Graphing Quadratic Functions 1. List a, b, and c. 4. What is the y-intercept? 5. Create a table and graph. X f(x) Quadratic Function f(x) = x² - 2x + 6 2. Find the axis of symmetry. F Y 10 9 8 7 6 5 4 3 2 1 -9-8-7-6-5-4-3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 3. Find the vertex. tx 1 2 3 4 5 6 7 8 9 10 X
Answers
The value of a, b, and c are 1, -2, and 6 respectively.
The y-intercept of this quadratic function is 6.
The axis of symmetry of this quadratic function is 1.
The vertex of this quadratic function is (1, 5).
How to calculate the axis of symmetry of a quadratic function?Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = x² - 2x + 6, we have:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(-2)/2(1)
Axis of symmetry, Xmax = 2/2 = 1.
Vertex (h, k) = (1, 5).
In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
y-intercept = 6.
Lastly, we would create a table and then graph the quadratic function as follows;
x y
0 6
2 2
5 11
Read more on quadratic function here: brainly.com/question/13159926
#SPJ1
Related Questions
Please help!!
In the triangle below, b =______. If necessary, round your answer to two
decimal places.
A
38°
Answer here
8
31.6°
25
SUBMIT
Answers
Answer:
Step-by-step explanation:
38.06
In the last several weeks, 66 days saw rain and 98 days saw high winds. In that same time period, 31 days saw both rain and high winds. How many days saw either rain or high winds?
Answers
133 days saw either rain or high winds.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Example: If an experiment has 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event will be as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
P(r) = 66 days
P(w) = 98 days
P(both) = 31 days
P(r or w) = P(r) + P(w) - P(both)
P(r or w) = 66 + 98 - 31
P(r or w) = 133 days
Learn more about probability here: https://brainly.com/question/24756209
#SPJ1
In the state of Pennsylvania 12% of students submit box tops for education to their school. A large school district in western Pennsylvania runs a contest to see if they can increase participation. The superintendent takes a random sample of 210 students from the district and finds that 35 have submitted box tops this year. Do these data provide convincing evidence that the contest has increased participation in the box tops for education programs
Answers
Answer:
Step-by-step explanation:
All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people
The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.
How to calculate the null hypothesis?To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.
We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).
Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.
Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.
To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:
z = (p' - p) / √(p x (1-p)/n)
where n is the sample size.
Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).
Using p = 0.12 and n = 210, we have:
z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08
The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.
To know more about the null hypothesis follow
https://brainly.com/question/15980493
#SPJ2
Consider the function f(x) = 4 − 2 sec x. Find the exact coordinates of three points on
the function where f has a horizontal tangent
Answers
The exact coordinates of points where the horizontal tangent exists are:
(0,2)
([tex]\pi[/tex],6)
([tex]-\pi[/tex],6)
What is meant by tangent?
A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.
Given function is f(x)=4-2secx
We can write it as
y=4-2secx
The slope of the tangent to this curve is:
[tex]\frac{dy}{dx} =-2secx*tanx[/tex]
Given that the tangent is horizontal, which means that the slope is zero.
-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].
So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].
When x=0 ⇒ y=4-2sec0
⇒y=2
When x=π ⇒ y=4-2secπ
y=6
When x=-π⇒ y=4-2sec(-π)
y=6
Therefore the exact coordinates of points where the horizontal tangent exists are:
(0,2)
([tex]\pi[/tex],6)
([tex]-\pi[/tex],6)
The graph is attached below.
To learn more about tangents of function, refer to the link below:
brainly.com/question/4470346
#SPJ1
Need help with this. Keep getting answer wrong
Answers
Answer:
see image
Step-by-step explanation:
First of all, the problem might be that we need to set this up differently than how it is written.
"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:
THAT - THIS
Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.
Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.
1/5 - 2/5 is -1/5.
And -1/4 - 1/4 is -2/4, which is -1/2.
see image.
Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.
Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A(3,7) and B(4,9)
Answers
Answer:
To perform a dilation with a scale factor of 2 centered at the origin, we need to multiply each coordinate of the original points A and B by the scale factor of 2.
The coordinates of point A after dilation are:
A′(2 * 3, 2 * 7) = A′(6, 14)
Similarly, the coordinates of point B after dilation are:
B′(2 * 4, 2 * 9) = B′(8, 18)
So, the endpoints of the dilated line segment are A′(6, 14) and B′(8, 18).
A = (3,7) becomes A′ = (2 * 3, 2 * 7) = (6,14)
B = (4,9) becomes B′ = (2 * 4, 2 * 9) = (8,18)
So, the new coordinates of A′ and B′ after dilation with a scale factor of 2 centered at the origin are (6,14) and (8,18), respectively
guysss solve this
there are "6" eggs layed on the table
I break "2" of them
I cooked "2" of them
I ate "2" of them
how many eggs did they left?
Answers
Answer:
Step-by-step explanation:
4.
first, you broke the 2 eggs, and then cooked the eggs. after cooking them, you ate the two eggs that you cracked and cooked.
Calvin will plant lily bulbs and iris bulbs in his front garden. He will plant a total of flower bulbs and as many iris bulbs as lily bulbs. The graph below shows the number of lily bulbs (x) and the number of iris bulbs (y) Calvin will plant. Bulbs to Be Planted Which statement describes the point of intersection on the graph?
A. Calvin will plant lily bulbs.
B. Calvin will plant iris bulbs.
C. Calvin will plant lily bulbs and iris bulbs.
D. Calvin will plant lily bulbs and iris bulbs. Lily Bulbs
Answers
The statement that describes the point of intersection on the graph is Calvin will plant lily bulbs and iris bulbs. Option C
What is point of intersection of a graph?The point of intersection on the graph represents the values of x and y where both conditions are satisfied.
In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.
So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".
Learn more about point of intersection at:https://brainly.com/question/343077
#SPJ1
4. The running track in this diagram consists of two parallel sections with semicircular sections at each end.
Determine the area of the running track.
Answers
The area of the running track, given the parallel sections and the semicircle sections, is https://brainly.com/question/30584763
How to find the area ?To find the area of the running track, you first need to find the area of the whole shape and then the area of just the inner section.
Area of whole shape :
= Area of both semicircles + Area of the rectangle
= ( π x 46. 41 ²) + ( 85 x ( 46. 41 x 2 ))
= 14, 659.06 m ²
Then, find the area of the inner section :
= ( π x 36. 41 ²) + ( 85 x ( 36. 41 x 2 ))
= 10, 356. 45 m ²
The area of the running track is :
= 14, 659.06 - 10, 356. 45
= 4, 302. 61 m ²
Find out more on area at https://brainly.com/question/30584763
#SPJ1
Suppose we have a bag of jelly beans 82% of the jelly beans orange, 14% are black, and 4% are green. Moreover, 15% of orange are sugar free, 70% of black beans are sugar free, and 90% of green beans are sugar free Suppose we select a jelly bean at random.
1. Construct a tree diagram to represent this situation
2. Find the probability of green bean and sugar free
3. Given the bean is sugar free, what is the probability that it is an orange bean?
Please I need help
Answers
Answer:
3/50
Step-by-step explanation:
3 g, 5 r, 2 o
3 + 5 + 2 = 10
Orange = 2 jelly beans
Probability of selecting an orange jelly bean: 2/10 or 1/5
If you put the jelly bean back in, there is still 10 jelly beans.
Green = 3 jelly beans
Probability of selecting a green jelly bean: 3/10\
Multiply the probabilities:
1/5 x 3/10
= 3/50
An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 years is approximated by dh/dt = 1.2t + 3, where t is the time in years and h is the height in centimeters. The seedlings are 11 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answers
(a) The height after t years is given by
h(t) = 0.6t² + 3t + 11
(b) The shrubs are 38 centimetres tall when they are sold.
What is the growth rate of the shrubs during the first year of growth?The growth rate of the shrubs during the first year of growth can be determined by setting t = 1 in the given differential equation dh/dt = 1.2t + 3. This gives us dh/dt = 1.2(1) + 3 = 4.2 centimeters per year.
Therefore, during the first year of growth, the shrubs will grow at a rate of 4.2 centimeters per year. This rate of growth is expected to increase as the shrubs age and reach the end of the 5-year growth period before they are sold by the nursery.
(a) To find the height after t years, we integrate the growth rate function with respect to t:
∫dh/dt dt = ∫(1.2t + 3) dt
h(t) = 0.6t² + 3t + 11
(b) The shrubs are sold after 5 years, so we plug in t = 5 into the function we found in part (a):
h(5) = 0.6(5)² + 3(5) + 11
= 38 cm
Therefore, the shrubs are 38 centimetres tall when they are sold.
To know more about Growth visit:
brainly.com/question/16465256
#SPJ1
the sum of two fractions is 5 3/8 one of the numbers is 7/9 what is the other number
Answers
Answer:
[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]
Step-by-step explanation:
Let the unknown fraction be x
We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9
First convert 5 3/8 to an improper fraction for easier calculation
[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]
Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]
Subtract [tex]\dfrac{7}{9}[/tex] on both sides to isolate x:
[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]
[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]
To compute the right side
Find the LCM of 8 and 9: 8 x 9 = 72Adjust the fractions based on LCM so we get 72 as a common denominator:[tex]\dfrac{43}{8}=\dfrac{43\cdot \:9}{8\cdot \:9}=\dfrac{387}{72}\\\\\\\dfrac{7}{9}=\dfrac{7\cdot \:8}{9\cdot \:8}=\dfrac{56}{72}\\\\[/tex]Subtract the numerators and use 72 as the common denominator
[tex]\dfrac{43}{8} - \dfrac{7}{9} = \dfrac{387}{72} - \dfrac{56}{72}\\\\\\= \dfrac{387-56}{72}\\\\= \dfrac{331}{72}[/tex]
[tex]= 4\dfrac{43}{72}[/tex]
Rewrite the equation in Ax+By=C form
y+2=-4(x-1)
Answers
Answer:
4x + y = 2
Step-by-step explanation:
y + 2 = - 4(x - 1) ← distribute parenthesis by - 4
y + 2 = - 4x + 4 ( add 4x to both sides )
4x + y + 2 = 4 ( subtract 2 from both sides )
4x + y = 2 ← in standard form
Solve the triangle using law of cosines. Round answer to the nearest tenth.
Answers
Using sine law and cosine law, s is 13.6 units and T is 37.7 degrees while U is 59.3 degrees
What is law of cosineThe Law of Cosines, also known as the Cosine Formula, is a fundamental mathematical relationship between the sides and angles of a triangle. It states that the dot product of two sides of a triangle is equal to the product of the third side and the cosine of the angle between the two sides.
The general form of the Law of Cosines is:
C^2 = A^2 + B^2 - 2ABcos(C)
where C is the angle between sides A and B, and A, B, and C are the lengths of the sides of the triangle. The formula can be rearranged to solve for any one of the sides or angles given the other two.
In this problem, we can easily solve for s.
s² = 8² + 12² - 2(8)(12)cos83
s² = 184.601
s = √184.601
s = 13.6 units
The value of angle T is calculated using sine law;
13.6 / sin 83 = 8 / sin T
sin T = 8(sin 83) / 13.6
sin T = 0.58385
T = sin⁻¹(0.58385)
T = 37.7°
Using sum of angle in a triangle;
T + S + U = 180°
83 + 37.7 + U = 180
U = 180 - 120.7
U = 59.3°
Learn more on cosine law here;
https://brainly.com/question/4316134
#SPJ1
What is 1/5 (3+2+5)^2
Answers
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
20
Step-by-step explanation:
1/5(3+2+5)^2
3+2+5 = 10
10^2 = 100
100/5 = 20
Solve for x with the given measures
Answers
Answer: X= -66
Step-by-step explanation:
If m angle UYV=56
Then WYX= -x-10=56
then X=-66
pls help!!
In the xy-plane, the point (2,10) lies on the graph of the
function f(x) = 2x2 + bx - 8. What is the value of b?
(answer choices in the image attached)
Answers
In the xy-plane, the point (2,10) lies on the graph of the function f(x) = 2x^2 + bx - 8. The value of b is 4.
What is linear equation?
A linear equation is an equation that describes a straight line in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope of a line is the measure of how steeply the line rises or falls, and the y-intercept is the point at which the line crosses the y-axis.
In a two-dimensional coordinate system, a linear equation represents a straight line that can be graphed by plotting pairs of x and y values that satisfy the equation. The line passes through all points that satisfy the equation and no others.
We can find the value of b by using the point-slope form of a linear equation, which states that the equation of a line with slope m that passes through the point (x1, y1) is given by y - y1 = m(x - x1).
In this case, the slope of the line is equal to 4x, and the point (x1, y1) is (2, 10), so we have:
y - 10 = 4x * (x - 2)
Expanding the right-hand side, we get:
y - 10 = 4x^2 - 8x
Matching this equation with the given function f(x) = 2x^2 + bx - 8, we see that b = 4.
So the value of b is 4.
Learn more about linear equation click here:
https://brainly.com/question/28871326
#SPJ1
Find the value of x that makes each sentence true.
If (5 1/5)^5=25x then x =
If (8 1/3)^2= 4x, then x =
Answers
The first equation is:
(5 1/5)^5 = 25x
To solve for x, we need to simplify the left side of the equation first.
(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776
So,
7776 = 25x
Therefore,
x = 7776/25 = 311.04
For the second equation:
If (8 1/3)^2 = 4x, then x =
We need to simplify the left side of the equation first.
(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81
So,
81 = 4x
Therefore,
x = 81/4 = 20.25
So the values of x that make each sentence true are 311.04 and 20.25, respectively.
please help me i’ll give you brainlist
Answers
Answer:
its c
Step-by-step explanation:
16% of the cows have already had calves. 32 have not had calves yet. How many are in the herd?
Answers
Answer:
There are approximately 38 cows in the herd.
Step-by-step explanation:
In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.
Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).
[tex]100\%-16\% = 84\%[/tex]
We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.
[tex]32 \text{ cows} = 84\% \cdot x[/tex]
Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.
[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]
[tex]x \approx 38 \text{ cows}[/tex]
So, there are approximately 38 cows in the herd.
Simplify the following as much as possible
A. csc x
B. sec x
C. sin x
D. cos x
Answers
Answer:
[tex]\textsf{C.} \quad \sin x[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]
Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:
[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]
Therefore:
[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]
Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:
[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]
[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]
Cancel the common factor cos²x:
[tex]=\dfrac{\sin^2x}{\sin x}[/tex]
Simplify:
[tex]= \sin x[/tex]
Therefore:
[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]
You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,
determine how long it will take for the object to hit the ground below. NEAREST TENTH
Answers
Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.
How long it will take for the object to hit the ground below?The equation for the vertical movement of an object will be:
H(t) = -16*t^2 + v0*t + h0
Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height, 55ft.
Then the height equation is:
H(t) = -16*t^2 + 85*t + 55
The object will hit the ground when the height is equal to zero, then we need to solve:
-16*t^2 + 85*t + 55 = 0
Using the quadratic formula we will get:
[tex]t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}[/tex]
We only care for the positive solution, which is:
t = (-85 - 103.7)/-32 = 5.9
So it will take 5.9 seconds for the object to hit the ground.
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center (−3, 2); passes through (−6, −6)
Answers
An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73
Finding an equation of a circleThe formula for finding the equation of a circle is expressed as:
(x-a)^2 + (y - b)^2 = r^2
Determine the value of r^2 using the distance between two points
r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9
r^2 = 73
Given the centre (a, b) as (-3, 2), the equatio of the circle will be;
(x-(-3))^2 + (y - 2)^2 = 73
(x+3))^2 + (y - 2)^2 = 73
Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73
Learn more on equation of the circle here: https://brainly.com/question/1506955
#SPJ1
This system of equations has been placed in a matrix:
y=650x + 175
y= 25,080 - 120x
Column 1
Column 2
Column 3
Row 1
-1
Row 2
120
Answers
Using matrix inversion, the value of x and y are 1.104 and 39.704 respectively
What is the solution to the equationsThe system of equations can be written in matrix form as:
| -650 1 | | x | | 175 |
| 120 1 | | y | | 25,080 |
To solve for x and y, we can use matrix inversion to get:
| x | | -650 1 |^-1 | 175 |
| y | = | 120 1 | | 25,080 |
Using matrix inversion, we get:
| x | | -0.00016 0.00875 | | 175 | | 1.104 |
| y | = | 0.00476 0.00004 | | 25,080 | = | 39.704 |
Therefore, the solution to the system of equations is x = 1.104 and y = 39.704.
Learn more on matrix inversion here;
https://brainly.com/question/12442362
#SPJ1
Solve -4(r-2/3)+4<-8. Show your work
Please help quickly I will give brainly and do step by step explanation thanks!
Answers
Answer:
11/3
Step-by-step explanation:
-4(r-2/3)+4<-8
-4r+8/3+4<-8
8/3+4<-8+4r
8/3+4+8<4r
44/3<4r
44/12=r
11/3=r
1. An arithmetic sequence is given using the recursive definition: b₁ = 8 and b₁ =b₁-₁-3. Which of the
n-1
following is the value of b,? Show the work that leads to your answer.
(1) 14
(2) 2
(3) 6
(4) 4
Answers
Answer:
To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:
b_n = b_1 + (n-1)d
where d is the common difference. In this case, d = -3.
So, we can plug in the values for b_1 and d to find b_n:
b_n = 8 + (n-1)(-3)
b_n = 8 - 3(n-1)
Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:
b_14 = 8 - 3(14-1)
b_14 = 8 - 3(13)
b_14 = 8 - 39
b_14 = -31
So, the value of b_14 is -31, and the answer is (1) 14.
f(x) = (x-7)³, find f¯¹(x).
Answers
The inverse function f-¹(x) as required to be determined from the given function; f(x) = (x-7)³ is; f¯¹(x) = ³√x + 7.
What is the inverse function f-¹(x)?It follows from the task content that the inverse function of the given function; f(x) = (x-7)³ is to be determined.
Therefore, let f(x) = y; so that we have;
y = (x - 7)³
make x the subject so that we have;
³√y = x - 7
x = ³√y + 7
By switching the variables; we have;
y = ³√x + 7
Therefore, the required inverse function; f-¹ as required is; f¯¹(x) = ³√x + 7.
Read more on inverse function;
https://brainly.com/question/3831584
#SPJ1
Please help me
If a rock is thrown upward on an exoplanet of a nearby star with initial velocity
Answers
Velocity of rock when it hits the ground is -22.9955152 ft/s
What is velocity?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time
Its position function is s(t) = –25t² + 1.86t
When it reaches back ground s(t) = 25 m/s
Substituting
s(t) = –25t² + 1.86t = 25
Using the quadratic formula (-b±√b²-4ac)/2a
(-1.86 ±√1.86-4*25*-25)2*25
(-1.86 ±√1.7298+625)50
(-1.86 ±√626.7298)/50
(-1.86÷25)50
(-1.86+25)50 or( -1.86 -25)50
48.14/50 = 0.9628
This figure is taken because its positive
Time = 0.9628 seconds
Now we need to find velocity when it reaches ground, that is velocity after 0.9628 seconds.
Differentiating s(t) equation
Substituting t = 0.9628 seconds
v(t) = –25(0.9628)² + 1.86(0.9628)
v(t) = -23.174596 + 0.1790808
Velocity of rock when it hits the ground is -22.9955152 ft/s
Learn more about velocity on https://brainly.com/question/30559316
#SPJ1
How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10?
0 triangles
2 triangles
1 triangle
Cannot be determined based on the given information
Answers
Based on the given information,
only one triangle is possible.
The correct option is C.
What is a 30-60-90 triangle?It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.
Given:
The angle measure of B = π/6 = 30°.
a = 20, and b = 10
That means,
m∠A = 2∠B = 2 x 30 = 60°.
Now, there is only one possibility of a triangle, and that triangle is 30-60-90 triangle.
Hence, only one triangle is possible.
To learn more about 30-60-90 triangle:
brainly.com/question/11751274
#SPJ1
Using the terms ‘development’ and ‘fidelity’, explain the value of terms that are essentially contestable. Show how these terms differ from others described as well-defined.
Answers
Step-by-step explanation:
we all know that development is positive change in society and fidelity is a process of fertilization of human in society that explain us development and fertilization are the process of positive changes in our environment and province
