ANY HELP WOULD BE REALLY APPRECIATED
Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given by h(t) = −16t^2 + 79t + 6, where h is in feet and t is in seconds. The height of Andre's baseball is given by the graph below (it's the attached image). Brett claims that his baseball went higher than Andre's, and Andre says that his baseball went higher.
1. Who is right? Fill out the table below to justify your answer. Approximate
when necessary (table is second attached image).
Answers
1. Brett was right because her baseball reached a maximum height of 103.52 feet.
2. A table that justifies Brett's claim is shown below.
In Mathematics and Geometry, the maximum value of any function is a point on the graph where the function reaches its highest point. Additionally, the maximum value of Brett's quadratic function can be determined by finding the axis of symmetry;
Axis of symmetry, x = -b/2a
[tex]h(t) = -16t^2 + 79t + 6[/tex]
where:
a = -16, b = 79, and c = 6.
By substituting the values of a and b into the formula, we have;
Axis of symmetry, x = -79/2(-16)
Axis of symmetry, x = 79/32 = 2.46875.
Now, we can determine the maximum value (vertex) as follows;
[tex]h(t) = -16t^2 + 79t + 6\\\\h(2.46875) = -16(2.46875)^2 + 79(2.46875) + 6[/tex]
h(2.46875) = 103.52 feet.
Based on the graph, we can logically deduce that the maximum height attained by Andre's baseball was below 80 feet. Hence, Brett was right.
Lastly, we would complete the table as follows;
t Brett Andre
0 6 6
1 69 58
2 100 78
3 99 67
4 66 6
5 0
In conlusion, we can logically deduce that Brett was right because her baseball reach a maximum height of 103.52 feet, which was greater than Andre's.
Related Questions
What’s the answer for this question:)
Answers
f (x) = x + 4 if -4 <= x <3
f (x) = 2x-1 if 3 <= x <6
We observe that the function is defined from x = -4 (including it) to x = 6 (without including it).
Therefore, the domain of the function is:
[-4, 6]
Answer:
[-4, 6]
option 3
What is -2(3x+12y-5-17x-16y+4) simplified?
-40x+8y+2
28x+8y+2
28x+6y+2
-28x-8y+2
Answers
Combine like terms:
[tex]=-2(-14x-4y -1)[/tex]
Distribute 02:
[tex]=28x + 8y + 2[/tex]
A simplified expression involves rewriting an expression in a simpler form
The simplified expression is: 28x+8y+2
The expression is given as:
-2(3x+12y-5-17x-16y+4)
Collect like terms
-2(3x-17x+12y-16y-5+4)
Evaluate the like terms
-2(-14x-4y-1)
Open the bracket
28x+8y+2
Hence, the simplified expression is: 28x+8y+2
Read more about expressions at:
https://brainly.com/question/723406
A function has a constant halving time. What type of function does this represent?
A. Decreasing linear
B. Exponential decay
C. Exponential growth
D. Increasing linear
Answers
[tex]A(t) = A_{0} ( \frac{1}{2} )^ \frac{t}{h} [/tex]
Where: A₀ is the initial amount
h is the half life time or the halving time.
t is the time
A(t) the amount that remains at time t
The previous function represents an Exponential decay function.
so, The correct answer is option B. Exponential decay
Answer:
b
Step-by-step explanation:
How would I find the diameter?
Answers
What is the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters? Round the answer to the nearest square meter.
A. 1,100 square meters
B. 1,112 square meters
C. 2,507 square meters
D. 2,605 square meters
Answers
[surface area of the cone]=pi*r²+pi*r*l
where
r is the radius
l is the slant height
l²=h²+r²
h=43 m
r=14/2---> 7 m
l²=43²+7²----> l²=1898--------> l=43.57 m
[surface area of the cone]=pi*7²+pi*7*43.57----> 1111.53 m²----> 1112 m²
the answer is the option
B. 1,112 square meters
After a 40% discount an item costs $360. what is the original cost
Answers
So...
OP = 360 / 100 - 0.40
OP = 360 / 0.60
OP = 600
The original price is $600.
To check, do 600 - (600 * 0.40) in a calculator. You get 600 - 240 = 360, the discounted cost.
Answer:
It is $600
Step-by-step explanation:
hope it helps, murdle
For the function f(x) = x2, what effect will multiplying f(x) by 1/2 have on the graph?
Answers
f (x) = x2
We apply the following transformation:
Vertical expansions and compressions:
To graph y = a * f (x)
If 0 <a <1, the graph of y = f (x) is compressed vertically by a factor a. (Shrinks)
We have then:
f (x) = (1/2) * x2
Answer:
is compressed vertically by a factor 1/2
2. How many real number solutions are there to the equation 0 = –3x² + x – 4? (1 point)
Answers
[tex] - 3 {x}^{2} + x - 4[/tex]
finding the determinant will tell us how many solutions
the determinant is
[tex] {b}^{2} - 4ac[/tex]
so we have
a=-3
b=1
c=-4
so the determinant is
[tex] {1}^{2} - 4( - 3)( - 4) = 1 - 48 = - 47[/tex]
now we know if d=0 there is 1 real solution if d<0 there are complex solutions and if d>0 there are 2 real solutions.
since d=-47<0 there are no real solutions only complex ones
Final answer:
The equation has no real number solutions.
Explanation:
To find the number of real number solutions to the equation 0 = –3x² + x – 4, we can use the discriminant of the quadratic equation. The discriminant is calculated as b² - 4ac, where a, b, and c are coefficients of the equation in the form ax² + bx + c = 0. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. And if the discriminant is negative, the equation has no real solutions.
In this case, a = -3, b = 1, and c = -4. Let's calculate the discriminant:
b² - 4ac = (1)² - 4(-3)(-4) = 1 - 48 = -47
Since the discriminant is negative, the equation 0 = –3x² + x – 4 has no real number solutions.
What is the focus of the parabola? [tex]y= \frac{1}{4} x^{2} -x+3[/tex]
Enter your answer in the boxes.
(__ , __)
Answers
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=1/4x²−x+3
where
a=1/4
b=-1
c=3
the coordinates of the focus are
(-b/2a,(1-D)/4a)
where D is the discriminant b²-4ac
D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> 2
y coordinate of the focus
(1-D)/4a------> (1+2)/(4/4)---> 3
the coordinates of the focus are (2,3)
The solution to 15 a2 − 1 = 5 2a − 2 is a = . The extraneous solution is a = .
Answers
15 / (a ^ 2 - 1) = 5 / (2a - 2)
Rewriting we have:
3 / (a ^ 2 - 1) = 1/2 (a - 1)
6 / (a ^ 2 - 1) = 1 / (a - 1)
6 (a - 1) = (a ^ 2 - 1)
6 (a - 1) = (a-1) (a + 1)
(a + 1) = 6
a = 6-1
a = 5
Answer:
The solution is:
a = 5
Answer:
5 and 1
1 is extraneous
Step-by-step explanation:
A bunch bowl is in the shape of a hemisphere. The top rim has a circumference of 116cm.
A) determine the volume of the punch bowl to the nearest cubic centimeter.
B) If there are 1,000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.
Answers
[tex]C=2\pi r[/tex]
[tex]116\:cm=2\pi r[/tex]
[tex]r=\frac{116}{2\pi }=18.462\:cm[/tex]
Part A
We can now compute for the volume of the hemisphere.
[tex]V=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{1}{2}\times \frac{4}{3}\pi \left(18.462\right)^3=13179\:cm^3[/tex]
Part B
We just need to convert the volume into its corresponding gallons
[tex]13179\:cm^3\times \frac{1\:Liter}{1000\:cm^3}\times \frac{1\:gallon}{3.785\:Liters}=3.5\:gallons[/tex]
Write the function associated with the graph below
Answers
Since the value of the function is decreasing exponentially as x decreases ,
The function is of the form [tex] y=ae^{bx}+c,b>0 [/tex].
Since the curve passes through (0,6),
[tex] 6=ae^{0}+c,6=a+c [/tex],
Since the curve passes through (-1,0),
[tex] 0=ae^{-b}+c [/tex].
Since [tex] y=-3 [/tex] is a horizontal asymptote,
[tex] -3=ae^{-\infty}+c,c=-3 [/tex]
From the above 3 equations,
[tex] c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3 [/tex].
Therefore, the required function is
[tex] y=9e^{\ln 3 x}-3\\
y=9*3^{ x}-3 [/tex].
It can be verified that the curve [tex] y=9*3^{ x}-3 [/tex] passes through [tex] (-2,-2) [/tex].
Express answer in exact form.
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)
Answers
Answer:
A = { 9/2 π - 9 } in^2
Step-by-step explanation:
I just did this
Hope this helps !
To find the area of the segment, subtract the area of the triangle from the area of the sector.
Explanation:To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we need to find the area of the sector formed by the circle and subtract the area of the triangle formed by the diagonal of the square.
https://brainly.com/question/22599425
#SPJ2
Use the grouping method to factor the polynomial below completely.
x3 – 4x2 + 3x – 12
A. (x2 + 4)(x – 3)
B. (x2 – 4)(x + 3)
C. (x2 – 3)(x + 4)
D. (x2 + 3)(x – 4)
Answers
Hope that helped!!!!!!
How much does the school have to charge for each candy bar to make a profit of 10 dollars per box?
Answers
A school purchases boxes of candy bars.
• Each box contains 50 candy bars.
• Each box costs $30.
How much does the school have to charge for each candy bar to make a profit of
$10 per box?
step 1
charge for each box $10
so
the new box cost $10+$30=$40
step 2
divide the new box cost to total candy bars
$40/50=$0.80
the answer is
the school have to charge for each candy bar $0.80
Write the equation of a horizontal line that passes through the point (3, -3).
Answers
If and represent rational expressions and b0 and y0, what is true of their product? Check all that apply.
Answers
Correct options are Options B, D, E. The product of two rational expressions (a/b) and (x/y) is a rational expression, specifically the ratio of ax and by, or equivalently ax/by. Incorrect options include ay/bx and a/y(x/b).
To determine the product of two rational expressions (a/b) and (x/y), where b ≠ 0 and y ≠ 0, let's explore the given options. Here are the truths about the product:
The product is a rational expression: When you multiply two rational expressions, the result is also a rational expression. This follows from the definition of rational expressions, which are ratios of polynomials.
The product is the ratio of ax and by: Mathematically, multiplying the numerators and denominators of the two rational expressions gives us (ax)/(by).
The product is equivalent to ax/by: This restates the above ratio in a simplified expression form, confirming that the multiplication results in (ax)/(by).
As we can see, the other expressions mentioned (ay/bx, a/y(x/b), a/(y(x/b))) are not correct representations of the product. Correct options are Options B, D, E.
Complete question:
If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.
A. The product is equivalent to ay/bx
B. The product is a rational expression.
C. The product is equivalent to a/y(x/b)
D. The product is the ratio of ax and by.
E. The product is equivalent to ax/b(y)
A quilt is in the shape of a regular pentagon. It is made from 5 pieces of fabric that are congruent triangles. Each triangle has an area of 16 inches.What is the area of the quilt?
Answers
16 × 5 = 80
The area of the quilt is 80 inches².
Final answer:
The area of the quilt, which is a regular pentagon made from five congruent triangles, is 80 square inches, determined by multiplying the area of one triangle (16 inches) by five.
Explanation:
The area of the quilt which is in the shape of a regular pentagon can be determined by calculating the area of the five congruent triangles that make up the pentagon. Since each triangle has an area of 16 inches, we can find the total area by simply multiplying the area of one triangle by the number of triangles.
To calculate the total area of the quilt:
First, determine the area of one triangle, which is given as 16 inches.Next, since there are five congruent triangles in the pentagon, multiply the area of one triangle by 5.The total area of the quilt would be 16 inches (per triangle) × 5 triangles = 80 inches.Therefore, the total area of the quilt is 80 square inches.
After creating a new email address, Gareth initially receives n emails per year. The number of emails received increases by 7% each year after that. The following expression represents the number of emails received after x years.
x(1 + 0.07)^x
Which of the following best represents the expression?
the product of the number of emails received initially and one plus the factor of increase raised to the number of years that the amount of emails Gareth received has increased
the product of the number of emails received initially and the factor of decrease raised to a period of x years
the product of the number of emails received initially and one plus the factor of decrease raised to the number of years that the amount of emails Gareth received has increased
the product of the number of emails received initially and the factor of increase raised to a period of x years
Answers
The formula to find the number of emails x years after making the email account is:
[tex]N(x)= N_{o}(1+0.07)^{x} [/tex]
where, [tex] N_{o} [/tex] is the number of emails in the first year.
So, the number of emails x years after creating the account is the product of [tex] N_{o} [/tex], the number of emails in first year, and (1+0.07)^x, the sum of 1 and rate of increased raised to the number of years.
Hence option A is the correct answer.
Answer:
The correct answer is Option A.
Step-by-step explanation:
Julio considers the reduction of the triangle.
What is the correct cross product that he should use to solve for the missing dimension?
(8)(12) = 21x
(8)(21) = 12x
(12)(8) = 12x
(12)(21) = 8x
Answers
Therefore, we can use the following relationship:
(12) / (21) = (8) / (x)
From here, we can clear to know the value of the incognita x.
Answer:
the correct cross product that should be used to solve for the missing dimension is:
(12) / (21) = (8) / (x)
Answer:
(12)(21) = 8x or d
Step-by-step explanation:
Help Please
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
First picture is how they want you to put the answers in & the second one is the grid with the numbers
Answers
According to the Venn diagram, 4 people own a car and a truck. 15+4=19 people own a car, and 4+9=13 people own a truck. This leaves us 36-(15+4+9)=36-28=8 people that do not own a car or a truck.
We put 8 in the Don't Own a Truck row under the Don't Own a Car column.
We put 4 in the Own a Truck row under the Own a Car column.
We put 19 in the Total row under the Own a Car column.
We put 15 in the Don't Own a Truck row under the Own a Car column.
We put 13 in the Own a Truck row under the Total column.
We put 9 in the Own a Truck row under the Don't Own a Car column.
We put 23 in the Don't Own a Truck row under the Total column.
We put 8 in the Down Own a Truck row under the Don't Own a Car column.
We put 36 in the Total row under the Total column.
We put 17 in the Total row under the Don't Own a Car column.
Please help me with 8, 9, and 10 thanks! Show work too
RANDOM ANSWERS WILL BE MODERATED!
Answers
8. hypotenuse / (short side) = 25/x = x/9
x² = 25*9 = 5²×3²
x = √(5²×3²) = 5*3 = 15
9. (long side) / (short side) = x/7 = 9/x
x² = 7*9
x = √(9*7) = 3√7
10. (short side) / (long side) = x/48 = 48/64
x = 48²/64 = 36
20 points!
Looking at circle O, ∠BOC is a(n)
Please contact your teacher immediately if you do not see the image.
Question options:
minor angle
central angle
inscribed angle
major angle
Answers
A central angle is one that goes through the center of a circle. It's two ends are the endpoints of the chord BC which you should draw on your sheet.
If you do, we can talk about the other answers.
An inscribed angle is one that has it's vertex on the circumference. <BAC is an example. A is the vertex.
A major angle is the part above BC that goes around the circle such that the angle is larger than 180 degrees. It is described above by BAC going clockwise. It is associated with the arc of a circle.
A minor angle is the angle not included in the major angle. In this case it is the angle formed by sweeping around from B to C underneath the chord BC
What is the radius of convergence of the maclaurin series (2x)/(1+x^2)?
Answers
1. You have to find the radius of convergence of the following Maclaurin series:
[tex](2x)/(1+ x^{2} ) [/tex]
2. Let's take the denominator and find the roots:
[tex]1+ x^{2} =0[/tex]
[tex] x^{2} =-1 \\ x= \sqrt{-1} \\ x1=i \\ x2=-i[/tex]
3. The roots are [tex]x1=i \\ x2=-i[/tex] and the distance from the origin is [tex]1[/tex].
Therefore, the answer is: [tex]1[/tex]
The radius of convergence of the maclaurin series is 1 unit.
It is given that maclaurin series [tex]\rm \frac{2x}{(1+x^2)}[/tex]
It is required to find the radius of the convergence of the maclaurin series.
What is maclaurin series?It is defined as the expansion of a function that provide the approximation of the given function at any point of function.
We have:
[tex]\rm \frac{2x}{(1+x^2)}[/tex]
To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:
[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]
From the complex number: the roots are imaginary:
[tex]\rm x_1 = i\\x_2 = -i[/tex]
i is the iota
and the distance from the origin (0,0) is 1.
Thus, the radius of convergence of the maclaurin series is 1 unit.
Learn more about the maclaurin series:
https://brainly.com/question/24188694
The square root of 53 lies between which two numbers?
Answers
There are a couple ways to find this. You could...
A. Use a calculator and simply find the square root of 53 (7.280...) OR
B. You could square each number (1^2, 2^2, 3^2...) until you get the closest 2 numbers (one less than and one greater than) to 53 (7^2 = 49) and (8^2 = 64).
I hope this helps!
how do you convert cos(x) into sin(x) and tan(x) ?
Answers
tan x
cos x = ---------- In other words, rewrite "cos x" in an expression as
tan x
-----------
sin x
Find the approximate surface-area-to-volume ratio of the Moon. The radius of the Moon is 1,080 miles. A. 0.0009 B. 0.0028 C. 360 D. 3,240
Answers
surface area of a sphere=4*pi*r²
volume of a sphere=(4/3)*pi*r³
the ratio surface area to volume
=4*pi*r²/[(4/3)*pi*r³]-----> 3/r----> 3/1080-----> 0.0028
the answer is
the option B. 0.0028
Anyone know this geometry question? Will give brainiest
Answers
This is because of the following rule:
When two lines are parallel, which is the occasion with AB and CD, then the corners in which the intecepting parallel lines (AC and BD) stand must be the same. So corner 6 is equivalent to corner 3, corner 1 and corner 5. Corner 2 and corner 4 are equivalent too.
Tom caught 4 fish and his son caught 12 fish.The number of fish that Tom caught was what percent of the total number of fish?
Answers
tom % of fish = 4 divided by 16 = 0.25 =25%
A. (-3,-5)
B.( -2,-2)
C. (4,9)
D.(13,5)
Answers
The appropriate choice is ...
D. (13, 5)