-by-step explanation:
[tex]2x^x-3x^x-x=(2-3)x^x-x=-x^x-x[/tex]
A 32-ounce package of a snack mix is 24 percent pretzel. How many ounces are pretzels? A. 0.706 B. 0.768 C. 7.06 or D. 7.68
Answers
Answer:
D.7.68
Step-by-step explanation:
100%= 32 ounces
24%= 24% x 32ounces = 768 ounces
100% 100
= 7.68 ounces
Help with this question please ~
Answers
Answer:
60°
Step-by-step explanation:
We can get the other two angles in the top triangle because they are alternate interior. Then we subtract them from 180.
180-82-38=60
PLEASE HELPP. BRAINLIEST
As of July 1, 2014, the population of India was about 1,267,000,000. How can you write this number in scientific notation?
1. Move the decimal point to the right of the first digit. What is the first factor?
2. Count the number of digits after the decimal point. How many places did you move the decimal point?
3. Did you move the decimal point to the right or to the left? What does this tell you about the power of 10 in the second factor?
4. What is the second factor written as a power of 10?
5. Write the population of India in scientific notation.
Answers
Answer:
12,670,000,000-I think if its moving right one
Step-by-step explanation:
Need help please
What are the measures of angles B and D?
A. ∠B = 55°, ∠D = 55°
B. ∠B = 55°, ∠D = 125°
C. ∠B = 97°, ∠D = 97°
D. ∠B = 83°: ∠D = 97°
Answers
Answer:
One basic property of a parallelogram is that opposite angles have the same value. Hence angle B = angle D. (2n+15°) = (3n-5°). Then have one side for the unknown. The equation will be 3n=2n+15°+5°. To get the n, simplify the equation: 3n-2n = 20° or n = 20°. Afterwards substitute the value of n to the angles. Angle B = (2(20)+15), Angle D = (3(20)-5). Lastly, simplify the equations. Angle B = (40+15°) = 55° and Angle D = (60-5°)=55°. Therefore the value of angles B & D are both 55°.
Step-by-step explanation:
In the diagram, ABC is a triangle in which AB = 4 cm, BC = 6 cm and angle ABC = 150°. The line CX is perpendicular to the line ABX.
(i) Find the exact length of BX and show that angle CAB = tan^-1 (3/4+3√3)
(ii)
Show that the exact length of AC is √52 + 24√3 cm.
Answers
Part (i)
Angle ABC is 150 degrees. The angle CBX is supplementary to this, so,
(angleABC)+(angleCBX) = 180
angle CBX = 180-(angleABC)
angle CBX = 180-150
angle CBX = 30 degrees
Because of the right angle marker at point X, we can find that triangle CBX is a 30-60-90 triangle. This special type of right triangle has its hypotenuse twice as long as the short leg, which we'll call y. The long leg is equal to y*sqrt(3) units.
The diagram shows BC = 6 is the hypotenuse, so the short leg is y = 6/2 = 3. The longer leg is y*sqrt(3) = 3*sqrt(3) which is the distance from B to X.
In summary so far,
CX = 3
BX = 3*sqrt(3)
We have enough information to find the tangent of angle CAB, and then find the actual angle itself.
tan(angle CAB) = opposite/adjacent
tan(angle CAB) = (CX)/(AX)
tan(angle CAB) = 3/(4+3*sqrt(3))
angle CAB = arctan( 3/(4+3*sqrt(3)) )
I'm using arctan in place of tan^(-1) which is the same basic function, just different notation.
========================================================
Part (ii)
Focus on triangle AXC. The legs we found were
AX = 4+3*sqrt(3)
CX = 3
Use the Pythagorean theorem to find the hypotenuse AC
a^2 + b^2 = c^2
(AX)^2 + (CX)^2 = (AC)^2
(AC)^2 = (AX)^2 + (CX)^2
(AC)^2 = (4+3*sqrt(3))^2 + (3)^2
(AC)^2 = (4+3*sqrt(3))(4+3*sqrt(3)) + 9
(AC)^2 = 4(4+3*sqrt(3))+3*sqrt(3)(4+3*sqrt(3)) + 9
(AC)^2 = 16+12*sqrt(3)+12*sqrt(3)+27 + 9
(AC)^2 = 52+24*sqrt(3)
AC = sqrt( 52+24*sqrt(3) )
Note that AC is a length so AC is positive. We don't have to worry about the plus minus.
This is known as a nested radical since one square root is buried in another.
We can write that as [tex]AC = \sqrt{52 + 24\sqrt{3}}[/tex] if you're curious as to how that looks on paper.
Using your calculator, you should find that,
[tex]\sqrt{52+24\sqrt{3}} \approx 9.673118[/tex]
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.
Given a scale factor of 2, find the coordinates for the dilation of the line segment with endpoints left parenthesis negative 1 comma 2 right parenthesis and left parenthesis 3 comma negative 3 right parenthesis.
A.(2,4) and (6,6)
B. (-2,2) and(6,-3)
C. (-2,4) and (6,-6)
D. (2,-1) and (-3,3
Answers
Answer:
i think its answer is option A
does anyone know this?
Answers
Answer:
2.4x10^-2
Step-by-step explanation:
since this number is a decimal you will use a negative number above the 10...
Choose the linear equation written in slope-intercept
form that matches each graph.
Answers
Answer:
D
Step-by-step explanation:
y-intercept or "b":
the line touches the y-axis at -4
slope:
the line rises 1, runs 1 every time
equation:
the y-intercept of -4 combined with the slope of 1/1 is the equivalent of
y=1x/1-4 OR in a more simplified format: D, y = x - 4
O Perímetro de triângulo isósceles mede 24cm. Qual é a medida de comprimento dos lados congruentes sabendo-se que o lado não congruente mede 7cm de comprimento?
Answers
Answer:
La longitud de los lados congruentes =
B = 8.5cm
C = 8.5 cm
Step-by-step explanation:
El perímetro del triángulo isósceles mide 24 cm.
El lado no congruente mide 7 cm de largo.
Lados congruentes significa lados que son iguales o iguales entre sí.
El perímetro de un triángulo es =
Lado A + Lado B + Lado C
Por lo tanto,
24 = 7 cm + B + C
24 - 7 = B + C
17 cm = B + C
Los dos lados son congruentes,
B = C
Por lo tanto, 17 cm / 2
= 8.5 cm
La longitud de los lados congruentes =
B = 8.5 cm
C = 8.5 cm
raised the points and will mark u as brainliest please help.
Answers
Answer:
1. x = 102. x = -63. 944. x = 2Step-by-step explanation:
1. F and M are equal angles and sum of internal angles = 180, so
2(7x + 5) + 30 = 18014x + 10 + 30 = 18014x = 140x = 102. Triangle is equilateral as all angles are equal, so all sides are equal:
4x + 43 = -2x + 74x + 2x = 7 - 436x = -36x = -63. Isosceles triangle with equal angles of R and T:
4x + 7 = 7x - 20 (using values as per picture not text)7x - 4x = 20 + 73x = 27x = 9Angle S is
180 - 2(4*9 + 7)= 180 - 2(43) = 180 - 86 = 944. Angle 2 is supplementary with 156 as isosceles triangles and vertical angles are equal, therefore:
180 - 156 = 6 + 9x24 = 6 + 9x18 = 9xx = 2Do these pairs of values (x and y) represent two quantities that are
proportional?
ху
3 12
520
624
9 36
Answers
Answer:
yes
Step-by-step explanation:
Each value of x multiplied by 4 gives the corresponding value of y, that is
3 × 4 = 12
5 × 4 = 20
6 × 4 = 24
9 × 4 = 36
Thus x and y are proportional and the constant of proportion is 4
What is the image of the point
(
1
,
−
4
)
(1,−4) after a rotation of
18
0
∘
180
∘
counterclockwise about the origin?
Answers
Answer:
The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)
Step-by-step explanation:
Rotation means that a point is being moved in clockwise or counterclockwise direction with some angle.
The rotation can be done in 90, 180, 270 degrees.
Given point is:
(1,-4)
When a point (x,y) is rotated 180° counter clockwise its coordinates become (-x,-y) the negative of original point.
So for the given point the coordinates will become (-1,4)
Hence,
The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)
Plz answer this math problem
Solve problems a,b,c,d,e,and f. With the graph
Answers
Answers:
a. f(-4)=2
b. f(0)=0
d. f(-5)=0
e. x when f(x)=-2 answer: 2
f. x when f(x)=0 answer: 0
Sorry, I can’t answer c. f(3)= because when x is three from the x-axis on the graph, the line that meets 3 from the x-axis doesn’t show a whole number y-coordinate on the graph :(
But I hope this helps and answers your question :)
What is the length of a segment with endpoints at (-3,4) and (4,4)
Answers
Answer:
The length is 8
Step-by-step explanation:
Start with a male and a female rabbit. After a month, they mature and produce a litter with another male and female rabbit. A month later, those rabbits reproduce and out comes — you guessed it — another male and female, who also can mate after a month. After a year, how many rabbits would you have?
Answers
Answer:
24 thereabouts
Step-by-step explanation:
Well every two months there are two new rabbits so I multiplied two and twelve. This got me twenty-four. I hope this helps! :) I don't know if this is right or not I attempted this in my head.
Answer:
The answer is D
Step-by-step explanation:
Took the test
I'm confused on how to do that?
Answers
Answer:
(8, 0), (12, 4), (16, 8)
Step-by-step explanation:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
(20, 12)
(4, - 4)
m = [tex]\frac{-4-12}{4-20}[/tex] = 1
y - 12 = (1)(x - 20)
y = x - 8
y = 8 - 8 = 0
y = 12 - 8 = 4
y = 16 - 8 = 8
* Ms. Quintero has visited 16 of the 50 states. What percent of the states has she visited? KEY Part (is) Whole(of) % 100 Whole
A.25%
B.32%
C.16%
D.8%
Answers
Answer:
B. 32%
Step-by-step explanation:
16/50 = 32% lol
goodluck!
I WILL GIVE YOU BRAINLIEST AND I WILL PAYPAL YOU 5 BUCKS, PLEASEE JUST SOMEONE ANSWER THIS QUESTION FOR ME
If a figure starts off in a Quadrant I and is reflected along the x-axis and then rotated 180 degrees about the origin, what quadrant will it land on?
Answers
Answer:
Quadrant 2
Step-by-step explanation:
It goes over the x axis and rotates 180 which is half a a circle.
Haha you don't got to pay someone to help you bro
bruh if you can help with algebra 2 please help
Answers
Answer:
what do you need?
Step-by-step explanation:
pictures would be nice
Answer:
yea sure whats the problem
Simply the expression 7y+4x+4-2x+8