A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:
f(t) = -16t^2 + 16t + 32
Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
A: 0.5 < t < 1
B: 0.5 < t < 2
C: 1 < t < 2
D: 1 < t < 1.5
Answers
Remember that to find the vertex [tex](h,k)[/tex] of a parabola of the form [tex]a x^{2} +bx+c[/tex] we use the vertex formula: [tex]h= \frac{-b}{2a} [/tex], and then, we evaluate our function at [tex]h[/tex] to find [tex]k[/tex].
We can infer for our parabola that [tex]a=-16[/tex] and [tex]b=16[/tex], so lets replace those values in our formula:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-16}{2(-16)} [/tex]
[tex]h= \frac{-16}{-32} [/tex]
[tex]h=0.5[/tex]
Now we now that the ball reaches its maximum height in 0.5 seconds.
Next, we are going to determine how long it takes for the ball to hit the ground. To do that we are going to set the time [tex]f(t)[/tex] equal to zero and solve for [tex]t[/tex]:
[tex]0=-16t^2+16t+32[/tex]
[tex]16t^2-16t-32=0[/tex]
[tex]16(t^2-t-2)=0[/tex]
[tex]t^2-t-2=0[/tex]
[tex](t+1)(t-2)=0[/tex]
[tex]t=-1[/tex] or [tex]t=2[/tex]
Since time cannot be negative, the answer is [tex]t=2[/tex]
We can conclude that a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground is B: 0.5 < t < 2
Answer:
A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:
f(t) = −16t2 + 16t + 32
Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
B is correct!
:)
Related Questions
what is 68 less than 5 times a number is equal to the number?
Answers
The number here is will be represented as under -
Let the number be x.
Thus, the 5 times the number will be = 5x.
Now, it says, the number is 68 less than 5 times a number.
The equation so formed will be -
5x - 68 = x
4x = 68
x = 68.
Thus, the number will be 17.
Let us re-check the number,
(5 × 17) - 68 = 17
85 - 68 = 17
17 = 17. Thus, the number will be 17.
When it comes to reimbursement packages, company a offers $175 plus $0.55 per mile. company b offers $200 plus $0.45 per mile. what number of miles driven would make the two reimbursement packages equal?
Answers
y = 0.55x + 175
y = 0.45x + 200
We equate both equations:
0.55x + 175 = 0.45x + 200
We clear the value of x:
0.55x - 0.45x = 200 - 175
0.10x = 25
x = 250 miles
Answer:
A number of thousands driven that would make the two reimbursement packages equal is:
x = 250 miles
Answer:250
Step-by-step explanation:
Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.
Answers
1. You have the area of the larger square shown in the figure above, is:
A=x²
2. Then, you have the area of the smaller square shown in the figure above, is:
A=3²
A=9
3. Therefore, the expression for the remaining shaded area is:
A=x²-9
A=(x-3)(x+3)
Joe will go to the swimming pool on 20 different days this month. • a one-day pass to the pool is $2.25. • a monthly pass to the pool is $30.00. how much money will joe save by buying a monthly pass
Answers
Jayden wants to find the dimensions of this parallelogram. He knows that the first step is to find the value of x. Which of these equations will result in the correct value of x?
A. 2x – 1 = x + 8
B. 2x – 1 = x + 1
C. x + 1 + 2x – 1 = 180
D. x + 1 = x + 1
Answers
Answer:
2x – 1 = x + 8
Step-by-step explanation:
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
Answers
P(t) = 1405233 * (1 - 0.011)^(t)
models the population at t years after 2010. Then, when P(t) = 1,200,000, we have
1200000 = 1405233 * (0.989)^t
(0.989)^t = 1200000/1405233
t = log(1200000/1405233)/log(0.989)
t = 14.27 years
This means 14.27 years after 2010. Therefore, the answer to this question is 2024.
A log function is a way to find how much a number must be raised in order to get the desired number. The population of the city will be 1,200,000 in the year 2024.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.
The decrease in the population of the city can be written as,
[tex]\rm Final\ population=(Initial\ population)\times (1-r)^n[/tex]
[tex]1,200,000=1,405,233(1-0.011)^n\\\\0.8539=(0.989)^n\\\\\rm log(0.8539)=n\ log(0.989)\\\\n= \dfrac{log(0.8539)}{log(0.989)}\\\\n=14.279 \approx 14.3[/tex]
Since the initial population was 1,405,000 in the year 2010, then the population of the 1,200,000 will be 14 years later.
Thus, the population of the city will be 1,200,000 in the year 2024.
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Anyone know this geometry question?
Answers
No combo of any of those angles add up to exactly 180 to suggest that they are parallel lines.
What is the sum of the arithmetic sequence 153, 139, 125, ..., if there are 22 terms?
Answers
[tex] S_{n} = \frac{n}{2}(2 a_{1}+(n-1)*d) [/tex]
n = number of terms = 22
a1 =First Term of the series = 153
d = Common Difference = 139 - 153 = -14
So, using the values, we get:
[tex] S_{22}= \frac{22}{2}(2*153+(22-1)*(-14)) \\ \\ S_{22}=132[/tex]
This means, the sum of first 22 terms of the series will be 132.
Answer:
Sum of the sequence = 132.
Step-by-step explanation:
The given sequence is 153, 139, 125,.......n terms.
Sum of the arithmetic sequence will be
S = n/2[2a + (n -1)d]
where n = number of terms
a = first term of the sequence
d = common difference
for the given sequence
a = 153
n = 22
d = 139 - 153 = -14
Therefore sum of 22 terms of the sequence will be
S = (22/2)[2×153 - (22-1)14]
= 11×[306 - 21×14]
= 11×[306 - 294] = 11×12 = 132
Sum of 22 terms of this sequence is 132.
Assume we have two lines which are perpendicular. If one line has a slope of 3, what is the slope of the other line? Enter your answer as an integer or fraction in lowest terms.
Answers
The slope of a line perpendicular to a line with a slope of 3 is -1/3. This is because perpendicular lines have negative reciprocal slopes.
Explanation:In mathematics, when two lines are perpendicular, their slopes are negative reciprocals of each other because the product of their slopes equals to -1. This means that if one line has a slope of 3, the slope of the other line would be the negative reciprocal of 3, which is -1/3. So, the slope of the other line is -1/3.
To understand this further, let's delve into the figure of Slope and the Algebra of Straight Lines. Here, 'm' represents the slope which is the rise over the run and 'b' is the y-intercept, which is the point at which the line crosses the y-axis. Considering the fact that the slope of the line is 3, there is an increase of 3 in the y-coordinate (or vertical axis) for every increase of 1 in the x-coordinate (or horizontal axis).
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What’s the answer for No.29 & 30 please hurry
Answers
4x -3(2x-3) = 31
distribute the -3(2x-3)
4x-6x+9 = 31
combine 4x-6x
-2x +9 = 31
subtract 9 from each side
-2x = 22
divide both sides by -2 to get x
x = 22 / -2 = -11
x = -11
now replace x in the first equation with -11 to solve for y
y = 2(-11) -3
y = -22 -3
y = -25
x = -11, y = -25 which is (-11,-25) so A is the correct answer
30) the solution is where the 2 lines cross which is at X = 2 and Y = 4 which is (2,4) so B is the correct answer
Make b the subject of the formula p=2a+b
Answers
p-2a=b
-b -b
p-b=2a
-p -p
-b=2a-p
/-1 /-1
b=-2a+p
hope this helps =)
I am really bad at math can someone please help and explain ?
Answers
root (10) ^ ((3/4) x)
Rewriting we have:
root (10) ^ ((1/4) 3x)
By power properties we can rewrite the expression as:
(8 ^ root (10)) ^ (3x)
Answer:
The equivalent expression is:
(8 ^ root (10)) ^ (3x)
option 4
36 ants including the queen created a new colony. after 9 monthe there are now 766 ants. at 17 months how many ants will live in the conoly
Answers
A cross section of a right triangular prism is created by a plane cut through the points shown and is also perpendicular to the opposite base.
what is the most specific name of the shape representing the cross section?
A. triangle
B. Rectangle
C. Trapezoid
D. Paralellogram
Answers
9514 1404 393
Answer:
B. Rectangle
Step-by-step explanation:
The cross section will be a rectangle, as illustrated in the attachment.
The correct answer is B. Rectangle.
To determine the shape of the cross section, we need to understand the properties of a right triangular prism and the nature of the plane cut. A right triangular prism has two congruent right triangles as its bases, and the lateral faces are rectangles.
When a plane cut is made through points that are vertices of the base right triangle and is perpendicular to the opposite base, the cross section will intersect all the lateral edges of the prism. Since the lateral edges are perpendicular to the base, the cross section will have four right angles, making it a quadrilateral.
Furthermore, because the cut is perpendicular to the opposite base, the cross section will have two pairs of parallel sides. One pair of parallel sides comes from the intersection with the two lateral faces that are parallel to each other, and the other pair comes from the intersection with the base and the top face of the prism, which are also parallel.
Given these properties, the most specific name for the shape of the cross section is a rectangle, as it is a quadrilateral with four right angles and opposite sides that are parallel and equal in length.
Therefore, the correct answer is B. Rectangle.
A triangle has vertices A (1, 5) B(2, 8) and C(2,0). It moves 3 units right and 5 units down.
HELP QUICK PLEASE
Answers
X is left to right, so moving 3 units right, you would add 3 to very X coordinate.
Y is moving up or down, moving 5 units down, means you would subtract 5 from every Y coordinate.
The new coordinates would be:
A(4,0) B(5,3) and C(5,-5)
The graph of f(t) = 3 • 2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
A. When it was purchased (year 0), the coin was worth $3.
B. In year 1, the coin was worth $6.
C. When it was purchased (year 0), the coin was worth $2.
D. Every year the coin is worth 3 more dollars.
Answers
Answer:
The answer is the option A
When it was purchased (year [tex]0[/tex]), the coin was worth [tex]\$3[/tex]
Step-by-step explanation:
we know that
The y-intercept of a function is the value of the function when the value of the independent variable is equal to zero
In this problem we have
[tex]f(t)=3(2^{t})[/tex]
the independent variable is the variable t
so
Find the y-intercept
For [tex]t=0[/tex] ------> year zero
Find the value of the function
[tex]f(0)=3(2^{0})=\$3[/tex]
That means ----> When it was purchased (year [tex]0[/tex]), the coin was worth [tex]\$3[/tex]
Find the ranges of the function ƒ(x) = |x + 4| + 1 and the range of the exponential function g(x) represented by the graph below.
Are they the same? Explain.
Answers
One of the ways you can answer this question is to graph both of the functions. You already have the graph of one of them. I've made the other one for you.
They don't look very much alike, do they?
You are asked for the ranges. The range of your graph is ∞ > y ≥ 1 which includes all the reals within that boundary.
The value of the range of the absolute value graph is ∞ > y ≥ 1 which includes all the reals within that boundary.
The graphs are not the same but the ranges are the same are the same <<< answer.
The spring has a stiffness k=200n/m and is unstretched when the 25 kg block is at
a. Determine the acceleration of the block when s=0.4m. The contact surface between the block and the plane has
Answers
This is a Physics problem involving Hooke's Law and Newton's second law of motion. The acceleration of a 25kg block when a spring it's resting on is extended by 0.4m is determined. The calculated acceleration is -3.2m/s², indicating the direction is opposite to the direction of displacement.
Explanation:The subject matter of this question is physics, specifically the area of mechanics dealing with forces, mass, and acceleration (Newton's Laws). The stiffness of a spring is given as k=200N/m and it is unstretched when the 25 kg block is resting on it. We're tasked with finding the acceleration of the block when the spring is extended by s=0.4m.
Firstly, let's find the force on the block using Hooke's Law which states that the force exerted by a spring is equal to the spring constant times the displacement (F=-kx). So, F=-200N/m*(0.4m)=-80N. The negative sign just indicates that the force is in the opposite direction of the displacement.
Secondly, we apply Newton's second law of motion (F=ma), where m is the mass and a is the acceleration. Rearranging the equation to find acceleration gives us a=F/m. Substituting our values gives a=-80N/25kg = -3.2m/s². The negative sign here indicates the direction of the acceleration, opposite to the direction of displacement. So, the acceleration of the block when the spring is extended by 0.4m is -3.2m/s².
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Which point is an x-intercept of the quadratic function f(x) = (x – 8)(x + 9)? (0,8) (0,–8) (9,0) (–9,0)
Answers
___________________________________________________________
Explanation:
___________________________________________________________
Given the quadratic function in "factored form" ;
→ with "y" substituted for: "f(x)" — as follows:
___________________________________________________________
→ " y = (x − 8)(x + 9) " ;
→ Find the "x-intercept" of the equation ;
→ {among the answer choices given} ;
___________________________________________________________
Note: The "x-intercept(s)" of an equation refer(s) to the coordinates of the point(s) on the graph of the equation at which the graphed equation crosses the "x-axis".
In other words, the "x-intercept(s)" of an equation refer(s) to the solution of the equation at which: " x = 0 " .
___________________________________________________________
At this point, let us consider our given answer choices:
___________________________________________________________
Note:
____________________________________________________________
Consider the first 2 (two) given answer choices:
____________________________________________________________
Choice: [A]: " (0, 8) " ;
Choice: [B]: " (0, -8) " .
____________________________________________________________
→ Both of these are INCORRECT ;
→ {since these 2 (two) answer choices have "non-zero" values as
"y-coordinates" .}.
Note that by definition, all "x-intercepts" MUST have "y-coordinates" with a value of "0" {zero}.
→ Both of these are INCORRECT ; since these 2 (two) answer choices have "non-zero" values as "y-coordinates".
→ Note that by definition, all "x-intercepts" MUST have "y-coordinates" with a value of "0" {zero}.
Note that:
___________________________________________________________
Choice: [A]: " (0, -8)" ; has "- 8" — [ not: "0" ] — as a: "y-coordinate" ;
and that :
Choice: [B]: " (0, 8) " ; has " 8 " — [not: "0" ] — as a: "y-coordinate".
____________________________________________________________
This narrows our answer choices to the last 2 (two) remaining choices:
____________________________________________________________
Choice: [C]: " (9, 0) " ; AND:
____________________________________________________________
Choice: [D]: " (- 9, 0) " .
____________________________________________________________
Note that both of them could be "x-intercepts" ; since both of them have
values of "0" {zero} as "y-coordinates" .
____________________________________________________________
→ Let us examining EACH of the remaining 2 (two) answer choices. It does not matter the order, but let us start with: Choice: [C]: " (9, 0) " .
→ Consider the original equation:
____________________________________________________________
→ " y = (x − 8)(x + 9) "
→ Note the answer choice given for Choice: [C]: " (9, 0)" .
→ This means that when we plug in "9" for "x" , we should get "0" for "y" ;
→ Let us plug in these values for "x" to see if "0" (for "y") holds true:
→ 0 =? (9 − 8)(9 + 9) ?? ;
→ 0 =? (1) ( 18) ?? ;
→ 0 ≠ 18 ;
→ As such: Choice: [C]: " (9, 0)" — is INCORRECT.
____________________________________________________________
→ At this time, we may assume that: "Choice [D]: " (-9, 0)" — the only remaining answer choice is the correct answer.
→ However, we shall examine this "answer choice" appropriately; as follows:
____________________________________________________________
→ Consider the original equation:
____________________________________________________________
→ " y = (x − 8)(x + 9) "
→ Note the answer choice for: [C]: " ( - 9, 0)" .
→ This means that when we plug in "-9" for "x" , we should get "0" for "y" ;
→ Let us plug in these values for "x" ; to see if "0" (for "y") ; holds true:
→ 0 =? (9 − 8)(- 9 + 9) ?? ;
→ 0 =? (1) ( 0) ?? ;
→ 0 =? 0 ?? ;
→ 0 = 0 ! Yes!
___________________________________________________________
As such:
__________________________________________________________
→ The correct answer is: Choice: [D]: " (-9, 0)" .
___________________________________________________________
if a recipe calls for 0.800 kg of flour , about how many ounces of flour does it need? (1lb=16 oz, 1 lb = 0.454 kg )
5.8 oz
11.0oz
28.2oz
227oz
Answers
1lb = 16 oz
1 lb = 0.454 kg
Applying the conversion of units we have:
(0.800) * (1 / 0.454) * (16/1) = 28.1938326
Rounding off we have:
28.2 oz
Answer:
it needs 28.2 oz of flour
Answer: The correct option is (C) 28.2 oz.
Step-by-step explanation: Given that a recipe calls for 0.800 kg of flour.
We are to find the number of ounces of flour that the recipe needs.
Given that
1 lb=16 oz and 1 lb = 0.454 kg
We will be using the UNITARY method for solving the given problem.
We have
0.454 kg = 1 lb
So, 1 kg will be equal to [tex]\dfrac{1}{0.454}~\textup{lb}.[/tex]
Therefore, 0.8000 kg is equal to
[tex]\dfrac{1}{0.454}\times 0.800=1.762~\textup{lb}.[/tex]
Now, 1 lb = 16 oz.
So, 1.762 lb = 16 × 1.762 = 28.19 = 28.2 oz.
Thus, the recipe needs 28.2 oz of flour.
Option (C) is CORRECT.
Algebra question ( Matrices and Determinants ) 20 points
Answers
The correct answer is option A
Answer:
.
Step-by-step explanation:
Use the graph below to answer the question that follows:
What are the amplitude, period, and midline of the function?
Amplitude: 4; period: 2π; midline: y = −1
Amplitude: 8; period: 2π; midline: y = 1
Amplitude: 8; period: π; midline: y = −1
Amplitude: 4; period: π; midline: y = 1
Answers
Amplitude:4 (total height of the graph divide 2)
period: 2π ( one full oscillation, 5π/2-π/2)
midline: y= -1 ( total height uses 8 boxes in
graph....midline would be equal
boxes on both side)
Answer:
Amplitude : 4
Period: 2π
Mid-line: y=-1
A is correct
Step-by-step explanation:
We are given graph of periodic function.
We need to find amplitude, period and midline of the function.
From graph:
Maximum value = 3
Minimum value = -5
[tex]\text{Mid-Line }=\dfrac{Max+Min}{2}[/tex]
[tex]\text{Mid-Line }=\dfrac{3-5}{2}=-1[/tex]
The mid-line equation, y=-1
Amplitude: Distance between mid-line and maximum value
Amplitude = 3-(-1) = 4
The amplitude of given graph is 4
Period: It is time when graph repeat their path.
In the given graph repeat their in 2π of interval.
The period of graph is 2π
The product of two consecutive integers is 156. what are the integers?" what type of equation should she create to solve this problem?
Answers
Answer:
12 and 13 or
- 13 and - 12
A quadratic equation r² + r - 156 = 0
Step-by-step explanation:
Let the first number be r, it means that the second will be r + 1.Given that the product of two consecutive integers is 156. we may interpret that to mean that
r(r + 1) = 156
r² + r - 156 = 0
r² + 13r - 12r -156 = 0
(r + 13)(r - 12) = 0
r = -13 0r 12
if r = -13, r + 1 = -12
If r = 12, r + 1 = 13
Marcia has $84 less than three times as much as sue. together they have $132. how much money does marcia have?
Answers
and then let 3x-84 = marcia
therefore
(x)+(3x-84)=132
4x-84=132
4x=216
x=54
however just solving for x doesnt completely solve. it only shows sues money because x = sue
for marcia
3x-84
3(54)-84
162-84
78
therefore Marcia has 78$.
To find out how much money Marcia has, a system of linear equations is set up and solved. Sue has $54, which means Marcia has $78 since she has $84 less than three times Sue's amount. They together have $132.
Explanation:The question involves solving a system of linear equations to determine how much money Marcia has if she has $84 less than three times as much as Sue. Together they have $132. To solve this, let's name the amount Sue has as S, and consequently, Marcia has 3S - $84. Adding both amounts, we get the equation S + (3S - 84) = $132.
Combining like terms gives us 4S - 84 = $132. We solve for S by first adding 84 to both sides, which yields 4S = $216. Dividing both sides by 4 gives us S = $54. Knowing Sue's amount, we can compute Marcia’s by multiplying Sue’s amount by three and then subtracting 84, so 3 x $54 - $84 = $162 - $84 = $78. Therefore, Marcia has $78.
Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a tota rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for X hours
Answers
Eliminate the parameter to find a cartesian equation of the curve. x = 3sin(t), y = 4cos(t)
Answers
To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. The cartesian equation of the curve is (x/3)^2 + (y/4)^2 = 1.
Explanation:To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. Starting with the given equations:
x = 3sin(t)
y = 4cos(t)
We can rewrite the equation for x as:
x/3 = sin(t)
And the equation for y as:
y/4 = cos(t)
Using the identities sin2(t) + cos2(t) = 1, we can square both equations and add them together:
(x/3)2 + (y/4)2 = (sin2(t) + cos2(t)) = 1
This is the cartesian equation of the curve.
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Which expression is equivalent to x+2+ [4x - x2+6x+8\x+4]
Answers
Answer: 4x
A graph of a linear function intersects the coordinate axes in points (1, 0) and (0, 2). What is the equation of this function?
Please answer! Thank you!!!
Answers
1) Find the slope : m=y2-y1/x2-x1 = 2-0/0-1 = 2/-1 = -2
2) y-y1 = m(x-x1)
y-0 = -2(x-1)
y = -2x + 2
The equation would be y = -2x + 2
y-y1 = -2(x - x1) where (x1,y1) is a point on the line
use x1 = 1 and y1 = 0:-
y = -2(x - 1)
answer is y = -2x + 2
you are purchasing a house 12 years from now the estimated purchase price is 171,600.00 you want to make a 20%down payment how much do you have to save per month to reach your goal
Answers
We need to save 20% of 171600; this is 0.2(171600) = $34320
We have 12 years to save for this; 12 months per year for 12 years is 144 months:
144x = 34320
Divide both sides by 144:
144x/144 = 34320/144
x = 238.33
Wich statement about the following equation is true ? 3x^2-8x+5=5x^2