The equatiοn οf the circle is (x + 6)(x+6) + (y + 2)(y+2) = 9.
What is circle ?A circle is a twο-dimensiοnal geοmetric figure that cοnsists οf all pοints that are equidistant frοm a single fixed pοint called the center. A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane in such a way that its distance frοm a fixed pοint is always cοnstant.
Tο find the equatiοn οf a circle, we need the cοοrdinates οf the center and the radius.
The center οf the circle is given as (-6, -2), sο the cοοrdinates οf the center are (h, k) = (-6, -2).
The pοint (-9, -2) is οn the circle, sο its distance frοm the centre is equal tο the radius. We can use the distance fοrmula tο find the radius:
[tex]\rm r = \sqrt{((x_2 - x_1)\times (x_2 - x1) + (y_2 - y_1)\times(y_2 - y_1))}[/tex]
[tex]= \sqrt{((-3)^2 + 0^2)[/tex]
= 3
Therefοre, the radius οf the circle is 3.
Nοw we can use the standard fοrm οf the equatiοn οf a circle, which is:
(x - h)(x-h)+ (y - k)(y-k)= r*r
Substituting the values we fοund, we get:
Simplifying:
(x + 6)(x+6) + (y + 2)(y+2) = 9
Therefοre, The equatiοn οf the circle is [tex](x + 6)(x+6) + (y + 2)(y+2) = 9[/tex].
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three true statements are
A) The radius of the circle is 3 unitsB) The center of the circle lies on the x-axisE) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.EXPLANATION :To see why A) is true, we can rearrange the equation to get it in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Completing the square, we have x² - 2x + y² - 8 = 0, which can be rewritten as (x - 1)² - 1 + y² - 8 = 0. Rearranging again, we get (x - 1)² + y² = 9, which is the equation of a circle with center (1, 0) and radius 3.To see why B) is true, note that the x-coordinate of the center of the circle is given by x = 1, so it lies on the x-axis.To see why E) is true, note that the equation x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3. We can rewrite the equation of the given circle as (x - 1)² + y² = 9, which is the equation of a circle with the same radius and a center shifted to (1, 0).Step-by-step explanation:
Standard form for a circle is ( x -h)^2 + ( y-k)^2 = r^2
h, k is the center r is the radius
x^2 -2x + y^2 = 8 arrange into standard form ( complete the square for 'x')
(x-1)^2 + y^2 = 8+1
(x-1)^2 + y^2 = 9 shows center is at 1, 0
radius = 3
So
The radius of the circle is 3 units.
The center of the circle lies on the x-axis (1,0 is on the x axis)
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Hellpppppp due soon
Answer:21.33 is the right answer for x
Which of these statements describe properties of parallelograms? Check all
that apply.
A. Consecutive angles are supplementary.
B. Opposite sides are parallel.
• C. Opposite angles are congruent.
D. Opposite angles are parallel.
E. Opposite sides are congruent.
• F. Diagonals perpendicularly bisect each other.
Answer:
The correct answers for this question are:
A. Diagonals bisect each other.
C. Opposite angles are congruent.
D. Opposite sides are parallel.
E. Consecutive angles are supplementary. Those are the statements that describe properties of parallelograms. They are also belong to the family of quadrilateral.
Step-by-step explanation:
Can someone pls help me solve this!! Will give brainliest!!
if I said that angle 1 in the diagram below was 122 degrees, how can the angle relationships be used to determine the rest of the angle measures. Include how you can use these angle relationships to prove that lines are parallel.
(add any theorems you would use)
Hello!
1= 122
2= 58
3= 58
4= 122
5= 122
6= 58
7= 58
8= 122
To find angle 2, you subtract 122 from 180 because angles 1 and 2 are supplementary angles. You can find angle 3 by using the vertical angles theorem. This means that angle 2 and 3 are congruent to each other. You can use the same for angle 4, meaning 1 and 4 are also congruent. You can use the alternate interior angles theorem to prove that 3 and 6 are congruent and then use the vertical angles theorem to prove that 6 and 7 are congruent. You can find angles 5 and 8 by proving that 5 is congruent to 4 using the alternate interior angles theorem and then once again using the vertical angles theorem to prove that angle 5 is congruent to angle 8. Let me know if this is too hard to understand, I will happily simplify it.
solve with explanation
2(12)-(-4)
Answer:
28
Step-by-step explanation:
2×12-(-4) - and - = +
24+4 + and + = +
28 + and - = -
- and + = -
Evan sold half his story books and then bought 17 more. He now has 32 books. With how many did he begin?
Evan sold half his story books and then bought 17 more. Evan had thirty bucks.
What is equivalent?
A mathematical statement is known as an equation, and the equal sign ('=') connects two expressions. At least one unknown variable must be determinable. For instance, an equation is 3x - 8 = 16. We achieve x = 8.
We will sοlve the prοblem by fοrming a οne variable equatiοn.
Let's say Evan started out with a lot of problems. Evan gave up half of his regular wares. He split two separate cakes.
He now has (x-x/2)=x/2 straight numbers.
He then gained 17 pounds.
Sο subsequent to purchasing 17 bοοks he has nοw (x/2+17) story bοοks
Given number οf stοry bοοks he has right nοw is 32.
By equating the two, we can construct a equation for one variable.
(x/2+17) = 32 Solving for x will be the equation:
(x/2+17) = 32; x/2 = 32- 17; x/2 = 15; x = 152; x = 30.
According to the initial equation, Evan had 30 books.
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Help with math problems
The expansion of the multiplication is [tex]-16+12\sqrt{3}[/tex] and [tex]5-13\sqrt{5}[/tex]
What is irrational numbers?Irrational numbers are real numbers that cannot be represented as simple fractions. If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to zero. [tex]\sqrt{2}, \sqrt{3}[/tex] are two examples.
distributive law
This property states that multiplying the total of two or more addends by a number produces the same result as multiplying each addend separately by the number and then putting the products together.
That is A(B+C)=AB+AC
According to the given information:
[tex](-2\sqrt{3} +2)(\sqrt{3}-5) = -2\sqrt{3}*\sqrt{3} + 10\sqrt{3} +2\sqrt{3} -10[/tex]
=[tex]-6+12\sqrt{3}-10[/tex]
= [tex]-16+12\sqrt{3}[/tex]
[tex](-2-3\sqrt{5})(5-\sqrt{5}) = -10+2\sqrt{5}-15\sqrt{5}+3*5[/tex]
= [tex]-10-13\sqrt{5}+15[/tex]
=[tex]5-13\sqrt{5}[/tex]
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Which right does the Fair Debt Collection Practices Act (FDCPA) give
borrowers?
OA. The right to negotiate debt
OB. The right to declare bankruptcy
C. The right to verify the amount owed
OD. The right not to receive phone calls
Answer: prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.
Step-by-step explanation:
prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.
The right to verify the amount owed is the right the Fair Debt Collection Practices Act (FDCPA) give borrowers The correct option is C.
What is FDCPA?The Fair Debt Collection Practices Act (FDCPA) is a federal law that governs the conduct of third-party debt collectors who attempt to collect debts on creditors' behalf.
Borrowers who are being pursued by debt collectors have several rights under the FDCPA.
One of the rights granted to borrowers by the FDCPA is the right to verify the amount owed.
This means that borrowers have the right to ask the debt collector for written confirmation of the debt, including the amount owed and the creditor's name.
The debt collector is required to provide this information within a reasonable time after receiving the request.
Thus, the correct option is C.
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PLEASEE HELPP I gotta do my missing assignments tn!! (And pls explain)
Answer:
29°
Step-by-step explanation:
In the first triangle,
46 + 30 + x = 180 (Angle sum property)
76 + x = 180
x = 180 - 76
x = 104
In the second triangle,
47 + 104 + y = 180
151 + y = 180
y = 29
Thus, the required angle is 29°.
Pls like and mark as brainliest!
Answer:
the answer is 29 degrees
Step-by-step explanation:
look at the picture below
PLSSS Help
Identify the two forms of the simplified expression x^5/x^10
And if you could please give a brief description. Thank you
Both formulations convey the same meaning and represent the same equation mathematical operation: x raised to the power of 5 divided by x raised to the power of 10.
What is the expression?In this format, the expression is shown using exponent notation. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The phrase can therefore be written as x⁵/x¹⁰.
In this method, the division symbol serves to represent the expression. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The expression is therefore (x⁵)/. (x¹⁰).
Therefore, the same mathematical operation is represented by both formulations, which both express the same meaning: x to the power of 5 divided by x to the power of 10.
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A bookstore manager will randomly select 1 of 5 newly
arrived fiction books and 1 of 4 newly arrived nonfiction
books for a window display. What is the probability that
the manager will select the shortest of the newly arrived
fiction books and the longest of the newly arrived
nonfiction books?
A. 5%
B. 10%
C. 20%
D. 45%
Answer:
Step-by-step explanation:
number of books are 5 so you will have to do 5 by hundred which will lead to twenty percent
The likelihood that the manager will choose the longest just-received nonfiction book and the shortest recently arrived fiction book is 1/20, or 5%.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
The probability of selecting the shortest fiction book is 1/5 and the probability of selecting the longest nonfiction book is 1/4. Since these events are independent, we can multiply their probabilities to find the probability of both events happening:
P(shortest fiction book and longest nonfiction book) = P(shortest fiction book) x P(longest nonfiction book) = 1/5 x 1/4 = 1/20
So the probability that the manager will select the shortest of the newly arrived fiction books and the longest of the newly arrived nonfiction books is 1/20, which is equivalent to 5%.
Therefore, the answer is option A.
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Which inequality is equivalent to
4x - 2y ≤ 8?
A. y ≤ 2r-4
B. y ≥ 2r-4
C. y ≤-2r-4
D. y ≥-2r-4
Answer:
B: y ≥ 2r-4.
Step-by-step explanation:
To solve for y, we need to isolate y on one side of the inequality. First, we can simplify the left side of the inequality by dividing both sides by 2:
2x - y ≤ 4
Then, we can subtract 2x from both sides to get:
-y ≤ -2x + 4
Finally, we need to isolate y by multiplying both sides by -1 and flipping the direction of the inequality:
y ≥ 2x - 4
Now we can see that the equivalent inequality is option B: y ≥ 2r-4.
WILL GIVE BRAINLIEST
Defense mechanisms
please just check my work, see if u can spot out any errors… thanks :)
Answer:
the is no error in your work
PLEASE HELP!! A cylinder has a volume of 128 cubic centimeters and a height of 6 centimeters. What is the volume of a similar cylinder with a height of 9 centimeters?
The volume of cylinder is 191 cubic centimeters.
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here cylinder with height 6 cm ,
Volume = 128 cubic centimeters.
Now using volume of cylinder formula then,
=> Volume V =
=> 128 = 3.14**6
=> = = 6.79406
=> r = 2.6 cm.
Now volume of cylinder with height 9 cm is ,
=> Volume V = 3.14**9 = 191 cubic centimeters.
Hence the volume of cylinder is 191 cubic centimeters.
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A dividend of 24 cent per share is paid on OIL search shares with a market value of $3.25 and a face value of $1.60. The percentage yield is
Answer:
7.38%
Step-by-step explanation:
A ramp is being built to ga up a vertical increase of 10 feet. Codes require the angle the
ramp makes with the ground to be no more than 15
. At least how long will the actual
ramp need to be to pass code?
The length of the ramp we need to build should be at least 38.61 feet to pass code.
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
We can use trigonometry to solve the problem. Let x be the length of the ramp we need to build. Then, the angle the ramp makes with the ground is given by:
sin(theta) = opposite/hypotenuse
where theta is the angle the ramp makes with the ground, opposite is the vertical increase of 10 feet, and hypotenuse is the length of the ramp x.
Solving for x, we get:
x = opposite/sin(theta) = 10/sin(15)
Using a calculator, we can evaluate sin(15) to be approximately 0.2588. Then, we can divide 10 by 0.2588 to get:
x ≈ 38.61
Therefore, the length of the ramp we need to build should be at least 38.61 feet to pass code.
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A fast-food restaurant promotes certain food items by giving a game piece with each item.
Advertisements proclaim that "25% of the game pieces are Instant Winners!" To test this claim, a frequent diner collects 20 game pieces and gets only 3 instant winners.
1. Identify the population, the parameter, the sample, and the statistic in this context.
The correct answer of population is all the game pieces and sample is 20.
How to find the percentage of winners?
As we know that a fast-food restaurant promotes certain food items by giving a game piece with each item, and proclaims that 25% of the game pieces are instant winners.
Population is all the game pieces.
Parameter is true proportion of all the game pieces that are winner.
Sample is 20, the game pieces that is collected.
Statistics is the proportion of the sample that are winners i.e. [tex]\frac{3}{20}[/tex]
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sample is the 20 and the statistic is 3/20 .
What is sample space ?A random experiment's sample space is the collection of all possible outcomes. A portion of the sample space is an event that is associated with a random experiment. Any outcome has a probability that is between 0 and 1. All outcomes have probabilities that add up to 1.
he population is all the game pieces that the fast-food restaurant produces.
The parameter is the proportion of game pieces that are instant winners in the population.
The sample is the 20 game pieces that the frequent diner collected.
The statistic is the proportion of instant winners in the sample. In this case, the statistic is 3/20 or 0.15 (15%).
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I need help please
(In picture)
The two forms of the expression
[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]
when simplified are
[tex] = {x}^{ - 5} [/tex]
x exponents negative 5 and
[tex]\frac{1}{ {x}^{5} } [/tex]
numerator 1 over denominator x exponents 5.
What are the two forms of simplified expression?Given:
[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]
When we have the same base but different powers in indices division, one of the bases is chosen and the powers are subtracted.
[tex] = {x}^{5 - 10} [/tex]
[tex] = {x}^{ - 5} [/tex]
[tex] = \frac{1}{ {x}^{5} } [/tex]
Therefore, the simplified expressions are x exponents negative 5 and numerator 1 over denominator x exponents 5.
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YZ is tangent to the circle at Z. Find the measure of minor arc WX
.
Step-by-step explanation:
the angle at Y = 1/2 × (arc angle WZ - arc angle ZX).
so,
42 = (arc angle WZ - 51)/2
84 = arc angle WZ - 51
135° = arc angle WZ
the arc angle WX is the remainder of the whole circle to the sum of the arc angles WZ and ZX :
arc angle WX = 360 - 135 - 51 = 174°
Calculate the surface area of this right triangular prism.
Total surface area of right triangular prism is 750cm²
Define the term right triangular prism?A right triangular prism is a three-dimensional geometric shape with three rectangular faces connecting the edges of its two parallel, congruent triangular bases.
Area of the two opposite side triangles (A₁) = 2 × ( [tex]\frac{1}{2}[/tex] × 12 × 5)
Area of the two opposite side triangles (A₁) = 60 cm²
Area of upper, lower and side rectangles (A₂) = (5×23) + (12×23) + (13×23)
Area of upper, lower and side rectangles (A₂) = 115 + 276 + 299
Area of upper, lower and side rectangles (A₂) = 690 cm²
Total surface area of right triangular prism = A₁ + A₂
Total surface area of right triangular prism = 60 + 690
Total surface area of right triangular prism = 750 cm²
Therefore, the total area of the right triangular prism is 750cm²
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What is the measure!, in degrees in degrees, of angle x?
Answer:23 degrees
Step-by-step explanation:
Ok! I'm a high school student so this is what I can see.
Angles A and the 130 are supper- angles meaning they add up to 180.
So that means A is 50.
Next I noticed by experience that A and B are vertical angles. So that means B is 50 as well.
And since this all have to equal to 360 angles. The equation is
360= 50+130+50+107+x or X= 360- (50+130+50+107)
And that is x=23
Happy Soving
Fwam is going to invest in an account paying an interest rate of 5.9% compounded
daily. How much would Fwam need to invest, to the nearest hundred dollars, for the
value of the account to reach $91,000 in 12 years?
In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.
what is interest ?In exchange for using borrowed funds or assets, a borrower must pay the lender interest. It is charged for a certain duration of time, typically until the loan is fully returned, and is typically stated as a percentage of the amount borrowed. This fee is known as the interest rate. For instance, if a bank lends you $1,000 at a 5% annual interest rate, after a year of borrowing the money you would still owe the bank $50 more in interest. The creditworthiness of the borrower, the risk of the loan, and current market conditions are frequently used to establish the interest rate.
given
We know that Fwam expects the account to be worth $91,000 in 12 years and that the interest rate is 5.9% compounded daily in this situation.
We must convert the interest rate and the time period to the proper units before we can use the formula.
We begin by converting the 5.9% yearly interest rate to a daily rate:
daily rate is equal to (1 + 0.059/365)(365/365)-(1-1) = 0.00015999.
4,380 days in 12 years, or 365 days per year.
We can now enter the values into the formula to find P:
$91,000 = P × 2.3226
P = $39,165.95
In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.
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how do i find these I’m so confused
Triangles BIG and MOP are similar so, the values of v, w, x, y are 36 cm, 156°, 46.7°, 43.2° respectively.
Describe Triangles?A triangle is a two-dimensional geometric shape that is formed by three line segments that connect three non-collinear points in a plane. These points are called the vertices of the triangle, and the line segments connecting them are called sides.
Triangles are characterized by several properties, including their side lengths, angles, and areas. Based on the lengths of their sides, triangles can be classified into three types:
Scalene triangle: A triangle in which all three sides have different lengths.
Isosceles triangle: A triangle in which two sides have the same length.
Equilateral triangle: A triangle in which all three sides have the same length.
Since triangles BIG and MOP are similar, we know that their corresponding angles are equal and their corresponding sides are proportional.
Let's first find the value of w in triangle BIG. We know that the sum of angles in a triangle is 180 degrees. Therefore, we can find angle BIG as follows:
angle BIG = 180 - angle BGI
= 180 - 24
= 156 degrees
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/42 = 48/v (since BI/IG = GB/BI)
v^2 = 4248
v = sqrt(4248)
v = 36
In triangle MOP, we can use the law of cosines to find the value of angle MOP:
cos(MOP) = (60^2 + 72^2 - y^2) / (26072)
cos(MOP) = (3600 + 5184 - y^2) / 8640
cos(MOP) = (8784 - y^2) / 8640
MOP = acos((8784 - y^2) / 8640)
MOP = 46.7 degrees (approximately)
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/60 = y/72 (since BI/MO = IG/MP)
y = (v/60)*72
y = (36/60)*72
y = 43.2 cm
Lastly, we can use the fact that the sum of angles in a triangle is 180 degrees to find the value of angle POM in triangle MOP:
angle POM = 180 - angle MOP - 126
= 180 - 46.7 - 126
= 7.3 degrees (approximately)
Therefore, we have:
v = 36 cm
w = 156 degrees
x = 46.7 degrees (approximately)
y = 43.2 cm
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A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $14 plus an additional $0.16 for each minute of calls.
Simplify the expression.
three tenths squared minus 17 plus the quantity negative 7 divided by the absolute value of 4.3 minus 7.8 end quantity times 2.67
−11.57
−11.60
−21.74
−22.25
I picked b please tell me why i am wrong
Answer:
D. -22.25
Step-by-step explanation:
First, we need to simplify the expression inside the parentheses
|-3.5| = 3.5
Next, we can simplify the expression inside the parentheses:
-7 ÷ |-3.5| = -2
Now we can simplify the entire expression:
3/10^2 - 17 + (-2) x 2.67 = 0.09 - 17 - 5.34 = -22.25
What is the solution of 3x+8/x-4>0
Answer:
Solve the inequality for
x
by finding
a
,
b
, and
c
of the quadratic then applying the quadratic formula.
All real numbers
Interval Notation:
(
−
∞
,
∞
)
Step-by-step explanation:
What value of x makes this equation true 0.6x-5=0.1x+7
Step-by-step explanation:
To solve for x, we'll first need to simplify the equation by combining like terms:
0.6x - 5 = 0.1x + 7
0.6x - 0.1x = 7 + 5
0.5x = 12
x = 12 / 0.5
x = 24
Therefore, the value of x that makes the equation true is 24.
what is the answer to 4n – 3?
Step-by-step explanation:
4n - 3 = 0
4n = 0 + 3
4n = 3
[tex]n \: = \frac{3}{4} [/tex]
A collection of 50 buttons is in a jar. The probability of reaching into the jar and retrieving a black button is 0.64. What is the probability that you will reach in the jar and retrieve a button that is not black?
Answer: The probability of reaching into the jar and retrieving a black button is 0.64. Therefore, the probability of reaching into the jar and retrieving a button that is not black is the complement of this probability, which is 1 - 0.64 = 0.36.
In other words, the probability of not getting a black button is the same as the probability of getting a non-black button, which includes all the other colored buttons in the jar. Since there are no other details given in the problem regarding the number of non-black buttons or the probability of retrieving each non-black button, we assume that they are all equally likely to be retrieved and simply calculate the probability of not getting a black button as the complement of the probability of getting a black button.
Therefore, the probability of reaching in the jar and retrieving a button that is not black is 0.36 or 36%.
Step-by-step explanation:
Alg 2 writing equations in vertex form
The vertex is (4,1), and the parabola opens b since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.
What is parabola?A parabola is a symmetrical U-shaped curve that can be formed by intersecting a cone with a plane parallel to one of its sides. It is a type of quadratic function, which can be expressed in the form of y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.
f(x) = x²+8x-3
To complete the square, we need to add and subtract the square of half the coefficient of x:
f(x) = (x²+8x+16) - 19 --> (x+4)² - 19
So, the equation in vertex form is: f(x) = (x+4)² - 19.
The vertex is (-4,-19), and the parabola opens upwards since the coefficient of the squared term is positive. The axis of symmetry is x=-4, and the domain is all real numbers. The range is [-19, ∞), since the minimum value is -19.
f(x)=-2x² + 16x-31
To complete the square, we need to factor out the leading coefficient of -2, and then add and subtract the square of half the coefficient of x:
f(x) = -2(x² - 8x + 16) - 31 + 32 --> -2(x-4)² + 1
So, the equation in vertex form is: f(x) = -2(x-4)² + 1.
The vertex is (4,1), and the parabola opens downwards since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.
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