The standard form of the equation of a parabola is y = -2x2 - 8x-13. What is the vertex form of the equation?
O A. y = -2(x-2)² - 5
OB. y = -2(x + 2)² - 5
O C. y = -2(x + 2)² -13
OD. y = -2(x-2)² - 13
Answers
In vertex form the equation of the parabola is [tex]y = -2(x+2)^{2} -5[/tex].
What is Vertex form if Parabola ?
When a graph crosses its symmetry axes, the vertex formula in mathematics may be used to get the vertex coordinate of a parabola. The vertex point is often represented by (h, k). We are aware that a parabola's conventional equation is y=ax2+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x2 is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x2 is negative. The standard form and vertex form of a parabola, as well as the vertex formula, will be covered in this article.
We are aware that the parabola's conventional form is y=ax2+bx+c.
So, y = a(x-h)2 + k is the vertex form of a parabola.
To determine a parabola's vertex, use the vertex formula. There are two methods for locating a parabola's vertex.
Vertex, (h, k) = (-b/2a, -D/4a)
Equation of the parabola,
y = [tex]-2x^{2} - 8x -13[/tex]
here ,
a = -2 , b = -8 and c = -13.
Therefore,
h = -b/2a = +8/-4 = -2 and,
k = -D/ 4a = [tex]-(b^{2} - 4ac)/4a[/tex] = -(64 - 104)/-8 = -40/8 = -5
So, the coordinate of vertex is (-2, -5)
So the vertex form of equation of parabola is
[tex]y = a(x-h)^{2} + k[/tex]
⇒ [tex]y = a(x+2)^{2} -5[/tex]
⇒ [tex]y = ax^{2} + 4ax +4a -5[/tex]
Equating this equation with equation pf parabola we get a = -2
So, in vertex form the equation of the parabola is [tex]y = -2(x+2)^{2} -5[/tex].
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Related Questions
what are two square roots of 484
Answers
Answer:
22, and -22
Step-by-step explanation:
22x22=484
-22x(-22)=484
I NEED HELP ASAP
FIRST TI ANSWER GET BRAINLEST
Answers
Answer:
2nd Option
Step-by-step explanation:
m=6
y=-3
so from equation
y=mx+c
y=6x-3
is the req ...... equation..
Answer: 2nd Option is the answer for this
Step-by-step explanation:
PLSS HELP MEEE!! It'll be very appreciated
Answers
Please help with this. I dont get it. How to solve?
Answers
The solutions are
a) The smallest possible value of x - y is A = -6
b) The largest possible value of 2x / y is B = 6
c) The largest possible value of x² + y² is C = 100
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the first inequality equation be represented as P
The value of P is
-4 ≤ x ≤ 6
Let the second inequality equation be represented as Q
The value of Q is
2 ≤ y ≤ 8
Now , the smallest value of inequality P is = -4
The largest value of inequality P is = 6
And , the smallest value of inequality Q is = 2
The largest value of inequality Q is = 8
a)
Let the smallest possible value of x - y be = A
The value of x - y is calculated as
The smallest value of P - smallest value of Q
Substituting the values in the equation , we get
A = -4 - 2
A = -6
Therefore , The smallest possible value of x - y is A = -6
b)
Let the largest possible value of 2x / y be = B
The value of 2x/y is calculated as
Largest value of x goes in numerator and smallest value of y goes in denominator to get the largest value of 2x/y
So , substituting the values in the equation , we get
B = ( 2 x 6 ) / 2
B = 12 / 2
B = 6
Therefore , The largest possible value of 2x / y is B = 6
c)
Let the largest possible values of x² + y² be = C
The value of x² + y² is calculated as
The largest value of x squared + the largest value of y squared
Substituting the values in the equation , we get
C = 6² + 8²
C = 36 + 64
C = 100
Therefore , The largest possible value of x² + y² is C = 100
Hence , The solutions are
a) The smallest possible value of x - y is A = -6
b) The largest possible value of 2x / y is B = 6
c) The largest possible value of x² + y² is C = 100
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function rule to find f(21)
Answers
Answer:
0
Step-by-step explanation:
x
f(x) = ------ - 3
7
21
f(21) = ------ - 3
7
f(21) = 3 - 3
f(21) = 0
I hope this helps!
asmita went to a blackjack table at the casino. at the table, the dealer has just shuffled a standard deck of 52 cards. asmita has had good luck at blackjack in the past, and she actually got three blackjacks with aces in a row the last time she played. because of this lucky run, asmita thinks that ace is the luckiest card. the dealer deals the first card to her. in a split second, she can see that it is a non-face card, but she is unsure if it is an ace. what is the probability of the card being an ace, given that it is a non-face card? answer choices are in a percentage format, rounded to the nearest whole number.
Answers
The probability of the card being an ace, given that it is a non-face card will be 0.1 or 10%
There are total 52 cards.
Out of 52, 26 are red and 26 are black.
Each of the four French suits—clubs (♣), diamonds (♦), hearts (♥) and spades (♠).—has 13 ranks in a regular 52-card deck. King, Queen, and Jack are the three court cards (face cards) in each suit, and their pictures are reversed (double-headed). The ten numerical cards, or pip cards, in each suit range in value from one to 10.
Out of 52 cards, (Kings, Queen, Ace) are faced card.
And each set of cards have 4 different colour and shades.
So, total number of faced card will be = 4*3 = 12
So, total number of not a faced card = 52-12 = 40
So, the value of P (It is an ace and it is not a face card) =4/52
So, the value of P(It is not a face card)=40/50
[tex]P\left(\frac{\text { It is a ace }}{\text { It is not a face curd }}\right) =\frac{P(\text { It is an ace and it is not aface carl) }}{P(\text { It is not a face card) }} \\\\ =\frac{\frac{4}{52}}{\frac{40}{52}}\\\\=\frac{4}{40}\\\\=0.1=10\% }[/tex]
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Comparing Guy montage and Harrion Bergeon and eeing how they are different, imilar and the negative reult of their dytopian world and their contrating fate
Answers
Montag serves as a metaphor for free thought in Fahrenheit 451. Guy doesn't fit in with society as Beatty or Mildred do.
In what ways is Harrison Bergeron's society like to our own?Although the parallels are subtle, there are some similarities between the modern world and the setting of "Harrison Bergeron" in the narrative. Egality is a topic that both of them address and that has issues and effects. Another resemblance is the conflict that results from competition and attempts to stop it from happening, both of which cause issues.
Which aspects of society are Harrison Bergeron's writings critical of?The manipulative and desensitizing impact of the mass media is one political practice in American culture that the short story "Harrison Bergeron" might be seen as an oblique indictment of. overregulation of some human actions. restricting freedom of speech
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help with both questions please
Answers
The solution of the compound inequality are
-2x ≤ 4 and 10 ≥ -2x
x ≥ -2 and -5 ≤ x10 < 3x - 2 OR -3x - 2 > 14
3 < x OR x < -5How to solve the compound inequalityA sentence or equation having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality.
To solve the compound inequality each of them is solved individually
-2x ≤ 4 and 10 ≥ -2x
-2x ≤ 4 10 ≥ -2x
dividing by a negative sign reverses the inequality
x ≥ -2 -5 ≤ x
plot attached
The solution of the inequality is x ≥ -2 and -5 ≤ x
10 < 3x - 2 OR -3x - 2 > 14
10 + 2 < 3x -3x > 14 + 2
12 < 3x -3x > 16
3 < x x < -5.333
3 < x x < -5
plot attached
The solution of the inequality is 3 < x OR x < -5
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how many ways can we have the 2n people stand in a line so that no person is standing next to their spouse?
Answers
The variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;
(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!
Explain the term exclusion and inclusion?Everything a study needs to meet the inclusion criteria is included. Exclusion criteria are indeed the elements that would exclude a study from inclusion. The following criteria should be taken into account: studies of this kind: It is crucial to choose publications with a study design that is relevant for the research issue.The step for the simplification are-
Utilizing exclusion and inclusion to determine that at least 1 wife is seated next to her husband in the total number of ways to seat 2n individuals in 2n chairs.Let A1 represent the attribute in which at least 1 wife can be seen sitting next to her husband.The wife and husband are then "merged" into one person. We have (nC1) options to select one pair from n couples, leaving us with (2n) to position (2n) "people" in order to obtain (2n)! and so forth.Finally, on a broad note:
(2n)! - (2(ⁿC₁)(2n - 1)! - 2²(ⁿC₂)(2n - 1)! + .....2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!
On further simplifying;
(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!
Thus, the variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;
(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!
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Two triangles each have an angle measuring 15 degrees. The first triangle also has an angle
measuring 20 degrees.
The second triangle must have an angle of which measure if the two triangles are similar?
Answers
The measure of the third angle = 105°.
What is angles?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The sum of the angles in a triangle is :
A° + B° + C° = 180°
Where A, B and C are the three angles in a triangle.
Hence, if two of the angles are given as : 55° and 20°
The measure of the third angle will be :
Let the measure of the third angle = C
(55 + 25 + C) = 180°
180° - (55° + 20°)
180° - 75° = 105°
The measure of the third angle = 105°
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A pharmaceutical person earns a 12% of commission of the total sales of the stains that he sell to the hospital. If he earns 800,000.00 in commission
Answers
Answer: $1,504,000
Step-by-step explanation:
First, take 800,000 divided by 100% = $8000
So we know that 1% is $8000
We are missing 88%, so take 8000 times 88 = $704,000
Then we add 800,000 with 704,000 = $1,504,000
So the total sales are $1,504,000
If you deposit $3,000 at 2.5% compounded continuously, what would your ending balance after 4 years?
Answers
You will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.
What is continuous compound interest?
In theory, continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.
The formula for continuously compounded interest is:
[tex]A = P * e^{rt}[/tex]
where:
A is the ending balance (the amount you will have after 4 years)
P is the principal (the initial amount you deposited, in this case $3,000)
r is the interest rate (2.5% per year, or 0.025)
t is the time in years (4 years)
Plugging these values into the formula, we get:
[tex]A = $3,000 * e^{(0.025 * 4)}[/tex]
Calculating this gives us an ending balance of $3,276.44.
Hence, you will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.
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Solve for a:(8^(-1))/(4^(-1))-a^(-1)=1.
Answers
The value of the a is 2.
What is the fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when used in conversational English.
We have,
8⁻¹ / 4⁻¹ - a⁻¹ = 1
By simplifying the given equation we get,
8⁻¹ - a⁻¹ = 1 * 4⁻¹
By further calculating the equation,
1/8 - 1/a = 1/4
4(1/8 - 1/a) = 1
4/8 - 4/a = 1
1/2 - 4/a = 1
4/a = 1/2
1/a = 4/2
a = 2/4
a = 2
Hence, the value of the a is 2.
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Write [tex]$\frac{2^{2010} + 2^{2008}}{2^{2005} - 2^{2003}}$[/tex] in the simplest form.
Answers
Answer:
160/3
Step-by-step explanation:
[tex]\frac{2^{2010}+2^{2008}}{2^{2005}-2^{2003}} \\ \\ =\frac{2^7 + 2^5}{2^2 - 1} \\ \\ =\frac{128+32}{4-1} \\ \\ =\frac{160}{3}[/tex]
what do you add to 4 5/8 to make 6
Answers
Answer: 1 3/8
Step-by-step explanation:
6 - 4 5/8 = 1 3/8
Since you are missing a part to the sum, you use subtraction to find the missing part.
PLEASE HELP!! WILL GIVE BRAINLIEST AND 13 POINTS!!
Solve for x
A. 10
B. 100
C. 64
Answers
Answer: 10
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]6^2 + 8^2=x^2\\\\36+64=x^2\\\\100=x^2\\ \\ x=10[/tex]
I NEED HELP PLEASE!!!!!!
What is the classification of each system?
Drag the answers into the boxes to match each system.
{x+5y=−2x+5y=4
{y=3x+4−2x+y=4
{3x+y=4−6x−2y=−8
Consistent Independent Consistent Dependent Inconsistent
Answers
Inequality classifications
x + 5y = −2 and x + 5y = 4 Inconsistent
y = 3x + 4 and −2x + y = 4 consistent and independent
3x + y = 4 and −6x − 2y = −8 consistent and dependent
What are inconsistent equations?A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.
x + 5y = −2
x + 5y = 4
subtracting gives
0 = -6 no solution
What are consistent and independent equations?A system is deemed consistent if it has at least one solution.
A consistent system is independent if it only has one solution.
-3x + y = 4
−2x + y = 4
subtracting gives
-x = 0
x = 0
substituting x to get y
-3 * 0 + y = 4
y = 4
What are consistent and dependent equations?A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.
3x + y = 4
−6x − 2y = −8
subtracting gives
9x + 3y = 12 - none cancels out meaning infinite number of possible solutions
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Pls help I inserted a picture and have one last chance ALSO IT HAS TO BE IN A INEQUALITY
Answers
9x10= 90°
180°- 90°= 90°
Because if you add 90+90= 180
aj sold 200 candy bars to raise money for their community softball league. Milk chocolate candy bars sold for $3 each, and dark chocolate candy bars sold for $4 each. Aj sold $675 worth of candy bars. The system of equations below represents the sales of candy bars.
m+d=200
3m+4d=675
How many dark chocolate candy bars did AJ sell?
Enter your answer in the box.
Answers
The number of dark chocolate AJ sold is 75
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. m and d . They are called simultaneous equations because the equations are solved at the same time.
If the number of Milk chocolate candy is m and the number of dark chocolate candy is d, then
m+d= 200 equation 1
3m+4d= 675 equation 2
to eliminate m we multiply both equations by 3
3m+3d= 600 equation 3
3m+ 4d=675 equation 4
subtract equation 3 from 4
d = 675-600
d= 75
Therefore the number of dark chocolate candy AJ sold is 75.
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Will give 5 stars and give thanks
Answers
Answer:
x=36
Step-by-step explanation:
The length of a secant segment and a tangent segment drawn to a circle drawn from an external point is:
whole secant * external secant = tangent^2
(12+x)*12=24^2
144+12x=576
12x=432
x=36
y=x+3
x-2y=-1
find x and y
Answers
[tex]y=x+3[/tex] for x
Flip the equation:
[tex]x+3=y[/tex]
Add -3 to both sides:
[tex]x+3+-3=y+-3[/tex]
[tex]\fbox{x = y - 3}[/tex]
__________________________________________________________
[tex]x-2y=-1[/tex] for y
Add -x to both sides:
[tex]x-2y+-x=-1+-x[/tex]
[tex]-2y=-x-1[/tex]
Divide both sides by -2:
[tex]\dfrac{-2y}{-2} =\dfrac{-x-1}{-2}[/tex]
[tex]\fbox{y = $\dfrac{1}{2}x+ \dfrac{1}{2} $}[/tex]
Does anyone know the area of this figure in square inches
Answers
The area is 120 [tex]cm^{2}[/tex].
What is area?Area is the size of a two-dimensional surface, usually expressed in square units, such as square feet or square meters. It is the amount of two-dimensional space enclosed within a given set of boundaries. Area can be calculated for various shapes, including squares, rectangles, triangles, circles, and more complex shapes. Area is also a measure of the amount of space an object occupies. In mathematics, area is used to measure the size of a shape or region in a plane. It can also be used to calculate the size of a figure, such as the area of a triangle, or to measure the area of an enclosed space, such as a garden or a room.
Given:
AB = CD = 8cm
AD = BC = 12cm
EF = DH = 4cm
So, the required area is A = Area (ABCEFD) = Area (ABCD) + Area (CEFD)
Area of ABCD = Area (ABCD) = AB × BC
⇒ 12 × 8 = 96 [tex]cm^{2}[/tex]
Area of CEFD = Area (CEFD) = 0.5 (CD + EF) × HD
⇒ 0.5 × (8 + 4) × 4 = 24[tex]cm^{2}[/tex]
Now, the required area is
⇒ A = 96 [tex]cm^{2}[/tex] + 24 [tex]cm^{2}[/tex] = 120 [tex]cm^{2}[/tex]
Hence, the required area of the figure is 120 [tex]cm^{2}[/tex].
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Find the area of the Composite Figure
Answers
The area of the composite figure is 242in² as per the given information in the figure.
What is meant by a rectangle?Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).
A crossed rectangle is a crossed (self-intersecting) quadrilateral made up of two opposing sides and the two diagonals of a rectangle[4] (therefore only two sides are parallel). It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic, with opposite sides of equal length and equal angles that are not right angles.
Area =Area of the down rectangle+ Area of the up rectangle+2×Area of the triangle
Area= (7×24)+(4×13)+2×(1/2)×b×4
Let, 13+2x=24
Here, x=b
So, 2b=11
b=11/2
Area= 168+52+4(11/2)
Area=168+52+22
Area=242in²
Therefore, the area of the composite figure is 242in².
So, option C is correct.
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solve for u. u/4-8=20
Answers
Answer:
u = 112
Step-by-step explanation:
u/4-8=20
u/4 - 8 + 8 = 20 + 8 ==> add 8 on both sides to isolate u
u/4 = 28
4 * u/4 = 4 * 28 ==> multiply by 4 on both sides to isolate u
u = 112
triangleCDE is reflected over the x-axis. What are the vertics of triangleC'D'E'?
Answers
The required vertices of the triangle C'D'E' are (-8, 1), (-6, 5), and (-2, 4) respectively.
Given that,
Triangle CDE is reflected over the x-axis. What are the vertices of triangleC'D'E' is to be determined.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The coordinates of vertices C, D, and E are (-8, -1), (-6, -5), and (-2, -4) respectively.
For the reflection across the x-axis is given as,
(x , y) = (x -y)
Now,
C(-8, -1) across the x-axis C'(-8 , 1)
D(-6, -5) across the x-axis D'(-6 , 5)
E(-2, -4) across the x-axis E'(-2 , 4)
Thus the required vertices of the triangle C'D'E' are (-8, 1), (-6, 5), and (-2, 4) respectively.
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Im very confused please help
Answers
Answer:
x=21
y=9/15 or 15/9
Step-by-step explanation
scale factor is either 15/9 or 9/15 - can't tell which way by the question
9/15x35=21
x=21
Lake Erie, the smallest of the Great Lake by volume, still holds an impressive 116 cubic miles of water. Suppose you start today dumping out the entire volume of Lake Erie using a cone cup. A typical cone cup has a diameter of 2 and 3/4 inches and a height of 4 inches. About how long would it take you to empty the lake if you could dump out one cup per second?
Answers
3.7261×10¹⁵ seconds is the time it would take you to empty the lake
How to determine how long it would take to empty the lake?
Given that:
Lake Eric can hold 116 cubic miles of water
One cup has a diameter of 2 and 3/4 inches and a height of 4 inches
Volume of cone cup = 1/3 πr²h
Volume of cone cup = 1/3×π×(11/8)²×4 = 7.92 cubic inches
Volume of Lake Erie = 116 cubic miles
To convert to cubic inches multiply by 2.544×10¹⁴:
Volume of Lake Erie = 116×2.544×10¹⁴ = 2.95104×10¹⁶ cubic inches
Time taken = 2.95104×10¹⁶ / 7.92 = 3.7261×10¹⁵ seconds
Therefore, it would take you 3.7261×10¹⁵ seconds to empty the lake
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hurry please last question it’s due in 20 minutes
Answers
Answer:
Step-by-step explanation:
2. Subtraction property of equality
3. Simplification
4. Subtraction property of equality
5. Simplification
6. You and a friend go to the store and purchase 3 candy bars that cost $0.84 each and 2 sodas that cost $1.80 each. You are going to split the cost. You pay for your half with a five dollar bill. How much change will you receive? Please SHOW your work.
A. $3.06
B. $1.60
C. $6.12
D. $1.94
Answers
Answer:
correct answer is D) $1.94.
Step-by-step explanation:
To solve this problem, we first need to calculate the total cost of the candy bars and the sodas. The candy bars cost $0.84 each, so 3 candy bars cost 3*$0.84=$2.52. The sodas cost $1.80 each, so 2 sodas cost 2*$1.80=$3.60. The total cost of the candy bars and sodas is $2.52+$3.60=$6.12.
Since you are going to split the cost with your friend, you will pay for half, which is $6.12/2=$3.06. You pay for your half with a five dollar bill, so you will receive $5-$3.06=$1.94 in change.
I hope it helps, let me know if you have another questions.
Answer:
Step-by-step explanation:
First, we need to find the total cost of the candy bars by multiplying the number of candy bars by the price per candy bar: 3 candy bars * $0.84/candy bar = $3*0.84=2.52Next, we need to find the total cost of the sodas by multiplying the number of sodas by the price per soda: 2 sodas * $1.80/soda = $2*1.8=3.60Then, we need to add the cost of the candy bars and the sodas to find the total cost: $2.52 + $3.60 = $<<2.52+3.6=6.12>>6.12Since you are paying for half of the total cost, you need to pay half of $6.12, or $3.06.If you pay for your half with a five dollar bill, you will receive $5 - $3.06 = $5-3.06=1.94 in change. Answer: 1.94.
What is the measure of c and b
Answers
Answer:
Step-by-step explanation:
im not 100% sure but probly 135
Answer:
angle c and b are 137 degrees both
Step-by-step explanation:
given angle is 43° and when subtracted from 180°
we have 137°.
using the alternative angle property the angle b is also 137°.