Question 9: Use the function f(t) = -16t² + 60t + 16 to answer Part A, B & C.
Part A: Use the quadratic equation
to find the x-intercepts of the
function. Show all work (2 pt)
Part B: Identify the line of
symmetry and vertex of the
parabola. (Give exact decimal
answers)
-b ± √b² - 4ac
2a
Answer (2 pt):
X-intercepts:
&
Line of symmetry (1pt):
Vertex (1pt):.
Hint: t =
-b
2a
8.01&8.04
Part C (3 pt): Graph the parabola using the
x-intercepts and vertex from Part A & B.
100
Highlight the word that completes the sentence (1 pt):
The vertex of he graph is a (max/min).
Answers
The x-intercepts of the function are (-0.25, 0) and (4, 0).
The line of symmetry is 1.875.
The vertex of the parabola is 72.25.
How to determine the x-intercepts of the quadratic function?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)
For the given quadratic equation f(t) = -16t² + 60t + 16, we have:
\(x = \frac{-(60)\; \pm \;\sqrt{(60)^2 - 4(-16)(16)}}{2(-16)}\\\\x = \frac{-60\; \pm \;\sqrt{3600 + 1024}}{-32}\\\\x = \frac{-60\; \pm \;\sqrt{3600 + 1024}}{-32}\)
x = -0.25 or x = 4.
Line of symmetry, Xmax = -b/2a
Line of symmetry, Xmax = -60/2(-16)
Line of symmetry, Xmax = 60/32
Line of symmetry, Xmax = 1.875
Vertex, f(1.875) = -16(1.875)² + 60(1.875) + 16
Vertex, f(1.875) = 72.25.
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Related Questions
My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answers
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories
what is the total number of unique triangles that can be made with the side lengths of 4cm, 5cm, and 10cm can be drawn? PLS HELP I WILL MARK BRAINLIEST
Answers
Answer:
One
Step-by-step explanation:
First, we need to check a triangle with these sides is possible. Since 4 plus 5 is 9, and 9 is less than 10, we can make a triangle with these sides.
To answer the question, we can only make one unique triangle. Why? They give us three lengths and a triangle has three sides.
However, if they are counting a triangle in different positions the answer will be greater. Since it would just be the same triangle, I am going with the answer of only one.
Pupils Per Teacher The frequency distribution shows the average number of pupils per teacher in some states of the United States. Find the variance and standard deviation for the data. Round your answers to one decimal place. Class limits Frequency 11–13 1 14–16 16 17–19 11 20–22 7 23–25 1 26–28 2
Answers
The variance and standard deviation for the given frequency of pupils per teacher in some states of US is
Variance= 4.62 = 4.6
Standard Deviation = 2.14 = 2.1
The frequency distribution shows the average number of pupils per teacher in some states of the United States.
Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data. On the other hand, if data consists of individual data points, it is called ungrouped data. The sample and population variance can be determined for both kinds of data.
The standard deviation(σ) of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
That means Standard Deviation = √variance.
For the given data the sum of frequencies(ni) = 1+16+11+7+1+2= 38.
Midpoint(mi) is 12,15,18,21,24,27.
ni * mi = 12,240,198,147,24,54.
Sum of ni * mi = 675.
Mean (u) = 17.76
mi - u is -5.76,-2.76,0.24,3.24,6.24,9.24.
(mi - u)^2 is 33.17,7.61,0.057,10.49,38.93,85.37.
Sum of (mi - u)^2 = 175.62.
Variance = Sum of (mi - u)^2 / sum of frequencies
=> 175.62/38
=> 4.62 = 4.6.
Standard deviation = √variance.
=> √4.62
=> 2.14 = 2.1.
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Draw the net and calculate the surface area .
Answers
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
Mack is selling beaded necklaces and beaded wristbands at the Craft Market.
A necklace requires 40 minutes to make.
A wristband requires 25 minutes to make.
Mack has 360 minutes to make the necklaces and wristbands.
.
●
.
Additionally,
Mack wants to make no more than 12 items.
When Mack sells the necklaces and wristbands at the Craft Market, he will make $3.00 profit per necklace and
$2.00 profit per wristband.
Let x = the number of necklaces Mack makes.
.
.
Let y= the number of wristbands Mack makes.
TEXT ANSWER
Question 14
1 Points
Evaluate each vertex ordered pair in the profit function. Which vertex yields the maxi-
mum profit?
Answers
Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.
We have,
The profit function is given by:
P(x,y) = 3x + 2y
The constraints are:
40x + 25y ≤ 360 (time constraint)
x + y ≤ 12 (item constraint)
x, y ≥ 0 (non-negative constraint)
To find the vertices, we need to solve the system of equations for each pair of intersecting lines. The vertices are the points where the lines intersect.
40x + 25y = 360
x + y = 12
Solving this system of equations, we get:
x = 6, y = 6 (vertex 1)
x = 9, y = 3.6 (vertex 2)
x = 0, y = 12 (vertex 3)
Now, we evaluate each vertex in the profit function:
P(6,6) = 3(6) + 2(6) = 24
P(9,3.6) = 3(9) + 2(3.6) = 30.6
P(0,12) = 3(0) + 2(12) = 24
Now,
Vertex 2 yields a maximum profit of $30.60.
Therefore,
Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.
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State the x and Y intercepts of the equation y=2/3x - 1/3
Answers
Answer:
x intercept is (1/2, 0).
y intercept = (0, -1/3)
Step-by-step explanation:
2/3x - 1/3 = 0
2/3x = 1/3
x = 1/3 * 3/2
x = 1/2.
y = 2/3(0) - 1/3 = -1/3.
Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.
Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.
Answers
The true statements are (A), (B) and (D)
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
As, from the given table we can see that
Melissa and Corey started on different trails.Melissa hiked up the trail for a longer period of time than Corey.Corey began his descent before Melissa.Learn more about this concept here:
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A side of the triangle below has been extended to form an exterior angle of 127. Find the value of x.
Answers
Answer:
37
Step-by-step explanation:
180-127=53
180-53-90=37
What is the image of the point ( − 1 , 2 ) after a rotation of 270 counterclockwise about the origin?
Answers
What is 14 to the the 1 power
Answers
Hey there!
Anything powered to the 1st is that number….. just like anything powered the zero is 0.
Anyway, let’s answer your question.
14^1
= 14 * 1
= 14
Therefore, your answer should be:
14
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
14
How do powers work?Powers in math are exponents that raise a given value to its power. As a simple rundown, when you raise something to an exponent, you are multiplying that value by itself as many times as the exponent declares.
For instance, if you were to raise 2 to the 2nd power (2²), this would mean that you are multiplying 2 two times: \(2\times2=4\)
SolveTo solve, raise 14 to the 1st power:
\(14^1 = 14 \times 1\)
\(14\)
The final answer is 14.
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Please, help me find the answer
Answers
The probability values for the questions posed are :
11/20probability of Public speaking given that student is majoring in Business Administration1/3A.)
Number of students Taking a public speaking class majoring in business administration.
10 + 45 = 55P(PS or BA) = 55/100 = 11/20
Therefore, the probability of PS or BA is 11/20
B.)
For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.
Hence, as inferred from P(A|B) ; probability of A given B.
C.)
P(PS|BA) = n(PSnBA) / n(BA)
n(PS) = 10+20 = 30
n(PSnBA) = 10
P(PS|BA) = 10/30 = 1/3
Therefore , the probability of PS|BA is 1/3.
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What is the volume of the cylinder below? Use 3.14 for Pi and round to the nearest tenth.
Answers
\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=10\\ h=7 \end{cases}\implies V=\pi (10)^2(7)\implies \stackrel{ using~\pi =3.14 }{V=2198~cm^3}\)
These three pizzas are all the same size. Which one has the greatest number of equal pieces?
Answers
Given the following question:
It tells us that these pizzas are the same size
We are trying to find out which one of these pizza's have the greatest number of equal pieces.
For first pizza
It's cut up in four different pieces and these four pieces are equal
For the second pizza it is cut up in three different pieces and these three pieces are equal.
For the third pizza it is cut up in two pieces, these pieces are indeed equal.
Again the question is asking us which one has the GREATEST NUMBER of equal pieces
4, 3, 2
4 > 3
4 > 2
= 4
Your answer is the first pizza.
Determine if the following table represents a quadratic function. X 1 2 3 4 5 Y 13 22 37 58 85
Answers
Answer:
Yes, the table represents quadratic function.
\(Y = 3X^2+10\)
Step-by-step explanation:
Given that table of values:
\(\begin{center}\begin{tabular}{ c c}X & Y \\ 1 & 13 \\ 2 & 22 \\ 3 & 37 \\ 4 & 58 \\ 5 & 85 \\\end{tabular}\end{center}\)
To find:
Whether the given table represents a quadratic?
Solution:
First of all, let us plot the given values on the coordinate xy plane.
Kindly refer to the attached image for the graph of given values.
The graph seems parabolic in nature which is the graph of a quadratic equation.
Now, let us try to find the equation from the given set of values from hit and trial.
Let Quadratic equation be:
\(y=ax^{2} +b\)
If the coefficient a = 1
\(f(1) = 13 = 1^2+12\)
\(f(2) = 22 = 2^2+18\)
\(f(3) = 37= 3^2+28\)
\(f(4) = 58 = 4^2+42\)
\(f(5) = 85 = 5^2+60\)
value of b is not same in each case.
Now, let us try coefficient a = 3
\(f(1) = 13 = 3 \times 1^2+10\)
\(f(2) = 22 = 3\times 2^2+10\)
\(f(3) = 37= 3\times 3^2+10\)
\(f(4) = 58 = 3\times 4^2+10\)
\(f(5) = 85 =3\times 5^2+10\)
Value of b = 10
So, we can clearly say that the given table represents a quadratic equation.
and the quadratic equation is:
\(Y = 3X^2+10\)
solve for x ~
\(x {}^{2} - 5x + 6 = 0\)
thankyou ~
Answers
x= 3, 2
\(\boxed{\bold{x = 2, 3}}\)
Stepwise Solving:
\(\rightarrow \sf x^2-5x + 6 = 0\)
\(\sf use \ the \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0\)
Identify the coefficients:
a = 1b = -5c = 6Solve for x:
\(\dashrightarrow \ \sf x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4 \ x \ 1 \ x \ 6}}{2 \ x \ 1}\)
\(\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{\left25-24}}{2}\)
\(\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{1}}{2}\)
\(\dashrightarrow \ \sf x=\dfrac{\left5\right\pm1}{2}\)
\(\dashrightarrow \ \sf x=\dfrac{\left5\right+ 1}{2} \ , \dfrac{\left5\right- 1}{2}\)
\(\dashrightarrow \ \sf x=\dfrac{6}{2} \ , \ \dfrac{4}{2}\)
\(\dashrightarrow \ \sf x= 3, \ 2\)
Your statement balance is $687.45. You have outstanding checks totaling $332.10 and an outstanding deposit for $124.21. What is your adjusted balance?
Answers
Answer:
261.48
Step-by-step explanation:
A kids pool had a small opening through which water sometimes leaked out. Water was poured into the pool from time to time. The graph shows the amount of water in the pool (y), in gallons, at certain times (x), in hours.
Which of the following statements best describes the amount of water in the pool ?
1) it is increasing during the time interval 4
2) it is increasing during the time interval 10
3) it is decreasing during the time interval 4
4) it is decreasing during the time interval 10
Answers
The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.
How to determine the the interval of the water in the pool?To determine the time interval of the water in the pool the following is carried out.
At 0 hour, the water is at the level of = 40 gallons
At 1 hour, the water decreased to = 25 gallons.
At 2 hours, the water decreased to = 10 gallons.
The water remained at a constant level till 4 hours.
Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.
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10 less triple x is at least 12. Find all the values of x
Answers
The value of x for the given expression will be 22/3.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the expression is triple x less by 10 is at least 12. The mathematical form of the expression can be written as below:-
3x - 10 = 12
3x = 10 + 12
3x = 22
x = 22 / 3
Hence, the value of x for the expression 3x - 10 = 12 is x = 22 / 3.
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Which expression represents the phrase below?
3 fewer than a number, p
A. 3-P B. p=3
3p
C. 3:p
D. p-3
Answers
Answer:
d) p - 3
3 fewer than menas you need to subtract 3
Step-by-step explanation:
The expression represents the phrase “3 fewer than a number, p” is (p-3).
Given
Expression; the phrase: “3 fewer than a number, p”
What is the phrase?
A small group of words standing together as a conceptual unit, typically forming a component of a clause:
The given number is p which is smaller than a number which is 3.
Expression; the phrase: “3 fewer than a number, p”
Then,
The expression represents the phrase is;
Hence, the expression represents the phrase “3 fewer than a number, p” is (p-3).
How do you know that the sum of (-2 3/4 ) and 5/9 is irrational
Answers
The sum is a fraction.
Which problem is even below
4,323
944
291
31
Answers
find the measure of angle A
Answers
Answer:
do 5x-27+7x-26=10x-23 because sum of two interior angle of a triangle is equal to the sum of one exterior angle and don't forget because it comes daily in exam
3
Mathematical Habit 3 Construct viable arguments
Sara bought a total of 20 sausage rolls and chicken pies. Each sausage
roll cost $1.50 and each chicken pie cost $2.50. The chicken pies cost $18
more than the sausage rolls. How many of each item did she buy?
Answers
The number of sausage rolls is 8 and the chicken pie is 12.
How many of each item did she buy?
The first step is to form a system of equations using the information in the question:
c + s= 20 equation 1
2.50c - 1.50s = 18 equation 2
Where:
c = number of chicken pies bought
s = number of sausage rolls bought
The elimination method would be used to determine the required values.
Multiply equation 1 by 2.50
2.5c + 2.5s = 50 equation 3
Subtract equation 2 from equation 3:
4s = 32
Divide both sides of the equation by 4
s = 32 / 4
s = 8
Substitute for s in equation 1:
c + 8= 20
c = 20 - 8
c = 12
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The value of a collectible toy is increasing exponentially. The two points on the graph
show the toy's initial value and its value 3 weeks afterward.
Answers
The question is incomplete. Here is the complete question.
Part A
The value of a collectible toy is increasing exponentially. The two points on the graph show the toy's initial value and its value 3 weeks afterward.
Express the toy's value t, in dollars, as a function of time w in weeks after purchase.
Part B
Write an expression to represent the toy's value 10 days after purchase
Answer and Step-by-step explanation: An exponential function is of the form: \(y=ab^{x}\)
Part A
Translating to the question, the toy's value as a function of time is
\(t=ab^{w}\)
To determine constants a and b, we use points given by graph.
First, (0,5) to find a:
\(5=a.b^{0}\)
a = 5
Now, (3,10) to determine b:
\(10=5b^{3}\)
\(b=\sqrt[3]{2}\)
b = 1.26
The toy's value as a function of time in weeks is \(t=5.(1.26)^{w}\)
Part B
Since, the function is in weeks:
1 week = 7 days
w weeks = 10 days
\(w = \frac{10}{7}\)
Replacing w:
\(t=5.(1.26)^{w}\)
\(t=5.(1.26)^{10/7}\)
Expression that represents toy's value after 10 days is \(t=5.(1.26)^{10/7}\).
I NEED HELP!!!!!!!!!!!!!!!!!
Answers
2*0.16 + 4*0.13 + 6*0.2 + 7*0.51
5.61
Test your knowledge of lines with the following:
Answers
What is 21n + 15 + n - 2 simplified ?
Answers
Answer:
=22n+13
Let's simplify step-by-step:
21n+15+n−2
=21n+15+n+−2
Combine Like Terms:
=21n+15+n+−2
=(21n+n)+(15+−2)
=22n+13
Answer:
=22n+13
A bird measures 8.9 cm tall in the photo, but is actually 46.9 cm tall. Approximately how long is the birds beak in real life if it measures 1.1 cm in the photo?
Answers
Answer: Approximately 5.7 cm
Five increased by the product of a number and 9 is greater than -27
As an inequality
Answers
Answer:
brhnrnr e euebe ehe we je euebe ejeje
Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2