Step-by-step explanation:
Step 1: Factor the equation
[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]
Step 2: Find the x-intercepts of the graph of f(x)
[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]
[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]
Step 3: Describe the end behavior of the graph of f(x)
Since the function is to the power of 2, that means that it is a parabola. And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.
Step 4: What are the steps you would use to graph f(x)
The first step that I would do is factor the equation. Then I would find the x-intercepts of the graph and plot them on the graph. I would then plug in 0 for all of the x values to get the y intercept. After doing that I would get the vertex using the vertex formula plotting it on the graph. Finally, I would connect all of the dots together to form the graph of the equation.
Answer:
The person above me is correct!
4. Write the number 3.8 in the form using integers, to show that it is a rational number. 8 11 38 10 10 38 100
Answer:
38 divided by 10 equals 3.8
find the differential equation of this function and indicate the order y = e^3x (acos3x +bsin3x)
Answer:
y"-6y'+18y=0
Second order
Step-by-step explanation:
Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.
y = e^(3x) (acos3x +bsin3x)
y'=3e^(3x) (acos3x+bsin3x)
+e^(3x) (-3asin3x+3bcos3x)
Simplifying a bit by reordering and regrouping:
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
y"=
3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)
+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)
Simplifying a bit by reordering and regrouping:
y"=
e^(3x) cos3x (9a+9b+9b-9a)
+e^(3x) sin3x (-9a-9b+9b-9a)
Combining like terms:
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
Let's reorder y like we did y' and y".
y = e^(3x) (acos3x +bsin3x)
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.
Let's start with the highest order derivative and work down
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
We need to get rid of the 18b and 18a.
This is what we had for y':
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.
So we have y"-6y'=
e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)
Now multiplying
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b
y"-6y'+18y=0
Also the characteristic equation is:
r^2-6r+18=0
This can be solved with completing square or quadratic formula.
I will do completing the square:
r^2-6r+18=0
Subtract 9 on both sides:
r^2-6r+9=-9
Factor left side:
(r-3)^2=-9
Take square root of both sides:
r-3=-3i or r-3=3i
Add 3 on both sides for each:
r=3-3i or r=3+3i
This confirms our solution.
Another way to think about the problem:
Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi
Note: +/- means plus or minus
So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i
Subtracting 3 on both sides gives:
r-3= +/- 3i
Squaring both sides gives:
(r-3)^2=-9
Applying the exponent on the binomial gives:
r^2-6r+9=-9
Adding 9 on both sides gives:
r^2-6r+18=0
What's the equivalent expression.
(2-7. 5)² =?
Answer:
The Answer of the above question is 30.25
Step-by-step explanation:
Hope it helps you.
how do we write a set in set- builder method?
Answer:
(×:x is a natural number up to 10) just an example
please help, it’s urgent !!!
Answer:
1. purple graph
2. orange graph
3. green graph
4. blue graph
What is the percent discount if a 12,500 car is now on special for 10,250?
Answer:
Step-by-step explanation:
the answer is 2250 percent is = 22.5
Answer:
18% discount
Step-by-step explanation:
Percent discount is found by the following formula:
[tex]\frac{original-discount}{original}[/tex]
In this scenario, the original is 12500 and the discount, or special is 10250.
We can plug this into the formula to get
[tex]\frac{12500-10250}{12500}[/tex]
We can simplify the numerator by subtracting, and we get that answer as 2250.
We get the remainder of the answer as 2250 divided by 12500. We divide that, and get the answer as 0.18, which can be rewritten as 18%.
What is the circumference of the circle in terms of [tex]\pi[/tex]?
a. 900[tex]\pi[/tex] in.
b. 90[tex]\pi[/tex] in.
c. 60[tex]\pi[/tex] in.
d. 30[tex]\pi[/tex] in.
Answer:
[tex]c. \: 60\pi \: in.[/tex]Step-by-step explanation:
Given,
Radius = 30 in
So,
Circumference
[tex] = 2\pi r[/tex]
[tex] = 2 \times \pi \times 30in.[/tex]
[tex] = 60\pi \: in.(ans)[/tex]
[tex] \sf \: r \: = 30 \: in. \\ \sf \: C \: = 2\pi r \\ \\ \sf \: C \: = 2\pi(30) \\ \sf \: C = 2 \times 30\pi \\ \sf \: C = \boxed{\underline{ \bf c. \: 60\pi \: in.}}[/tex]
An experiment to investigate the survival time in hours of an electronic component consists of placing the parts in a test cell and running them under elevated temperature conditions. Six samples were tested with the following resulting failure times (in hours): 34, 40, 46, 49, 61, 64. (a)Calculate the sample mean and sample standard deviation of the failure time. (b)Determine the range of the true mean at 90% confidence level. (c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time
Answer:
a) The sample mean is of 49 and the sample standard deviation is of 11.7.
b) The range of the true mean at 90% confidence level is of 9.62 hours.
c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Step-by-step explanation:
Question a:
Sample mean:
[tex]\overline{x} = \frac{34+40+46+49+61+64}{6} = 49[/tex]
Sample standard deviation:
[tex]s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7[/tex]
The sample mean is of 49 and the sample standard deviation is of 11.7.
b)Determine the range of the true mean at 90% confidence level.
We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0.150
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. So
[tex]M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62[/tex]
The range of the true mean at 90% confidence level is of 9.62 hours.
(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.
This is the confidence interval, so:
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.
The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.
The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Match each equation to its graph.
1. y= x-2
2. y= -2x
3. x= -2
4. y= -2
The equation of the graph is : x = -2
What is a graph?A graph is a pictorial representation of the locus of a certain point.
How to draw a graph?A graph can be drawn by picking some fixed points from the locus of the point.
Here, the straight line passes through the points are : (-2,1); (-2,2); (-2,-5);(-2,-5).
Hence, the straight line is to be parallel to the x-axis and the equation of the graph is x= -2.
Learn more about graph here :
https://brainly.ph/question/6429575
#SPJ2
the first four terms of a sequence are shown below:
7,4,1,-2
which of the following functions best defines this sequence?
A) f(1)=7, f(n+1)= f(n)+3; for n>= 1
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
C) f(1)=7, f(n+1)= f(n)-4; for n >= 1
D) f(1)=7, f(n+1)= f(n)+4; for n >= 1
9514 1404 393
Answer:
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
Step-by-step explanation:
The first term of the sequence is 7 and the next (4) is found by adding -3 to that: 4 = 7-3. This is described in answer choice B.
Change these percentages to decimals.
30%
45%
60%
5%
1%
55%
80%
10%
Rewrite the following expanded notation in standard form. 600,000 + 80,000 + 1,000 + 400 + 70 + 5
Answer:
this is the answer
681,474
Use calculus to find the absolute maximum and minimum values of the function. f(x) = 5x − 10 cos(x), −2 ≤ x ≤ 0 (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
Answer:
gkg8fyaueajrkvxogogzoggkdggkdyyskyyeykektkykyksskysysskkyky
Answer:
The absolute maximum is about -5.84 at x = -2.
And the absolute minimum is about -11.28 at x = -π/6.
Step-by-step explanation:
We want to find the absolute maximum and minimum values of the function:
[tex]\displaystyle f(x) = 5x-10\cos x\text{ for } -2\leq x\leq 0[/tex]
First, we should evaluate the endpoints of the interval:
[tex]\displaystyle f(-2) = 5(-2) - 10\cos (-2) \approx -5.8385[/tex]
And:
[tex]f(0) = 5(0) -10\cos (0) = -10[/tex]
Recall that extrema of a function occurs at its critical points. The critical points of a function are whenever its derivative is zero or undefined.
So, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ 5x - 10\cos x\right][/tex]
Differentiate:
[tex]\displaystyle f'(x) = 5 + 10\sin x[/tex]
Set the function equal to zero:
[tex]\displaystyle 0 = 5+10\sin x[/tex]
And solve for x:
[tex]\displaystyle \sin x = -\frac{1}{2}[/tex]
Using the unit circle, our solutions are:
[tex]\displaystyle x = \frac{7\pi}{6} + 2n\pi\text{ or } \frac{11\pi}{6} + 2n\pi \text{ where } n\in \mathbb{Z}[/tex]
There is only one solution in the interval [-2, 0]:
[tex]\displaystyle x = \frac{11\pi}{6} - 2\pi = -\frac{\pi}{6}\approx -0.5236[/tex]
Thus, we only have one critical point on the interval.
Substituting this back into the function yields:
[tex]\displaystyle\begin{aligned} f\left(-\frac{\pi}{6}\right) &= 5\left(-\frac{\pi}{6}\right) - 10\cos \left(-\frac{\pi}{6}\right) \\ \\ &=-\frac{5\pi}{6} - 5\sqrt{3}\\ \\ &\approx -11.2782 \end{aligned}[/tex]
In conclusion, the absolute maximum value of f on the interval [-2, 0] is about -5.8385 at x = -2 and the absolute minimum value of f is about -11.2782 at x = -π/6.
We can see this from the graph below as well.
Hi can someone answer this question please thank you
Answer:
25
Step-by-step explanation:
5:20
We want to get the second number to 100
100/20 = 5
Multiply each term by 5
5*5 : 20*5
25 : 100
x is 25
Given that,
→ 5 : 20 :: x : 100
Then we have to,
find the second number to 100.
→ 100/20
→ 5
Now multiply each term by 5 in 5:20,
→ 5 × 5 : 20 × 5
→ 25 : 100
→ x = 25
Now these ratio will be,
→ 5 : 20 :: 25 : 100
Hence, the value of x is 25.
WHAT IS THE ANSWER TO 9-3:3= ?
I NEEDD HELP I ONLY GOT 2 MIN I WILL GIVE BRAINLY
Answer: 8
Hope this help :)
Classify the following triangle 120 degrees
options
a. acute
b.Scalene
c.isosceles
d.obtuse
e.right
f. equilateral
Answer:
I think it is Obtuse.
Step-by-step explanation:
120 Degrees - Obtuse
39.948859° What is the measurement in degrees, minutes, and seconds?
Answer:
try to calculate
here some examples
Step-by-step explanation:
Decimal Degrees to Degrees, Minutes, Seconds Calculator
Enter decimal degrees to convert to minutes and seconds. See the formulas below to see how it’s done.
Angle:
Decimal:
47.31
°
degrees, minutes, seconds to decimal
Degrees, Minutes, & Seconds:
47° 18′ 36″
I hope it helps
the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?
Answer:
The coefficient of the squared term is 1/25.
Step-by-step explanation:
We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.
And we want to determine the coefficient of the squared term of the equation.
Since we are given the vertex, we can use the vertex form of the quadratic:
[tex]\displaystyle y = a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.
Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:
[tex]\displaystyle y = a(x-2)^2-4[/tex]
y = -3 when x = -3. Solve for a:
[tex]\displaystyle (-3) = a((-3)-2)^2-4[/tex]
Simplify:
[tex]\displaystyle 1 = a(-5)^2\Rightarrow a = \frac{1}{25}[/tex]
Therefore, our function in vertex form is:
[tex]\displaystyle f(x) = \frac{1}{25}\left(x-2)^2-4[/tex]
Hence, the coefficient of the squared term is 1/25.
Answer:
-5
Step-by-step explanation:
from a p e x
for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?
9514 1404 393
Answer:
21
Step-by-step explanation:
The number who bought expensive tickets is 3/5 of the number who bought cheap tickets.
(3/5)(35) = 21
21 people bought the more expensive ticket.
Answer:
21 people
Step-by-step explanation:
$9.75 $14.50
5 people to 3 people
35 people to ? people
consider the proportions: 5/3 = 35/?
we need the equivalent fraction of 5/3 that has 35 on the denominator
so 5/3 = (5/3)(7/7) because 7/7 =1, and 5*3 =35
5/3 = 5*7/3*7 = 35/21
3.3.C-1
If one tablet of calcium pantothenate contains 0.5 gram, how much is contained in
n 2 1/4 tablets? How many tablets are needed to make up 2.3 grams?
A fraction calcium pantothenate contains 0.5 gram of a tablet 5 tablets to make up 2.3 grams.
To calculate the amount of calcium pantothenate contained in a given number of tablets, use the given information that one tablet contains 0.5 grams.
Amount in n 2 1/4 tablets:
To calculate the amount of calcium pantothenate in n 2 1/4 tablets, we need to calculate the total amount for each part (whole tablets and the fraction of a tablet) and then sum them up.
Amount in n whole tablets: n tablets × 0.5 grams/tablet
Amount in 1/4 tablet: (1/4)× 0.5 grams
So, the total amount in n 2 1/4 tablets would be:
Total amount = n ×0.5 + (1/4) ×0.5 grams
Tablets needed to make up 2.3 grams:
To calculate the number of tablets needed to make up 2.3 grams of calcium pantothenate, set up a proportion using the given tablet amount (0.5 grams/tablet).
Let x be the number of tablets needed.
0.5 grams/tablet = 2.3 grams / x tablets
Cross-multiply:
0.5 × x = 2.3
x = 2.3 / 0.5
x = 4.6
To know more about fraction here
https://brainly.com/question/10354322
#SPJ3
the cost of 2 pairs of trousers and 3 shirts is $825 it shirt cost $50 less than the trouser. find the cost of each shirt and trouser
Answer:
a pair of trousers cost = x = 195 $
one shirt costs = x - 50 = 145 $
Step-by-step explanation:
let the cost of trouser be x.cost of shirt = (x - 50)2 pairs of trousers cost = 2x 3 shirts cost = 3(x - 50)= 3x- 150
2 trousers and 3 shirts cost = 825
=> 2x + 3x - 150 = 825
=> 5x = 975
x = 195
a pair of trousers cost = x = 195 $
a pair of trousers cost = x = 195 $ one shirt costs = x - 50 = 145 $
how many itegers from 15 to 85, inclusive are multibles of 8
Answer:
9 multiples
Step-by-step explanation:
16,24,32,40,48,56,64,72,80
9
√12 + √10 − √2) is
(a) A positive rational number
(b) Equal to zero
(c) An irrational number
(d) A negative integer
Hello!
[tex] \bf \sqrt{12} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} \times 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} } \sqrt{ 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \boxed{ 2 \sqrt{3} + \sqrt{10} - \sqrt{2}} [/tex]
Answer: (c) An irrational number
Good luck! :)
Karl wants to raise money for charity. He designs a game for people to play.
Karl uses a ten sided dice for the game. The dice is numbered 1 to 10.
Each person will roll the dice once. A person wins the game if the dice lands on a multiple of 4.
Ali plays the game once,
a) Work out the probability that Ali will win the game.
(2 m
Answer:
0.2 = 20% probability that Ali will win the game.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
The 10 sides that the dice can land, which means that [tex]T = 10[/tex]
Desired outcomes:
Sides that are multiple of 4, that is, side 4 and side 8, so [tex]D = 2[/tex]
Work out the probability that Ali will win the game.
[tex]p = \frac{D}{T} = \frac{2}{10} = 0.2[/tex]
0.2 = 20% probability that Ali will win the game.
The total number of vertices adjacent to the vertex is called?
Answer:
The degree of vertex is the total number of vertices adjacent to the vertex .
The total number of vertices adjacent to the vertex is called degree of the vertex.
What is vertex?" Vertex is defined as when two adjacent side meet at one point."
According to the question,
The degree of a vertex is always as the total number of adjacent side to the vertex.
If adjacent sides far away from each other degree is more.
If adjacent sides near to each other degree is less.
Hence, the total number of vertices adjacent to the vertex is called degree of the vertex.
Learn more about vertex here
https://brainly.com/question/12563262
#SPJ3
This table shows the ratio of number of people to liters of Find the missing values in the ratio table
ginger ale needed.
A=
People
Ginger Ale
Answer:
A= 2 B= 6
Step-by-step explanation:
Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech and 40% attended both events. If a randomly selected delegate is known to have attended the dinner speech, the probability that he also attended the breakfast forum is
Answer:
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Attended the dinner speech.
Event B: Attended the breakfast forum.
70% attended the dinner speech
This means that [tex]P(A) = 0.7[/tex]
40% attended both events.
This means that [tex]P(A \cap B) = 0.4[/tex]
The probability that he also attended the breakfast forum is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
How far will fiona jog (in feet)
Answer:
1780 ft
Step-by-step explanation:
We need to find the perimeter of the rectangle, given by
P= 2(l+w) where l is the length and w is the width
The units need to be the same
Change 230 yds to ft
230 yd * 3 ft/ y = 690 ft
P = 2(690+200)
P = 2(890)
P =1780
Plsss HELP!!!
*image included
Avery made 6 litres of hot chocolate for the 4th annual bonfire with his family. If
each cup holds of a litre of liquid, how many cups can Avery fill?
Answer:
Avery can hold 6 cups
Step-by-step explanation:
so you have a 6 litre of hot chocolate and for every cup you remove 1 litre of hot chocolate wich makes you get 6 cups of hot chocolate
