Complete the squareto find the vertexof this parabola.yy? -4 2-8y-12=0([?], [ ]
Answers
ANSWER
The vertex is (-7, 4)
EXPLANATION
We usually see the equation of a parabola with this form:
\(y=a(x-h)^2+k\)Where (h, k) is the vertex of the parabola.
But in this problem, the variables are changed, so we're looking for an equation like:
\(x=b(y-k)^2+h\)The vertex is also point (h, k).
To complete the square we have to see the terms that contain y: y² - 8y
We know that a perfect square has the form:
\((a\pm b)^2=a^2\pm2ab+b^2\)If the term that contains y with exponent 1 has a coefficient 8, then we can find the second number of the binomial for the perfect square:
\((y+n)^2=y^2+2yn+\cdots=y^2-8y+\cdots\)let's not think of the third term just yet. For now we have to concentrate on the second term:
\(\begin{gathered} 2yn=-8y \\ 2n=-8 \\ n=-4 \end{gathered}\)The second number for the perfect square is -4:
\((y-4)^2=y^2-8y+16\)Now we have to put this inside the equation. Since now we have a third term that is 16 we have to subtract 16 so we keep the equation true. I'll replace y²-8y by (y-4)²-16:
\(-4x+(y-4)^2-16-12=0\)We can add 4x on both sides so we have the x and y separate:
\(\begin{gathered} 4x=(y-4)^2-16-12 \\ 4x=(y-4)^2-28 \end{gathered}\)And finally we have to divide both sides by 4:
\(x=\frac{1}{4}(y-4)^2-7\)So in this case k = 4 and h = -7. The vertex is (-7, 4)
Related Questions
calculate 25.13 -(4.6²-3x5)
Answers
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Answers
4x - 5 = 2x + 7
First, let's simplify the equation by combining like terms:
4x - 2x = 7 + 5
2x = 12
Next, divide both sides of the equation by 2 to solve for x:
x = 12 / 2
x = 6
Therefore, the value of x that satisfies the equation is 6. None of the provided answer options (27, 37, 47, 57) are equal to 6.
Which is greater the 3ed multiple of 10 ot 6th multiple of 5
Answers
Evaluate the following expression when x = -5 and y = 25.
A. -3,130
B. -630
C. 3,120
D. 620
Answers
what is the y-intercept of the graph of the line whose equation is y=-2/5x+4
a -5/2
b -5/2
c 0
d 4
Answers
Answer:
d 4
Step-by-step explanation:
the graphing form is y=mx+b, b is the y-intercept.
If we look at the equation we see that b is +4.
Multiply by 10s 3,721 times 30
I NEED DONE ASAP PLEASE
Answers
Answer:
111630
Step-by-step explanation:
Please help asap questions in photo
Answers
The information concerning the following circumferences are listed below:
Case 1: 9π inches
Case 2: 14π centimeters
Case 3: 25π meters
Case 4: 9.6π yards
Case 5: 15π inches
Case 6: Diameter: 66 / π feet, Cost: 29.7 US dollars.
How to calculate circumferences
Circumferences (s) are the perimeter of a circle, we can measure it by means of the following formula:
s = 2π · r = π · D
Where:
r - RadiusD - DiameterNow we proceed to determine the circumferences for each case:
Case 1
s = π · (9 in)
s = 9π in
Case 2
s = 2π · (7 cm)
s = 14π cm
Case 3
s = π · (25 m)
s = 25π m
Case 4
s = 2π · (4.8 yd)
s = 9.6π yd
Case 5
s = 2π · (7.5 in)
s = 15π in
Case 6
First, determine the diameter of the circumference:
d = s / π
d = 66 / π ft
Second, calculate the cost of the rope:
C = (66 ft) × (0.45 USD / ft)
C = 29.7 USD
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Given the problem below what mistake did Bob make in solving the equation? Bob and his friends paid $30 for 3 sandwiches and and 3 bottles of water.
-Each sandwich cost the same amount.
-The bottles of water cost $1.50 each.
The equation 3(x + 1.50) = 30 can be used to determine x, the cost of each sandwich. Bob solved the equation using these steps: 3(x + 1.50) =30
3x + 1.50 = 30
3x = 28.50
x = 9.50
Answers
Answer:
Bob forgot to distribute 3 to 1.50 in the parentheses
Step-by-step explanation:
Bob made the mistake in his first step.
In the equation 3(x + 1.50) = 30, the 3 has to be distributed to both x and 1.50.
But, Bob only distributed it to x, which led him to get the wrong answer.
So, Bob's mistake when solving was that he forgot to distribute the 3 to 1.50
Suppose the life time (in hours) of a battery brand is normally distributed. A random sample of 16 batteries results in a sample variance of
3.25
hours
2
. We want to test if there is significant/sufficient evidence in the sample data to claim that the variance of the battery life population is different than 4 hours
2
at significance level of
0.05
. Which of the following is INCORRECT? A.
H 0
:σ 2
=4 vs H 1
:σ 2
=4
B. The test statistic is found to be
12.1875
C. We should reject the null hypothesis and there is sufficient evidence to claim that the variance of battery life is different than 4 hours
2
at significance level of
0.05
. D. None of the above.
Answers
there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
answer is D. None of the above.
To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:
X2 = (n-1)*(s2/σ2)
where n is the sample size, s2 is the sample variance and σ2 is the population variance.
In this case, n = 16, s2 = 3.25 and σ2 = 4
X2 = (16-1)*(3.25/4) = 12.1875
The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
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Find the: x and y intercepts, asymptotes, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, -coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. Using this information, sketch the graph of the function.
SHOW STEPS
Answers
The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).
How to find x-intercepts?
To find the x-intercepts, we set y = 0 and solve for x:
(x⁴/4) - x² + 1 = 0
This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.
To find the y-intercept, we set x = 0:
y = (0/4) - 0² + 1 = 1
So the y-intercept is (0, 1).
To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.
To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.
To find the critical points, we take the derivative of the function and set it equal to zero:
y' = x³- 2x
x(x² - 2) = 0
x = 0 or x = sqrt(2) or x = -sqrt(2)
These are the critical points.
To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.
Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).
We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:
Interval (-infinity, -sqrt(2)):
Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.
Interval (-sqrt(2), 0):
Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.
Interval (0, sqrt(2)):
Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.
Interval (sqrt(2), infinity):
Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.
Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).
To find the inflection points, we take the second derivative of the function and set it equal to zero:
y'' = 3x² - 2
3x² - 2 = 0
x² = 2/3
x = sqrt(2/3) or x = -sqrt(2/3)
These are the inflection points.
To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.
Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).
We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:
Interval (-infinity, -sqrt(2/3)):
Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.
Interval (-sqrt(2/3), sqrt(2/3)):
Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.
Interval (sqrt(2/3), infinity):
Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.
Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).
To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:
y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509
Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).
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In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (b) What is the probability that a subject would guess more than 20 correct in a series of 36 trials?
Answers
The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001
How to find the pobability that a subject would guess more than 20 correct in a series of 36 trialsIn a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.
Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.
The probability of guessing more than 20 correct is:
P(X > 20) = 1 - P(X ≤ 20)
Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).
Therefore: P(X > 20) = 1 - 0.9999 = 0.0001
So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).
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The cost for two different companies to make x candles is shown on the graph.
Which comparison between the two companies is accurate?
A) The cost per candle made is $1 greater for Quick Wick.
B) There is a $1 difference between the initial values of the two companies.
C) Quick Wick will make 50 candles at a higher cost than Wax Art.
D) Quick Wick will make more candles when the cost is $600.
Answers
Answer:
D) Quick Wick will make more candles when the cost is $600.
Step-by-step explanation:
Find the initial value (b) and the cost per candle (m), to write the equation of each line in the slope-intercept form, y = mx + b. This will help for easy comparison.
✔️Wax Art:
m = change in y/change in x
Using (10, 140) and (20, 180),
m = (180 - 140)/(20 - 10) = 40/10
m = 4
Cost per candle = $4
To find b, substitute (x, y) = (10, 140) and m = 4 into y = mx + b
140 = 4(10) + b
140 = 40 + b
140 - 40 = b
100 = b
b = 100
Initial value = $100
To get the equation, substitute m = 4 and b = 100 into y = mx + b
y = 4x + 100
✔️Quick Wick:
m = change in y/change in x
Using (10, 120) and (30, 180),
m = (180 - 120)/(30 - 10) = 60/20
m = 3
Cost per candle = $3
To find b, substitute (x, y) = (10, 120) and m = 3 into y = mx + b
120 = 3(10) + b
140 = 30 + b
120 - 30 = b
90 = b
b = 90
Initial value = $90
To get the equation, substitute m = 3 and b = 90 into y = mx + b
y = 3x + 90
Let's analyse each option given using the information we now have:
✔️Option A: INCORRECT
Cost per candle for made is $1 less for Quick Wick. I.e. cost per candle for Quick wick is $3. Cost per candle for Wax Art is $4.
✔️Option B: INCORRECT
Difference between the initial value sof the two companies = $100 - $90 = $10
✔️Option C:
Find the cost of making 50 candles for each company by substituting x = 50 into each of their equations. Thus:
Wax Art => y = 4x + 100
y = 4(50) + 100
y = $300
Wax Art will make 50 candles for $300
Quick Wick => y = 3x + 90
y = 3(50) + 90
y = $240
Quick Wick makes 50 candles for $240
As we can see, Quick wick is making 50 candles at a lower cost than Wax Art.
Therefore, option C is INCORRECT.
✔️Option D: find out how many candles (x) each company will make when the cost is $600.
Substitute y = 600 in each equation of both companies
Wax Art => y = 4x + 100
600 = 4x + 100
600 - 100 = 4x
500 = 4x
500/4 = x
x = 125 candles
Quick Wick => y = 3x + 90
600 = 3x + 90
600 - 90 = 3x
510 = 3x
510/3 = x
x = 170 candles
Quick Wick will make more candles when he cost is $600.
Therefore, option D is the only CORRECT statement of comparison.
Which theorem states, "The angles in any polygon always add to 180 times two less than the number of sides"?
Triangle Angle Sum Theorem
Polygon Angle Sum Theorem
Triangle Exterior Angle Theorem
Polygon Exterior Angle Sum Theorem
Answers
Answer:
Polygon Angle Sum Theorem
Step-by-step explanation:
The triangle answers do not apply to generic 'polygon'
and the last choice polygon exterior angle sum is always 360 degrees
simplify the expression
5(m+1) -1 =
Answers
5(m+1) - 1 = 5m + 5 - 1
5m + 4
Answer:
We would distribute the 5,
5(m+1) - 1 = 5m + 5 - 1
5m + 4
Step-by-step explanation:
Efficiency is the ratio of output work to input work, expressed as a percentage. Light bulbs put out less light energy than the amount of electrical energy that is put into the bulb. An illustration of a wide arrow with a light bulb at the tail of it labeled electrical energy 100 J, breaks into a small arrow going forward labeled light 10 J and a larger curling away labeled heat 90 J. The goal of the bulb is to produce light. What is the efficiency of this bulb as it works to put out light? 10% 80% 90% 100%
Answers
Answer:
10%
Step-by-step explanation:
Using the given formula with the given data, we have ...
efficiency = output work / input work
= (10 J)/(100 J) = 0.10 = 10%
Answer:
A) 10%
Step-by-step explanation:
10/100=10
2x + y = 18
complete the table
Answers
Answer:
x y
9 0
8 2
5 8
Step-by-step explanation:
(9, 0) , (8, 2) , and (5, 8) --> all three points satisfy the equation 2x + y = 18.
Answer:
Plug the equation into a graphing calculator, and you'll get these:
(9, 0) , (8, 2) , and (5, 8)
HELP!!!Joe can type 40 words every 2 minutes. How many words can he type in 5 minutes?
Answers
Answer:100
Step-by-step explanation:
40+40 =80 +20=100
Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answers
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84The figure below shows points PQRS on a circle centre O. QP is produced to X Angle XPS = 77 and angle PSO = 68⁰. R Find the size of angle PQO. 0 68% 770 S X
Answers
Answer:
Step-by-step explanation:
The transformation T that transposes every matrix is definitely linear. Which of these extra properties are true? (a) T2 = identity transformation. (b) The kernel of T is the zero matrix. (c) Every matrix is in the range of T. (d) T (M) = -M is impossible
Answers
Option (a) T2 = identity transformation. (b) The kernel of T is the zero matrix. (c) Every matrix is in the range of T. this are true extra properties.
The transformation T that transposes every matrix is indeed linear.
Let's analyze each of the extra properties:
(a) T² = identity transformation: This is true. When you transpose a matrix twice (apply T twice), you get the original
matrix back.
Step 1: Apply T to a matrix M to get its transpose M'.
Step 2: Apply T to the transpose M' to get (M')' which is equal to M.
(b) The kernel of T is the zero matrix: This is true. The kernel of T consists of all matrices M such that T(M) = 0. Since the
transpose of a zero matrix is still a zero matrix, the kernel of T only contains the zero matrix.
(c) Every matrix is in the range of T: This is true. Given any matrix M, there exists another matrix M' such that T(M') = M.
This is because T(M') = M implies M' = T(M), so the transpose of any matrix M can be found by applying T to M.
(d) T(M) = -M is impossible: This is false. It is possible for T(M) = -M in the case of skew-symmetric matrices. A skew
symmetric matrix M satisfies the property that its transpose M' = -M.
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Please help me answer this question?
Answers
Answer:
2+2
Step-by-step explanation:
2 + 4!
3-5
3_4
3-6
2-5
2+5
2_3
2-5
Answer:
(A) 12x³ - 12x
(B) -288
(C) y = -288x - 673
(D) x = 0, 1, -1
Step-by-step explanation:
See images. If it's not clear let me know.
aye i need sum help wid dis
Answers
Answer:
angle 2
Step-by-step explanation:
adds up to 180 degrees
Answer:
5
Step-by-step explanation:
Can someone help me understand it.
Answers
The coordinate of point B is (√3, 1 ).
The coordinate of point C is (3√3/2, 3/2).
What are the coordinates of point B and C?The coordinate of points of B and C is calculated by applying the following formula as follows;
The given coordinate of point A;
A = ( √3/2, 1/2)
Fromm the given coordinate of point A, we can see that;
one unit measure in x axis = √3/2, with a correspond half (1/2) in y - axis
The coordinate of point B is calculated as;
point B; x-axis = (√3/2 x 2) = √3
point B; y axis = 1
B = (√3, 1 )
The coordinate of point C is calculated as;
point C; x-axis = (√3/2 x 3) = 3√3/2
point C; y axis = 3/2
C = (3√3/2, 3/2)
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calculate the average power radiated by each square meter of the sun's surface. (hint: the formula for the surface area of a sphere is a
Answers
The average power radiated by each square meter of the sun's surface is approximately 386 W/m². This value is calculated by dividing the total power radiated by the sun (approx. 386 billion Megawatts) by its surface area (approx. 6.08 x 10¹⁸ square meters). The formula for the surface area of a sphere is 4πr².
Sun Power Output CalculationThe average power radiated by each square meter of the sun's surface can be calculated as follows:
Calculate the total power radiated by the sun:The total power radiated by the sun is approximately 386 billion
Megawatts (3.86 x 10³³ erg/s).
Calculate the surface area of the sun:The surface area of the sun can be calculated using the formula for
the surface area of a sphere:
A = 4πr², where r is the radius of the sun (approx. 6.96 x 10⁸
meters).
Plugging in the values, we get:
A = 4π (6.96 x 10⁸)² = 6.08 x 10¹⁸ square meters.
Divide the total power by the surface area:Finally, divide the total power by the surface area to get the
average power radiated by each square meter of the sun's surface:
P = 3.86 x 10³³ erg/s / 6.08 x 10¹⁸ m² = 386 W/m².
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Translate the word phrase into a math expression.
1 less than a number.
n + 1
1−n
15 ÷ n
n−1
ACK ACK I NEED HELP PLZZ im dummmmm
Answers
N-1
Hey there!
The answer is n - 1.
Let's pretend the number is 15, so 1 less than "15", if you think about it, would be 14, and to get there, you do 15 - 1, now let us switch "15" back to a number "n", and now we have "n - 1"
Did you catch on? ;)
I would love to help you anytime
Olivia collect square pieces of cloth to make a quilt. She keeps the square pieces of cloth in a craft box. She has 18 purple squares ,34 green squares, 14 white squares, 26 blue squares, and 8 black squares. She selects one square at random and returns it to the craft box then she selects a second Square, at random what is the probability that the first Square selected is white and the second Square select it is purple
Answers
Answer:
\(P(White\ and\ Purple) = 2.52\%\)
Step-by-step explanation:
Given
\(Purple = 18\) \(Green = 34\) \(White = 14\)
\(Blue = 26\) \(Black = 8\)
Required
Probability of first selecting white and then selecting purple
The total boxes is:
\(Total = 18+34+14+26+8\)
\(Total = 100\)
The probability is represented as:
\(P(White\ and\ Purple)\)
And the solution is:
\(P(White\ and\ Purple) = P(White) * P(Purple)\)
\(P(White\ and\ Purple) = \frac{n(White)}{Total} * \frac{n(Purple)}{Total}\)
\(P(White\ and\ Purple) = \frac{14}{100} * \frac{18}{100}\)
\(P(White\ and\ Purple) = \frac{14*18}{100*100}\)
\(P(White\ and\ Purple) = \frac{252}{10000}\)
\(P(White\ and\ Purple) = 0.0252\)
or
\(P(White\ and\ Purple) = 2.52\%\)
Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.
Answers
Step-by-step explanation:
Team A time is 1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr
Team B = 1 / ( 1/3 + 1/3) = 1 1/2 hr
Team A wins !
I have more question then this
Answers
Answer:
3/ 25
Step-by-step explanation:
3 squares
Each square inside those is equal to 25 cubes.
3/ 25
a regular polygon has 33 sides find the size of each interior angle
Answers
Answer:
169.09 degrees
Step-by-step explanation:
Interior Angle of a polygon with 33 sides = (n-2) x 180/n degrees = (33-2) x 180/33 degrees = 169.09 degrees
33 sides
to find:the size if each interior angle.
solution:\( \frac{360}{33} \)
\( = 10.91\)
\(180 - 10.91\)
\( = 169.09\)
\( \frac{169.09}{33} \)
\( = 5.12\)
hence, the size of each interior angle is 5.12°
Which one of the following is a term in the following expression?
a²b³c⁴-abc+a+b-d+e
the choices are in the picture
Answers
Answer:
it's blocked for me, I'm susing my school computer
Step-by-step explanation: