The Equation of parabola ( y + 8 )² = 12( x - 2 )
In math, what is a parabola?
A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.
All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.
Given,
Directrix is known as x=a Directrix=a=3 Equation of parabola
(Y-y1)²= 4a(X-x1)
Vertex (X1,Y1) = (2,-8)
Directrix=a=3
Equation of parabola
( y - y₁ )² = 4a( x - x₁)
( y - ( -8))² = 4 * 3(x - 2 )
( y + 8 )² = 12( x - 2 )
Learn more about parabola
brainly.com/question/21685473
#SPJ4
Solve the following system of equations graphically on the set of axes below.
y=-x-6
x-2y=-6
Plot two lines by clicking the graph.
Click a line to delete it.
The graph shows the elevation of a hiker compared to ground level.
What is the y-intercept?
Answer:
-15
Step-by-step explanation:
100 points
Pls pls pls help
What is the measure of angle R in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the hundredths place (2 decimal places).
m∠R=
Answer:
m∠R = 61.92°------------------------------------
Use trigonometry.
Since all three sides are known, you may choose either sine, cosine or tangent.
We'll use sine here:
sine = opposite leg / hypotenusesin ∠R = TS/TRsin ∠R = 60/68sin ∠R = 0.8823m∠R = arcsin 0.8823m∠R = 61.92°If a nonlinear system depends on a parameter, then the equilibrium points can change as the parameter varies. In other words, as the parameter changes, a bifurcation can occur. Consider the one-parameter system family of systems dx = x2 – a =-y(+2+1), where a is the parameter.(a) Show that the system has no equilibrium points if a < 0. (b) Show that the system has two equilibrium points if a > 0. (c) Show that the system has exactly one equilibrium point if a = 0. (d) Find the linearization of the equilibrium point for a = 0 and compute the eigenvalues of this linear system.
If a<0, then there is no x-null lines, the system has no equilibrium points.
If a=0, it has only one equilibrium points.
If a>0, the system has two equilibrium points.
Points are (-√a,0) and (√a,0)
The system changes from no fixed points to two fixed points when it increases through a=0.
a is a bifurcation point.
The Jawbian matrix,
J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]
Now,
J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0
J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a
If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.
To know more about Parameters refer to:
http://brainly.com/question/29344078
#SPJ4
The graph represents Tamira's motion detector walk. Complete the following sentences based on the graph.
Note that:
For 1) To compute the average rate (AR), divide the change in y-values by the change in x-values. That is:
AR = (5-2)/5-4)
= 3/1
= 3ft/sec.
For 2) we must use the same formula above:
(2-5)/(10-7)
= -1 ft/sec.
Learn more about Average Rate:
https://brainly.com/question/12395856
#SPJ1
Full Question:
See attached graph
revie
the blanks.
Leo and his friends like to collect and trade cards from a certain combat card game. Leo used
his allowance to purchase 9 booster packs and 5 premade decks, which included a total of
253 cards. For his birthday, he received 7 booster packs and 5 premade decks, which
included a total of 229 cards. How many cards come in every booster pack and every
premade deck?
Convert from point slope form to slope intercept form.
Slope U/D, (5,0)
Please help me!!!!!!!
Answer:
x = 5
Step-by-step explanation:
assuming you mean the slope of the line id undefined and passes through (5, 0 )
A line with an undefined slope is a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (5, 0 ) with x- coordinate 5 , then
x = 5 ← equation of line
A certain academic program boasts that 87% of their graduates find full-time employment in their field within the first year of graduation. The academic director is concerned that market factors may have adversely affected the full-time placement rate and decides to perform a Hypothesis Test to see if her concern is warranted.The hypothesis test is performed at a 5% significance level and the resulting p-value is 0.07.Assume that all conditions for testing have been met and choose the statement that contains the correct conclusion.Options:a.there is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05.b.there is sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05. c.there is sufficient sample evidence to conclude that the full-time placement rate is 87% because the p-value is greater than 0.05.c.there is not sufficient sample evidence to conclude that the full-time placement rate is 87% because the p-value is greater than 0.05.
The correct conclusion is A. Since the p-value is greater than the significance level, there is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05.
For the null hypothesis, 87% of the graduates find full-time employment in their field within the first year of graduation. It is tested if the proportion is still of 0.87, so:
H₀: p = 0.87
For the alternative hypothesis, less than 87% of the graduates find full-time employment in their field within the first year of graduation. It is tested if it has decreased, so:
H₁: p < 0.87
Since the p-value is greater than the significance level (p-value is greater than 0.0), we do not reject the null hypothesis, and thus, the correct conclusion is A.
Learn more about null hypothesis at: https://brainly.com/question/28920252
#SPJ4
which of the following characteristics is/are true about the distribution of the response variable in a logistic regression model? a. it is a Bernoulli distribution b. it can be any distribution over rhe interval (0,1) c. it can be any distribution from the exponential family d. it is a distribution from the canonical exponential family
It can be any distribution from the exponential family is true about the distribution of the response variable in a logistic regression model.
What is logistic regression model?Logistic regression is a popular method for solving prediction and classification issues. Among these use cases are: Fraud detection: Logistic regression methods can assist teams in identifying data abnormalities that suggest fraud. The logistic model is a statistical model that represents the chance of an event occurring by making the event's log-odds a linear combination of one or more independent variables. Logistic regression is used in regression analysis to estimate the parameters of a logistic model.
Here,
The distribution of the response variable in a logistic regression model can be any distribution from the exponential family.
To know more about logistic regression model,
https://brainly.com/question/15326879
#SPJ4
78 POINTS BRANLIEST CHECK WILL DELETE U IF WRONG ANSWER
Answer:
Below
Step-by-step explanation:
For the boxes:
the sum of all three angles = 180 for a triangle
soooo : 28 + x-4 + 2x = 180
then x = 52 via algebra
Given the matrix [2 5 5 13], (a) does the Inverse of the matrix exist? Your answer is (Input Yes or No): (b) If your answer is yes, write it as [a_11 a_12 a_21 a_22], find a_11 = a_12 = a_21 = a_22 =
Yes, the inverse of the matrix exist and a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2
The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity.
The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.
According to the question,
The matrix given is [tex]\left[\begin{array}{cc}2&5\\5&13\end{array}\right][/tex]
Let Matrix be A
To check if its inverse exist , We have to find out the determinant
|A| = 13(2) - 5(5)
=> 26 - 25
=> 1
Determinant is non zero
Hence , Inverse exist
(b) To find the inverse , we have to find the adjoint of A
adj A = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]
Inverse is ratio of adj A and determinant A
A⁻¹ = adj A / |A|
=> [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex] / 1
=> A⁻¹ = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]
a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2
To know more about Inverse of matrix here
https://brainly.com/question/4017205
#SPJ4
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) 5 f(x) a = 2 1 + x
The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
Given that,
We have to get the first four nonzero terms of the series for f(x), centering at the specified value of a, use the definition of a Taylor series. (Separate your responses into a list using commas.)
f(x)=5/1+x and a=2
We know that,
Take
f(x)=5/1+x and a=2
f(2)=5/1+2=5/3
f'(x)=-5/(1+x)² f'(2)=-5/(1+2)²=-5/9 (differentiating)
f''(x)=10/(1+x)³ f''(2)=10/(1+2)³=10/27
f'''(x)=-30/(1+x)⁴ f'''(2)=-30/(1+2)⁴=-30/81=-10/27
Using the taylor series
F(x)=f(a)-(x-a)f'(a)+(x-a)²/2!f''(a)-(x-a)³/3!f'''(a)+....
F(x)=f(2)-(x-2)f'(2)+(x-2)²/2f''(2)-(x-2)³/3!f'''(2)+....
F(x)=5/3-(x-2)(5/9)+(x-2)²/2(10/27)-(x-2)³/6(-10/27)+....
F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
Therefore, The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
To learn more about series visit: https://brainly.com/question/15415793
#SPJ4
1.25y-0.35y=585
Solve for y
Answer:
y = 650
Step-by-step explanation:
0.9y = 585
y = 650
Answer:
[tex]y = 650[/tex]
Step-by-step explanation:
[tex]1.25y-0.35y=585[/tex]
[tex]0.9y=585[/tex]
[tex]y = \frac{585}{0.9}[/tex]
[tex]y = 650[/tex]
Find a formula for the general term an of the geometric sequence:
{ 10/3, 10/9, 10/27, 10/81, 10/243}
Express the common ratio r as a fraction and place in parentheses!
an = __________
Answer: [tex]\displaystyle \frac{10}{3}\left(\frac{1}{3}\right)^{n-1}[/tex]
======================================================
Explanation:
a = 10/3 is the first term
r = 1/3 is the common ratio
Multiply each term by r = 1/3 to get the next term.
Example:
(10/3)*(1/3) = 10/9
We then plug those two items into the formula
[tex]a_n = a(r)^{n-1}[/tex]
to end up with the answer shown above.
The value of n is a positive integer.
sara correctly solves a system of two linear equations and finds that the system has no solution. if one of the two equations is -
When two system of linear equations solved by Sara represents the lines parallel to each other then the equations have no solution.
Step by Step explanation:
Given system of two linear equations :
Let us consider system of two linear equation with Sara has :
y = 3x + 7
y = 3x + 9
Here both the lines have same slope = 3
Lines are parallel to each other.
Solve the equation by elimination method :
y = 3x + 7
y = 3x + 9
0 = 0x - 2
⇒ -2 = 0 which is not possible and has no solution.
Therefore, when the system of linear equations with Sara has no solution it represents lines are parallel to each other.
Learn more about linear equations here
brainly.com/question/11897796
#SPJ4
Which statement is true about the functions f(x)=-15x^2+32 and g(x)=-17x^2+5x+32? a. f(x) and g(x) have the same zeros. b. f(x) has a higher maximum than g(x). c. f(x) and g(x) have the same y intercept. d. f(x) and g(x) are odd functions.
None of the Options are true both the given functions are parabolic functions.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given function are, f(x)=-15x²+32 and g(x)= -17x²+5x+32,
Zeros for the functions are,
x = ± 1.461 and x = -1.233 and 1.527,
Where g(x) has a higher maximum than f(x), the Intercept of f(x) is greater than g(x). As shown in the graph.
Thus, none of the options are true because both of the supplied functions are parabolic.
Learn more about function here:
brainly.com/question/21145944
#SPJ1
State if the three side lengths form an acute, obtuse or right triangle. 9m, 12m, 15m
The three side lengths; 9m, 12m, 15m as given in the task content would form a right triangle.
What type of triangle is formed by the three side lengths as given in the task content?It follows from the task content that the type of triangle formed by the side lengths given is to be determined.
On this note, recall that given three side lengths, a, b and c where c is the longest of all three side-lengths;
if; c² > a² + b² .....Obtuse triangle.
if; c² < a² + b².......Acute triangle.
if; c² = a² + b²........Right triangle.
On this note, since;
15² = 12² + 9²
225 = 144 + 81
225 = 225.
The three side lengths in discuss would form a right triangle.
Read more on Pythagoras triples;
https://brainly.com/question/11994763
#SPJ1
manny has just filled out his deposit ticket for his savings account. he hands it to the teller and the teller hands it back to manny. the teller explains to manny that the deposit ticket cannot be accepted in its current form. what must manny do to the deposit ticket in order for the teller to process the deposit ticket? a deposit ticket. the ticket has not been signed for cash back. the date is december 16. a. manny forgot to sign the deposit ticket for less cash back
The manny must do his signature on the deposit ticket in order to get deposited the cashback ticket.
What is cashback?
Cashback is a type of reward program offered by some retailers and online merchants that gives customers money back for making purchases. It is a way for retailers to reward customers for their loyalty and encourage them to keep coming back to their store. Cashback can be offered in the form of a fixed amount, a percentage of the purchase price, or a combination of both. Cashback rewards may be paid in cash or as credits to the customer's account, and they may be used to purchase additional items from the store or to offset future purchases.
When teller sees the deposit ticket he must have seen that it is not signed by manny hence he returned this to manny now manny just have to do one work that to sign that deposit ticket after that teller will accept that deposit ticket and manny will get his required cashback easily in his bank account
To learn more about cashback click the link:
https://brainly.com/question/25708125
#SPJ1
Answer:
a edge
Step-by-step explanation:
Question 29 The Valley of Ashes symbolizes the emotional turmoil and feelings of the characters the working class who enable the lifestyles of the wealthy the negative economic impact of prohibition laws Gatsby's fears
The Valley of Ashes symbolizes the emotional turmoil and feelings of the characters the working class who enable the lifestyles of the wealthy the negative economic impact of prohibition laws Gatsby's fears organized crime
What is the Valley of Ashes?On the north shore of Long Island, the valley of ashes was a two to three thousand acre marshland that encircled the Flushing River mouth. This small river primarily serves as an inlet into Flushing Bay, which is an arm of the East River, with tidal water flowing through it rather than fresh water.
It is a metaphor for the moral and societal decay brought on by the unrestrained pursuit of wealth, as the wealthy indulge in only their own pleasure. The emotional turmoil and feelings of the characters from the working class that support the lifestyles of the wealthy are symbolized by The Valley of Ashes. the damaging effects of prohibition laws on the economy Gatsby worries about organized crime.
Learn more about Valley of Ashes on:
https://brainly.com/question/14449158
#SPJ1
Can someone help me solve this?
The length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm² respectively.
What is a Rectangle?A rectangle is a polygon in two dimension with four sides with opposide sides are equal and all the angles are right angles.
Given smaller rectangle is 1/2 scale drawing of the original figure. So the dimensions of the smaller rectangle will be half of the dimensions of the bigger rectangle.
For bigger rectangle,
Length = 36 cm
Width = 28 cm
Area = 1,008 cm²
So for smaller rectangle,
Length = 36/2 = 18 cm
Width = 28/2 = 14 cm
Area = 18 × 14 = 252 cm²
Hence the length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm².
To learn more about Rectangles, click :
https://brainly.com/question/29123947
#SPJ1
Evaluate the expression 6x +4 9/10 when x=2/3
Answer:
8 [tex]\frac{9}{10}[/tex]
Step-by-step explanation:
substitute x = [tex]\frac{2}{3}[/tex] into the expression
(6 × [tex]\frac{2}{3}[/tex] ) + 4 [tex]\frac{9}{10}[/tex]
= (2 × 2) + 4 [tex]\frac{9}{10}[/tex]
= 4 + 4 [tex]\frac{9}{10}[/tex] ( add the whole numbers )
= 8 [tex]\frac{9}{10}[/tex]
On the grid above, flag F is rotated around point S. Which of the images does NOT result from this transformation?
A.
image 3
B.
image 2
C.
image 1
D.
All of the images result from this transformation
.
A figure in the flag has rotational symmetry if the figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure.
What is symmetry?Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Something is symmetrical when it is the same on both sides. A shape has symmetry if a central dividing line (a mirror line) can be drawn on it.To learn more about symmetry refer to:
https://brainly.com/question/1002723
#SPJ1
Find an explicit description of Nul A by listing vectors that span the null space. 1 2 3 0 A = 0 0 1 0 A spanning set for Nul A is (Use a comma to separate answers as needed.)
An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.
What is the explicit description of a null space matrix?
To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.
The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.
To find a spanning set for Nul A, we can use the following steps:
Row reduces the matrix A to a reduced row-echelon form using elementary row operations.
Identify the free variables in the row-reduced matrix.
For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.
The set of vectors created in step 3 form a spanning set for Nul A.
For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:
[1, 2, 3, 0] -> [1, 2, 3, 0]
[0, 0, 1, 0] -> [0, 0, 1, 0]
The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:
x3 = [0, 0, 1, 0]
x4 = [0, 0, 0, 1]
These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.
Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.
To learn more about the null space matrix, visit:
https://brainly.com/question/27959040
#SPJ4
order these numbers for least to greatest -4,5,-2,1,0
Answer: 0, 1, 5, -2 ,-4
Step-by-step explanation: hope it helps
Please help!!!!!!!!!!
Answer: [tex]6^{\frac{1}{12} }[/tex]
Step-by-step explanation:
Fawzia is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee is $20 and the one-time joining fee is $100. Make a table of values and then write an equation for C,C, in terms of t,t, representing the total cost of the gym membership over tt months.
Answer: See below
Step-by-step explanation:
C=20t+100
t= number of months
C= total cost over t number of months
Table of values
t C
1 120
2 140
3 160
4 180
5 200
Which linear function has the greatest rate of change?
A. The Equation
B. The Table
C. The graph
Answer:
The graph
Step-by-step explanation:
The graph has a slope of 4, the equation has a slope of 3, the table has a slope of 2.
a recipe asks for 223cups of raisins. how many cups of raisins are needed to make 12of a recipe? multiply. express the answer in simplest form. enter the answer in the box.
The anwer of number of cups of raisins required for 12 recipes needing 223 cups of raisins each are 2676.
Multiplication operation will be required to find the number of cups of raisins. The expression to be formed for calculation is-
Total number of cups = number of recipes × number of cups for one recipe
Keep the values in formula to find the total number of cups
Total number of cups = 12 × 223
Performing multiplication on Right Hand Side of the equation
Total number of cups = 2676
Thus, 2676 cups are required for recipe.
Learn more about expression -
https://brainly.com/question/723406
#SPJ4
The University is conducting a similar analysis on how much of the 80-minute TR class sessions are used for instruction. There is evidence from a previous study that the population standard deviation for duration time is
2.1
minutes. A random selection of 83 class sessions this semester yields an average duration time of 78 minutes. (a) Calculate a
90%
confidence interval the parameter of interest. (No interpretation needed in your final answer; just the numeric interval.) (a) [5 pts] (b) What is the minimum sample size required to estimate the mean duration time of TR classes to within
0.5
of a minute with
99%
confidence? (b) [5 pts] (c) Suppose that the sample standard deviation for duration times in this study is
2.6
minutes. Calculate a
95%
confidence interval for
σ 2
, the population variance.
The minimum sample size required to estimate the mean duration time of TR classes is t distribution confidence interval.
The confidence interval is 75.0694 and 76.9306.
Given that
(a) This is t-distribution confidence interval because sample standard deviation is given and also sample size is less than 30.
(b)
CI for 95%
n 28
mean 76
value of 95% CI and df = 27 (using table) 2.0518
std. dev. 2.4
SE = standard deviation/n² 0.45356
ME = t*SE 0.93062
Lower Limit = Mean - ME 75.06938
Upper Limit = Mean + ME 76.93062
95% CI (75.0694 , 76.9306 )
95% CI=75.0694 , 76.9306
(c)The 95% confidence interval estimate of the population mean is within 75.0694 and 76.9306 (lower bound and upper bound)
To know more about Standard Deviation refer to:
http://brainly.com/question/12402189
#SPJ4
find the minimum value of x for which the laser beam passes through side b and emerges into the air.
Hence the minimum value of x is 18 cm
what is minimum value?a minimal requirement of coverage that is applicable to employment-based health plans. You cannot receive a premium tax credit if you purchase a Marketplace insurance plan if your employer's plan satisfies this criterion and is deemed "affordable."
given,
Within 10 cm of the A, a laser beam will pierce the water.
Snell's law permits us to state:
[tex]n_{1}sin\alpha ^{2} = n_{2}sin\beta^{2}[/tex]
Where,
is equal to 1, which is air's refractive index.
a measure of water's refractive index is [tex]n_{2}[/tex] = 1.33
At the interface, we can formulate a formula using Sell's law.
θ[tex]_{2}[/tex] = 38.7°
x= 18 cm
hence the minimum value of x is 18 cm.
To know more about minimum value visit:-
https://brainly.com/question/14316282
#SPJ4