A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
Answers
As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,
(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.
(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.
As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.
We are required to determine the correct time domains for four different situations, by observing the plotted graph.
Part (A) is to determine the correct time domain where the water balloon's height remains the same.
From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
Part (B) is to determine the correct time domain where the height of the water balloon is increasing.
From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.
Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.
From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.
Since, [(30/1) > (10/0.5) > (30/3)],
Or, [30 > 20 > 10],
Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).
Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.
Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.
Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.
Time Domain: Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to the time interval over which, the function occurs.To learn more about Time Domain, click on the link below.
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Related Questions
Please help ASAP, will mark brainliest!
Which of the following proves these triangles are congruent?
Answers
Explanation:
ASA = angle side angle
It refers to knowing two pairs of congruent angles, and a pair of congruent sides between the angles.
The angle markers tell us which angles are congruent. The shared overlapped sides are congruent (since any segment is congruent to itself; aka reflexive property).
ASA is slightly different from AAS in that the congruent sides for AAS are not between the congruent angles.
q(x) = 1⁄2x−3; q(x) = −4
Answers
We can solve with functions exactly as we do algebraic equations. Our goal is to isolate the variable.
Solving the QuestionWe're given:
[tex]q(x) = \dfrac{1}{2}x-3\\\\q(x) = -4[/tex]
Solve using substitution:
[tex]\dfrac{1}{2}x-3=-4[/tex]
Isolate x:
[tex]\dfrac{1}{2}x=-4+3\\\\\dfrac{1}{2}x=-1\\\\x=-2[/tex]
Answerx = -2
Please answer with show work. Trigonometry!
Answers
So I wrote cosx = 6.2/23
Thus x = cos^-1 (31/115)
Name a pair of vertical angles.
Answers
The pair of vertical angles are
∠1 and ∠3∠2 and ∠4There are four angles made by the intersection of two lines. Those are ∠1, ∠2, ∠3 and ∠4
Vertical angles are the each of opposite angles formed when two lines meet each other at a point. So whenever two lines intersect each other four angles are formed and each set of opposite angles are called vertical angles
Here, two lines intersect each other and ∠1, ∠2, ∠3 and ∠4 are formed.
∠1,∠3 and ∠2,∠4 are the opposite angles
So the vertical angles are ∠1,∠3 and ∠2,∠4
Hence, the pair of vertical angles are
∠1 and ∠3∠2 and ∠4Learn more about vertical angles here
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2|x+3|+1>3
what the soulution??
Answers
A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Divide both sides of the inequality 2|x+1/3|3 to make it simpler:|x+1/3| < 3/2.
Consider the center of the group of numbers that fulfill 2|x+1/3|3 to be x = -1/3.
The maximum value of this set is obtained by adding 3/2 to this -1/3:
-1/3 + 3/2, or -2/6 + 9/6, or 7/6.
The bottom limit of this solution set is obtained by subtracting 3/2 from this and then -1/3:
-1/3 - 3/2, or -2/6 - 9/6, or - 11/6.
The answer range is (7/6, -11/6).
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I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answers
Answer:4,3,8
Step-by-step explanation:
Q10. Farmer John's apples were eaten by wasps, others were rotten and the rest were quality apples in the ratio 4: 10: 20 respectively. 20 apples had been eaten by wasps. a) How many rotten apples were there?
Answers
If wasps had eaten 20 apples then, 50 rotten apples were there and the rest of the apples were quality apples in the ratio of 4: 10: 20 respectively.
This is a problem from simple mathematical equations. We can solve this problem by following a few steps.
Let's consider x as the highest common factor of apples eaten by wasps, rotten and quality apples.
So, the number of apples eaten by wasps is, 4 × x = 4x
The number of rotten apples is, 10 × x = 10x
The number of quality apples is, 20 × x = 20x
As, we all know HCF of the numbers × ratio of numbers = The numbers
So, 4x = 20 as per the question.
Therefore, x = 5.
Now, we can write that the HCF is 5.
So, the number of rotten apples ≡ HCF × 10 = 5× 10 = 50.
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(2x+6)° (x+9)° find X
Answers
Answer:
sama sma tayi
Step-by-step explanation:
3×3()56(7)
HELP PLS IS DUE AT 10PM
Answers
Answer:
AS shown in the purse
Step-by-step explanation:
A. The school attendance happens in the sixth week
B. A(13) ≈ 42$
meaning : In the Thirdteenth week. The student attendance rate is 425
C. A(x)=400 =) x = 10
in the tenth week.The student attendance rate is 400
D.in the fourth week the least attendance nce.
E. It has 450 students
The number of attendance increased to 450.
And the area was flat
Which of the following expressions is equivalent to 2x + 3?
6(2)x
8(2)x
the quantity 2 to the power of x end quantity over 6
the quantity 2 to the power of x end quantity over 8
Answers
The expressions which is equivalent to 2x + 3 would be 4x + 6.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions. To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
We need to find the expressions which is equivalent to 2x + 3
Thus, we will Use the Distribute Property of Multiplication by multiplying the number outside the parenthesis with the numbers inside.
Let the expression be multiplying by 2 then;
2(2x + 3)
4x + 6
Hence, we can say that the expressions which is equivalent to 2x + 3 would be 4x + 6.
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how many books does matt have to sell to make 30$ for the week
Answers
Answer:
4 books a day
Step-by-step explanation:
$30 ÷7=4.28
so If you sell 4 books a day you get $30 I'n the end of the week
simplify this expression please. express using positive exponents only
Answers
2 - distribute the 5 and simplify
Answer - h^30j^30/g^15
The coordinates of the endpoints of MN are M(4,14) and N(13,8). Point O is on MN and divides it such that MO:NO is 2:1. What are the coordinates of O? Write your answers as integers or decimals. (, ) Submit
Answers
The coordinates of Point O that is on MN and divides it such that MO:NO is 2:1 is; (10, 10)
What are the coordinates that divide the line segment?We are given a line segment as MN with its' endpoint coordinates as;
M(4,14) and N(13,8)
Now, point O divides MN such that MO:NO is 2:1.
Now, the formula for the coordinate of the point that divides a line segment in the ratio a:b is;
(x, y) = (ax₂ + bx₁)/(a + b), (ay₂ + by₁)/(a + b)
Since point O is the point that divides the line segment in the ratio 2:1, we have;
O(x, y) = (2*13 + 1*4)/(2 + 1), (2*8 + 1*14)/(2 + 1)
O(x, y) = (30/3), (30/3)
O(x, y) = (10, 10)
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identify the terms , constants , coefficients and variables in the equation 13x + 5y - 2 = 3
Answers
Constants(constantly alone): 2, 3
Coefficients: 13, 5
Variables: x,y
Answer: 13 and 5= coeeficients, x and y = variables, -2 and 3 =constants
Step-by-step explanation:
The division 4+5i/2-4i is performed by multiplying the numerator and denominator by _
Answers
The division of (4+5i) / (2-4i) is performed by multiplying the numerator and denominator by 2+4i and the result of the given expression is (-3/5) + (13/10) i
The given expression is
(4+5i) / (2-4i)
Here we have to divide the given complex number
First multiply both numerator and denominator by 2+4i
(4+5i) / (2-4i) × (2+4i) / (2+4i)
= [tex]\frac{(4+5i)(2+4i)}{(2-4i)(2+4i)}[/tex]
Multiply the terms in the numerator and denominator.
= [tex]\frac{8+16i+10i-20}{2^2+4^2}[/tex]
= (-12+26i) / 20
= (-12/20) + (26/20)i
Divide both numerator and denominator by common terms
= (-3/5) + (13/10)i
Hence, the division of (4+5i) / (2-4i) is performed by multiplying the numerator and denominator by 2+4i and the result of the given expression is (-3/5) + (13/10)i
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What’s r^2-15=t+19 as a sentence?
Answers
Answer:
solve the following system of equations by using gauss elimination method
Given the function g defined by the formula g(x)=x-5/2 find the following: a. g(9)
b.g(0) c. 8(3)
d g(17)
NEED HELP RIGHT NOW!!! WILL GIVE 20 POINTS
Answers
For the given function g(x) , the values at given points :
a. g(9) = 2
b. g(0) = -2.5
c. g(3) = -1
d. g(17) = 6
What is function?A function is a set of rules that assigns each element of a set a unique element of another set.
If f is a function and f(x) = x+2, then if we have to find value of at x= 1 ,put 1 in place of x,
Then f(1 ) = 1+2 =3
Given that a function g is such that
g(x) = (x -5)/2
This the values of the function g at given points:
a. g(9) = (9-5)/2 = 4/2 = 2
b. g(0) = (0-5)/2 = -5/2 = -2.5
c. g(3) = (3-5)/2 = -2/2 = -1
d. g(17 ) = (17-5)/2 = 12/2 = 6
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Zoie was snorkeling 0.5 meters below sea level. To get a closer look at some marine life, she decided to dive down another 2 meters. How far below sea level does Zoe descend?
Answers
Answer: 2.5 meters below sea level
Step-by-step explanation:
0.5 + 2 = 2.5
Hope this Helps!
100 draws are made at random with replacement from a box containing these 6 tickets: 5, 1, 2, 4, 3, 6 a. what is the smallest possible value the sum of the 100 draws could be?
Answers
The solution of the given conditions are;
a. Smallest possible value of 100 draws = 100
b. Largest possible value of 100 draws = 600
c. Average of the box = 3.6
d. The expected value of the sum = 360
e. Standard Error = 0.189
Given tickets: 5, 1, 2, 4, 3, and 6.
Value of n = 100
Question a :
Smallest possible value of 100 draws = 100 * (Least of the ticket values)
= 100 * 1
= 100
Question b :
Largest possible value of 100 draws = 100 * (Highest of the ticket values)
= 100 * 6
= 600
Question c :
Average of the box = (5+1+2+4+3+6) / 6
= 22/6
= 3.6
Question d :
The expected value of the sum = 100 * the Average of the box
= 100 * 3.6
= 360
Question e :
Given, SD = 1.89
Standard Error =?
Standard Error = SD/[tex]\sqrt{n}[/tex]
SE = 1.89/√100
= 1.89 / 10
= 0.189
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May I please get help with this. For I am confused and have tried multiple times
Answers
Solution
Given the graphs below
For the graph of figure A and B:
Figure A and figure B are congruent.
Hence, yes they are congruent.
The transformation that map figure A onto figure B is to rotate figure A clockwise 90° about the origin.
For the graph of C and D:
Figure C and figure D are congruent.
Hence, yes they are congruent.
The transformation that map figure C onto figure D is reflect figure C over the y-axis
- Use the remainder thrm to determine if (x-2) is a
factor of f(x) = (3x4-3x³-9x² + 5x - 2) what is the remainder?
Answers
(x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].
What is a remainder theorem?Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a) that isn't essentially an element of the polynomial, you will find a smaller polynomial along with a remainder.
The Remainder Theorem: If (x-a) is a factor of the f(x) then f(a) = 0
Here,
f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex]
substitute a = 2
[tex]f(2)=3(2^{4}) -3(2) ^{3}-9(2)^{2}+5(2)-2[/tex]
= 48-24-36+10-2
= 32-36
f(2) = -4
f(2) [tex]\neq 0[/tex]
Hence, (x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].
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solve for x x/3 = 10
Answers
Answer:
[tex] \huge \sf \: x = 30[/tex]
Step-by-step explanation:
x/3 = 10
[tex] \frac{x}{3} = \frac{10}{1} [/tex]
Cross multiply
x = 30
Cancel out the 3 in x/3 with multiplication because multiplication is the inverse of Division.
(Remember to do it on both sides)
x/3*3 = 3 * 10 —> x = 30
Your answer is x = 30
Apologies if this is wrong.
I dont quite understand what this question is asking for.
Answers
By using the table of values, we have the following:
The value of f(-7) is equal to 4.The value of f(15) is equal to 0.The value of f(3) is equal to 2.The value of f(-4) is equal to 15.If f(x) = 5, the value of x is equal to 4.If f(x) = 2, the value of x is equal to 5.If f(x) = 0, the value of x is equal to 15.If f(x) = -6, the value of x is equal to 2.What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).
In this exercise, you're required to determine the value of each function based on the value of x shown in the table above. Therefore, you would identify the input variable (x-value) that corresponds to the value of the output variable (y-value or f(x)) in the given table and vice-versa.
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find the term to be added to 7g²-3g to make a perfect squre then factorize
Answers
Answer: Look at step by step
Step-by-step explanation:
(ax + b)(ax + b) = [tex]a^{2}[/tex] [tex]x^{2}[/tex]+ 2abx + [tex]b^{2}[/tex]
Substitute g into x
[tex]a^{2}[/tex] = 7
a = [tex]\sqrt{7}[/tex]
2ab = -3
b = -3 / (2 x [tex]\sqrt{7}[/tex])
[tex]b^{2}[/tex] = 9 / (4 x 7) = 9/28
So the term to be added to make a perfect square is 9/28
When factorized would get ([tex]\sqrt{7}[/tex]x - 3/2[tex]\sqrt{7}[/tex])([tex]\sqrt{7}[/tex]x - 3/2[tex]\sqrt{7}[/tex])
If this doesn't help, maybe it is best you ask your teacher instead of listening to a random person on the internet. Hope this helps though
...........................................
Answers
Answer:
-5 2
Step-by-step explanation:
a grocery store wants to examine the relationship between the sales amounts each day at two different locations, store a and store b. the sales amount each day, in dollars, was recorded for 10 days at each store. the least-squares regression line is yˆ
Answers
The mean of the 10 sales amounts for store A is $40,000
The least-squares regression line is
y=-3000+1.2x
where
x represents the sales amounts each day at store A
y represents the sales amounts each day at store B
we have
y=$45,000
substitute the value of y in the linear equation and solve for x
45000=-3000+1.2x
1.2x=48000
x=40000
therefore
The mean of the 10 sales amounts for store A is $40,000
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A cube-shaped
sculpture has a volume of
64 cubic feet. What is the
length of each edge of the
cube?
The length of each edge is
feet.
Convince Me! How can
you find the cube root of
64?
Answers
Check the picture below.
9x+7 what it is bc (9x+7)(-3x+20) is 39?
Answers
The value of the variable x is 2 and length of the segment AB = 25 and length of segment BC is 14.
What is segment addition postulate?If a Line segment AC is given in a plane and B is some point between the points A and C on the line segment AC. Then two segments of the line segment ac are formed that are AB and BC. and length of AC is equal to the sum of lengths of AB and BC.
Then AC = AB +BC
Given that B is point on the line segment AC
Length of AB line = 9x+7
Length of BC = -3x +20
Length of AC = 39
Using segment addition postulate,
we have AC = AB +BC
⇒ 39 = 9x+7 + (-3x) +20
⇒ 39 = 9x -3x +7+20
⇒39 = 6x +27
⇒ 39-27 = 6x
⇒ 12 = 6x
⇒ 2 = x
∴ Length of AB will be = 9(2) +7 = 25
∴ Length of BC will be = -3x + 20 = -3(2) +20 = 14
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The complete question is mentioned in the picture below:
dont understand so help
Answers
Answer:
D
Step-by-step explanation:
Look at the original figure that is complete. The left side of the figure has a length of 3 units, the top of the figure has a length of 2 units and the bottom of the figure has a length of 3 units.
If you multiply each of those lengths, you will have 9 (3x3), 6 (2x3) and 9 (3x3). Do you see in the large figure to the right, that you have a left side of 9, a top of 6 and a bottom of 9? That is what you original figure looks like if we multiply the sides by 3. We are missing the right side point. That is the point on the right side that points inward.
If you look at the original shape and start at the left had bottom corner, you would have to move up one and one to the right to plot the point to finish the figure. So, for the new figure we would need to go up three and three to the right to put the last point. That would be point D.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
The statements that are true about the quadratic function and its graph include the following:
The value of f(–10) = 82The graph of the function is a parabola.The graph contains the point (20, –8).How to determine the true statements about this function and its graph?In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.
Next, we would determine the statements about the quadratic function and its graph that are true:
At point (-10, 82), we have:
f(x) = 1/5 x² – 5x + 12
f(x) = x²/5 – 5x + 12
f(-10) = -10²/5 – 5(-10) + 12
f(-10) = 82
At point (20, -8), we have:
f(x) = 1/5 x² – 5x + 12
f(x) = x²/5 – 5x + 12
f(20) = 20²/5 – 5(20) + 12
f(20) = -8
In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.
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Complete Question:
Consider the quadratic function f(x) = 1/5 x² – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).