Complete the square to determine if the equation is a circle, quadratic (parabola) or other. Show all work and graph the circles and quadratics on a grid.

Complete The Square To Determine If The Equation Is A Circle, Quadratic (parabola) Or Other. Show All

Answers

Answer 1

The equation of the ellipse, circle, and parabola will be written as (x + 9)² / 4 + (y - 1)² / 16 = 1, (x + 4)² + (y - 3)² = 40, and y = - (x + 3)²/ 4 + 1, respectively.

How to draw the graph of the function?

Equation A is transformed as,

16x² + 4y² + 96x - 8y + 84 = 0

16(x² + 6x + 9 - 9) + 4(y² - y + 1 - 1) + 84 = 0

16(x + 9) - 144 + 4(y - 1)² - 4 + 84 = 0

16(x + 9)² + 4(y - 1)² = 64

(x + 9)² / 4 + (y - 1)² / 16 = 1

This is the equation of the ellipse.

Equation B is transformed as,

x² + y² + 8x - 6y - 15 = 0

x² + 8x + 16 + y² - 6y + 9 - 15 = 16 + 9

(x + 4)² + (y - 3)² = 40

This is the equation of the circle.

Equation C is transformed as,

x² + 6x + 4y + 5 = 0

x² + 6x + 9 - 9 + 4y + 5 = 0

y = - (x + 3)²/ 4 + 1

This is the equation of the parabola.

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Complete The Square To Determine If The Equation Is A Circle, Quadratic (parabola) Or Other. Show All

Related Questions

8 over 3 / 3 simplified

Answers

Answer:

8

Step-by-step explanation:

if you mean 8/ (3/3), Then you get 8 because 3/3 = 1 and 8/1 is 8. Also if you put that equation into a calculator then you get 8

c rounded to the nearest 10 is 640.
d rounded to the nearest 10 is 420.

what are the lower and upper bounds of c + d?

Answers

The bounds of C is 635 - 644

The bounds of D is 415 - 424

The lower bounds of C + D can be found by adding 635 + 415, which is 1050

The upper bounds of C + D can be found by adding 644 + 424, which is 1068


So, the lower bounds of C + D is 1050 and the upper bounds is 1068

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. 

The upper bound is 1068 and the lower bound is 1050

What is the upper bound and lower bound of a number?

The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value.

Given here, c rounded to the nearest 10 is 640 and d rounded to the nearest 10 is 420. Then we have the minimum and maximum value as

Min C = 635 and Max C = 644 & Min D=415 and Max D = 424

Therefore the upper bound for c+d = 644+424

                                                           = 1068

    And the lower bound for c+d = 635+415

                                                      =1050

Hence The upper bound is 1068 and the lower bound is 1050

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If the point (x, y) is in Quadrant III, which of the following must be true?
x < 0 and y>0
x < 0 andy<0
Submit
x > 0 and y>0
x > 0 and y < 0

Answers

Answer: x < 0 and y < 0

Step-by-step explanation:

quadrant three is here

                      |

        II            |        I

                      |

--------------------|-------------------

                      |

        III           |        IV

                      |

    here /\

so, the x is to the left which is negative, and the y is down which is negative. x is less than zero, and y is less than zero

Tickets to a sporting event cost $125 each. What's a reasonable domain and range.

Answers

The domain and the range of a function is the set of input and output values of the function.

The domain is the set of all whole numbers.

The range is the set of all whole numbers.

Let the number of tickets be x, and the revenue be y.

So, the revenue function will be:

y = 125

The number of tickets cannot be less than 0.

So, the domain of the revenue function is

domain=0,∞

The above means that, the domain is the set of all whole numbers

Similarly, the revenue cannot be less than 0.

So, the range of the revenue function is

range = 0,∞

The above means that, the range is also the set of all whole numbers (in multiples of 125).

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Which translation takes y=|x| to y=|x+3|-1 ?
(A) 3 units right, 1 unit down (C) 3 units left, 1 unit down
(B) 3 units right, 1 unit up (D) 3 units left, 1 unit up

Answers

The translation is given by option (C)3 units left ,1 unit down.

A translation occurs when you a graph is moved either horizontally or vertically. That is to say, each point on the parent graph gets translated in one of four directions: left, right, up, or down. There is usually addition or subtraction involved in translation.

Let us consider the function y=|x+3|-1 which is translated from the parent function of y=|x|.

The following steps are followed for the translation of the function:

There is an horizontal shift to the left of the parent function about 3 units .There is a vertical shift downwards of 1 unit.

The translation can be seen in the attached graphical representation of the two functions.

The blue line represents the translated function while the red line represents the parent function.

Therefore the translation required for the function y=|x+3|-1 from y=|x| is 3 units left and one unit down .

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mr. fullingham has 75 geese and 125 turkeys. what is the ratio of te number of geese to the total number of birds in simplest terms

Answers

The total number of birds will be 75 geese + 125 turkeys = 200.

So the ratio of geese to birds is 75:200

DIG DEEPER A three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and p packages of plastic. An art club purchases 6 identical kits for (180+58.5p) dollars. Write an expression that represents the cost of one kit.​

Answers

Answer:

Step-by-step explanation:

mdcmmmm

Pls help! Slope Question

Answers

The slope between points C and D is 12/7 = 1.71

How to find the slope between points C and D?

We know that the slope between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by:

s = (y₂ - y₁)/(x₂ - x₁)

In this case, the coordinates of point C are (0, 0)

The coordinates of point D are (7, 12)

Then the slope on that interval is:

s = (12 - 0)/(7 - 0) = 1.71

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Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP
?hours

Answers

The mean lifetime of a bulb is 31. 57

What is mean?

Mean can be defined as the average of a given set of values or elements.

The formula for the mean of a given set of values is expressed as;

Mean = sum of the occurrence of the values/ number of values

Or

Mean = sum of terms/number of terms

From the information given, the frequency of the lifetime of the bulbs were given as;

34, 31, 94, 40 , 0 , 17, 5

The sum of the terms is given as:

= 34 + 31 + 94 + 40 + 0 + 17 + 5

= 221

The number of terms = 7

Substitute into the formula

Mean = 221/ 7

Mean = 31. 571

In 2 decimal place

Mean = 31. 57

Thus, the mean lifetime of a bulb is 31. 57

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Given f(x) = 3x + 3, write a new function if the y-intercept is increased by two units.

Answers

Answer:

f(x) = 3x + 5

Step-by-step explanation:

Because if the y-intercept is increased by two units in the slope formula where b is the y-intercept, then the answer is 3x + 5.

help plss

Answers

okay i will help u out ok!!


Use the Change of Base Formula. What is the value of each expression?
b. log₄18

Answers

The value of the given expression that is log₄ 18 = 2.084

A logarithm operation can be rewritten as a fraction of logarithms with a new base using the change of base formula.

Example: logₐ b = (logₓ b) / logₓ a)

Therefore, log₄ 18 = (log₁₀ 18) / (log₁₀ 4).....eq(i)

We know, log₁₀ 4 = 0.602

We can write log₁₀ 18 as log₁₀(2x9).

Using the product rule of logarithms, log₁₀ 18 = log₁₀2 + log₁₀9log₁₀ 18 = 0.301 + 0.954log₁₀ 18 = 1.255

Substituting the value of log₁₀ 18 = 1.255 in eq(i) we get,

log₄ 18 = 1.255/0.602log₄ 18 = 2.084

The final answer to the question is log₄18 = 2.084 using the change of base formula.

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1. Solve for x:
1/3x = -26

Answers

1/3x = -26

To solve for this, we can divide both sides by 1/3 since it is the coefficient. This would look like:

1/3 / 1/3 = 1
-26 / 1/3 = -78

x = -78

Which table represents a linear function?

Answers

b because they will go at an angle


What are the solution(s) of 2(x+3)²/₃=8 ?

Answers

The solution is 5

Rewriting the expression -

2(x+3)²/₃=8

Divide Left Hand Side and Right Hand Side of the equation -

(2(x+3)²/₃)÷2 = 8÷2

Performing division to find the solution

(x+3)²/₃ = 4

Taking cube on both sides of the equation

((x+3)²/₃)³ = 4³

The exponent on Left Hand Side will be multiplied cancelling 3, as it is common in both numerator and denominator

(x + 3)² = 64

Now, taking square root on both sides of equation

√(x + 3)² = √64

Solving the square root on both sides of equation

x + 3 = 8

Shifting 3 to Right Hand Side of the equation

x = 8 - 3

Performing subtraction

x = 5

Hence, the solution of equation is 5

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Notes:
For semiannual premiums, use 51% of the annual rate.
For quarterly premiums, use 26% of the annual rate.
For monthly premiums, use 9% of the annual rate.
For females, use the age of a male three years younger.
Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value of $50,000. What will his annual premium be, if his age for insurance purposes is thirty-one?

(Use a thousands comma where applicable.)

Answers

The annual insurance premium that Will C. Lowe will be paying is $ 766.5

What is insurance premium?

Insurance premium is annual, quarterly, semi annual or monthly payments that has to be paid accordingly to keep our insurance policy active.

Annual insurance premium can be calculated by multiplying the face value per $1000 of the policy by the rate of the insurance of policy.

Given is that Will C. Lowe is 31 year old male who wants to buy a ordinary whole life insurance policy with a face value of $50,000.

From the table we can see that rate of insurance for a 31 year old male for a ordinary whole life insurance policy  is 15.33

Then annual premium = (face value per $1000)*(rate of insurance)

                                     = $ (50,000/1000)*(15.33) = $766.5

Therefore, the annual insurance premium that Will C. Lowe will be paying is $766.5

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can someone please tell me what 383.0 divided by 90 is?????????

Answers

Sure!!!

The answer is 4.25555!

Hope this helps! Have a great day! :D :)

Answer:

The answer is 4.2555555556

Pleas look at screenshot

Answers

/9/=9
/-10/=10

The absolute value of both of them would be positive , cause the absolute value of a number is never negative .

The blue dot is at what value on the number line -16 to -10

Answers

Tbh I truly don’t know I’m srry for wasting your time but I gotta get this homework done ASAP

Please help!!
Solve for a:
b(a + f) = M

Answers

Answer: a = (M/b) - f

Identify the like terms in the list.
16y ^6, 2y^ 5, 4y ^2, 10y, 16y^ 2

Answers

Answer:

4y^2

16y^2

Step-by-step explanation:

16 y^6 matches nothing. The powers on the letter must be the same to have like terms.

2y^5 has the same comment.

4y^2 and 16y^2 are similar terms. Both have y^2

10y matches nothing

In the figure, AC=86. Find BC.

Answers

Bc would equal too 12cm

Michael is doing an underwater handstand. His feet are sticking up 0.5 meters above the surface
hands are 1.8 meters directly below his feet.
of the water. Michael's
What is the position of Michael's hands relative to the surface of the water?

Answers

Answer:

Step-by-step explanation:

Answer:

michael is doing an underwater handstand . His feet are sticking up 0.5 meter above the surface handsare 1.8 meters directly below his feet of the water

michael handsrelative to the surface of the water

Step-by-step explanation:


If z=30 when x=3 and y=2 , write the function that models the relationship.
z varies directly with x and inversely with y .

Answers

z = 20 x/y is the variation of equation.

How to write the function that models the relationship?

A relationship between a set of values for one variable and a set of values for other variables is known as a variation.

One of the most fundamental concepts in mathematics is the idea of a function, in part because functions are a useful tool for describing and illuminating patterns.

given that

z=30 when x=3 and y=2

z varies directly with x that means z is directly proportional to x.

z = kx .................(1)

z varies inversely with y means z is inversely proportional to y.

z = k 1/y ................(2)

both equation 1 and 2

z = k x/y

k = zy/x

now, find the value of k using given information.

k = 30(2)/3

k = 60/3

k = 20

now,

z = k x/y

z = 20 x/y

This is the variation of equation.

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3xy+5x+2+3y+x+4 answer

Answers

The equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x  + 3y  + 6

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3xy + 5x + 2 + 3y + x + 4

Collect the like terms in the above expression

So, we have

3xy + 5x + 2 + 3y + x + 4 = 3xy + 5x + x  + 3y  + 4+ 2

Evaluate the like terms in the above expression

So, we have

3xy + 5x + 2 + 3y + x + 4 = 3xy + 6x  + 3y  + 6

Hence, the equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x  + 3y  + 6

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Which expression is NOT equivalent to ⁶√16 ²?
(A) (16 r²)¹/₆ (B) 4 r¹/₃ (C) (4 r)¹/₃ (D) ∛4 r}

Answers

The correct option is (B) [tex]4 r^\frac{1}{3}[/tex]

The exponential expression  [tex]4 r^\frac{1}{3}[/tex] is not equivalent to ⁶√16r².

What is exponential expression ?

In, mathematics a exponential function or exponential expression is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as  [tex]a^x[/tex] .Or we can say that there is always has something power something rule in case of exponents.

where, a is the base expression of function

          x = exponent of expression

According to question,

the expression,[tex]\sqrt[6]{16r^2}[/tex]  can be written in following ways:

Case 1 : if we simplify the expression using fractional method ,

            then, [tex]\sqrt[6]{16r^2}[/tex] = [tex]({16r^2})^{\frac{1}{6}} = (4r)^\frac{2}{6 } = (4r)^\frac{1}{3 }[/tex]

            i.e. option (A) and (C) are satisfying the expression

Case 2 : if we simplify the equation exponentially ,

             then, [tex]\sqrt[6]{16r^2} = 3\sqrt{4r}[/tex]

             i.e. option (D) is satisfying the expression

Hence, the expression is not equivalent to ⁶√16r² is option B.

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Calculate (7.15 x 10^9) - (4.56 x 10^8).

2.59 x 10^1
2.59 x 10^9
6.694 x 10^8
6.694 x 10^9

Answers

Answer:

D. 6.694 * 10^9

Step-by-step explanation:

The exponent is 9 because the result of the first equation had 9 digits. It is positive because the decimal moves to the right.

John calculates an arc length involving a circle with a radius of 9 inches. The associated central angle has a measure of radians. John's work is shown

Answers

Answer:

Step 3, computed the radius multiply by the center angle

Step-by-step explanation:

{arc-length: a *  r}

arc-lenght= 3\pi * 9 = 27pi inches. John made his first error in sept 3, he listes the correct equations, but he should have computed the radius by the center angle

Answer:

Step-by-step explanation:

Kaylee deposits $500 into a savings account with a 3% intrest rate what will her balance be in 3 years

Answers

Answer: $576.99 in 3 years

Step-by-step explanation:

Answer:

546.36

Step-by-step explanation:

Interest rate calculator

Are the lines paraellel, perpendicular, or neither? b) line 1 : y+1/3x=4 line 2 y=3x-2

Answers

perpendicular bc u flipped the reciprocal
I believe what the other person said was correct I think
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