Simplify (9y²-x² )÷ (xy+3y²)

Answer:

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

Step-by-step explanation:

x² + y² - 2x - 8 = 0

x² - 2x + y² = 8

Complete the square in x.

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

Center: (1, 0); radius: 3

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

h and k represent the coordinates at the center.

r is the radius of a circle.

The midpoint of the given points represents the center of this circle:

h = (4 + 4)/2 = 4

k = (5.5 + 10.5)/2 = 8

Next, we would determine the radius by using the distance formula for coordinates:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

r = √[(4 - 4)² + (10.5 - 5.5)²]

r = √[0² + 5²]

r = √25

r = 5 units.

Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

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Answer:

I think that is is C

Step-by-step explanation:

The Vertical Line Test determines whether or not a curve on the graph is a function. This one passes the vertical line test because no vertical line can intersect the curve more than once. I hope that helps!

It takes 15 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

The relation between distance 'd', time 't', and speed 's' is given by the formula,

s = d/t or

d = st or

t = d/s

It is given that,

The distance to uncle's house = 444 miles

The time taken to drive to uncle's house = 12 hours

So,

speed = (444)/12 = 37 miles/hour

Then the time to drive 555 miles(to Atlanta) is calculated by,

time t = (555)/37 = 15 hours

Therefore, it takes 15 hours to drive to Atlanta at 555 miles of distance.

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Mathematical logic is important as it's a way to learn new experience through continuous self assessment.

Logic is important as it enables us to form sound judgements and beliefs.

The study of logic can help as it can help us to understand disagreement and ambiguity.

It also helps us in making a reasonable emotional life.

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Answer:

[tex]y = \sqrt{ \frac{\pi \: x - A {}^{} }{\pi} } [/tex]

Step-by-step explanation:

To make y subject of formular, we place y in terms of other variables.

[tex] A = \pi \: x {}^{2} - \pi \: y {}^{2} \\ making \: y \: subject \\ A + \pi \: y {}^{2} = \pi \: x {}^{2} \\ \pi \: y {}^{2} = \pi \: x {}^{2} - A \\ Dividing \: bothsides \: by \: \pi \\ y {}^{2} = \frac{\pi \: x { - A}^{} }{\pi} \\ Squarerooting \: bothsides \\ y = \sqrt{ \frac{\pi \: x - A {}^{} }{\pi} } [/tex]

Answer:

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

Step-by-step explanation:

A -----------------------z------------B

          Left      Speed(km/h)      Time

Car:   12PM            X  

Van:   12PM           60

Car/Van

DistanceCar        AB + z

DistanceVan       Az

Ratio:                  (AB+z)/Az  = 7/5

Time until both meet = T (in hours)

Distance Car:            xT

Distance Van:           60T

====

  xT = AB + z

  60T = Az

---

(xT/60T)= (7/5)

x = 60(7/5)

x = 84 km/h

=====

Time for car to reach B is:    time (hr) = 108 km/(84 km/h)

                                                 time = 1.286 hours

Distance for at 1.289 hours is:    distance (km) = (60 km/h)*(1.286 h)

                                                   distance = 77.14 km

At 1.286 hours, the car reverses direction.  The van is (108 km - 77.14 km) or 30.86 km away.

Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours.  The sum will be 30.86 km when they meet, at time of T.

Car Distance + Van Distance = 30.86 km

T(84 km/h) + t(60 km)

They meet when they are 0 km apart, which can be modeled with the following equation:

Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.

Let t be the time after 1.286 hours that both vehicles meet/collide.

t*(60 km/h)  +  t(84 km/h) = 30.86 km

t(60+84) = 30.86 km

t(144 km/h) = 30.86 km

t = 0.2143 hr

Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.

=================

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

==============

CHECK

Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?

Car distance is (1.5 hr)(84 km/h) = 126 km

Van distance is (1.5 hr)(60 km/h) = 90.0 km

Ratio is 126/90 or 1.4

Ratio of 7/5 is 1.4

YES

The computation of the equation shows.that x is -4 and y is 0.6.

4x + 5y = -1

-5x - 8y = 10

The value of x and y will be calculated thus:

-5 × (4x + 5y = -1)

4 × -(5x - 8y = 10)

-20x - 25y = 5

-20x -32y = 40

Add the equation

57y = 45

y = 45/75 = 0.6

Since 4x + 5y = -1

4x + 5(0.6) = -1

4x + 3 = -1

x = -1 - 3

x = -4

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The amount of packing material is 1506 cubic inches

The given parameters are:

Can

Radius, r = 7 inches

Height, h = 18 inches

Box

Base dimension, l = 15 inches

Height, h = 19 inches

The volume of the can is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]V_1 = 3.14 * 7^2 * 18[/tex]

[tex]V_1 = 2769[/tex]

The volume of the box is

[tex]V =l^2h[/tex]

So, we have:

[tex]V_2 =15^2 * 19[/tex]

[tex]V_2 =4275[/tex]

The amount of packing material is;

Amount = V2 - V1

This gives

Amount = 4275 - 2769

Evaluate

Amount = 1506

Hence, the amount of packing material is 1506 cubic inches

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The transformation for circle 1 exists (x+9), (y+5) and the scale factor of circle 1 exists 2.

Scale exists described as the ratio of the length of any object on a model to the actual length of the exact object in the entire world.

The function transformation rules: f(x)+b changes the function b units upward. f(x)−b shifts the function b units downward. f(x + b) shifts the function b units to the left.

Circle 1

center: (−4, −2)

Radius: 3 centimeters

Circle 2

center: (5, 3)

Radius: 6 centimeters

Transformations can be used to circle 1 to verify that the circles exist similar.

As circle 2 and circle 1 do not contain the exact coordinates

So, circle 1 has to utilize transformation rules.

The difference between the coordinates of circle 2 and circle 1 exists

[tex]$x_2 - x_1 = 5 - (-4 ) = 9[/tex]

[tex]y_2 - y_1 = 3 - (-2) = 5[/tex]

Therefore, transformation for circle 1: (x+9), (y + 5)

The scale factor between circle 2 and circle 1 exists

The radius of Circle 2 = 2 [tex]*[/tex] radius of circle 1

Therefore, the scale factor of circle 1 = 2

Therefore, the transformation for circle 1 exists (x+9), (y+5), and the scale factor of circle 1 exists 2.

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Answer:

15

Step-by-step explanation:

First, we can plug -1/2 into the equation and get -6(-1/2 -2). Then, we can convert -2 into a fraction to get -4/2. If we subtract -4/2 from -1/2, we get -6(-5/2). We then multiply this and get 30/2 which simplifies to 15

a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.

b. Sheila can afford the babysitter for 6 hours and 30 minutes.

c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.

d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

a. We assume the hours affordable to Sheila be x hours.

Per hour charge of the babysitter = $10.

Time taken by the babysitter traveling = 1.5 hours.

Therefore, total chargeable time = 1.5 + x.

Therefore, the total charge by the babysitter = $10(1.5 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 10(1.5 + x) = 80.

b. We are asked to determine the hours Sheila can afford to hire the babysitter.

We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.

Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.

10(1.5 + x) = 80,

or, 1.5 + x = 8,

or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.

Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.

c. Per hour charge of the new babysitter = $15.

Time taken by the new babysitter traveling = 1 hour.

Therefore, total chargeable time = 1 + x.

Therefore, the total charge by the new babysitter = $15(1 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 15(1 + x) = 80.

d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.

To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as  follows:

15(1 + x) = 80,

or, 1 + x = 80/15,

or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.

Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

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Answer:

B.) 54π units²

Step-by-step explanation:

First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.

a² + b² = c²                              <----- Pythagreom Theorem

3² + b² = 15²                            <----- Insert side lengths

9 + b² = 225                            <----- Solve 3² and 15²

b² = 216                                   <----- Subtract 9 from both sides

b = 14.7 units                          <---- Take square root of 216

Now, we can use the surface area of a right cone equation to find the final answer.

r = 3 units

h = 14.7 units

SA = πr(r + √(h² + r²))                              <----- Surface Area equation

SA = π(3)(3 + √(14.7² + 3²))                     <----- Insert values

SA = π(3)(3 + √(216 + 9))                         <----- Solve 14.7² and 3²

SA = π(3)(3 + √225)                                <----- Add 216 and 9

SA = π(3)(3 + 15)                                     <----- Take square root of 225

SA = π(3)(18)                                            <----- Add 3 and 15

SA = 54π units²                                     <----- Multiply 3 and 18

Answer:

D

Step-by-step explanation:

simplified is 1 1/2, 1.5 or 3/2

Answer: A. 1/9, 3, 27

Step-by-step explanation:

3^x for x = -2

= 3^-2 = 1/9

3^x for 1

= 3^1 = 3

3^x for 3

= 3^3 = 27

hope this helped

Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.

The form of quadratic equations is given as

ax2 + bx + c = 0

So, for the quadratic equation, we have

x² - x = 12

Let's make it into quadratic form

x² - x - 12 = 0

Bill solved it as

x(x - 1) = 12

This is wrong, because quadratic equations must be written in the form before solving for the variables

Jenna solved it as

x 2 - x - 12 = 0

Jenna is correct because she converted the equation to a quadratic form before solving for the variables.

Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.

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The discriminant of the quadratic equation is -20 and there are two non real solutions.

The discriminant of a quadratic equation uses the equation:

[tex]b^{2} -4ac[/tex]

Where the value of this calculation can tell you what solutions there are, plug known values in:

[tex]x^{2} +6x+14[/tex]

a=1

b=6

c=14

[tex]b^{2} -4ac[/tex]

which is equal to -20 on putting the values of a,b and c in the equation

As -20 < 0, this means that there is not a real solution, resulting in the first option being correct.

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The required answers are:

a. The linear approximating polynomial at a = 1: P₁(x) = x - 2

b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²

c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.

Using Taylor polynomial series, the required approximating polynomials are calculated.

The Taylor polynomial series is

Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n

Where fⁿ(a) is the nth derivation of f(x) at a

The first order(linear) Taylor polynomial series is

P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹

The second order(quadratic) Taylor polynomial series is

P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) +  [tex]\frac{f''(a)}{2!}[/tex](x - a)²

The given function is f(x) = -1/x at a = 1

f(a) = f(1) = -1

f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1

f''(x) = -2/x³; f''(a) = f''(1) = -2

a. Linear approximating polynomial:

From the Taylor series, we have

P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹

On substituting,

P₁(x) = -1 + (1/1!)(x - 1)¹

       = -1 + (x - 1)

       = x - 2

b. Quadratic approximating polynomial:

From the Taylor series, we have

P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) +  [tex]\frac{f''(a)}{2!}[/tex](x - a)²

On substituting,

P₂(x) = f(1) + (1/1!)(x - 1) +  (-2/2!)(x - 1)²

        = -1 + (x - 1) - (x - 1)²

        = -1 + x - 1 - (x² - 2x + 1)

        = x - 2 - x² + 2x - 1

        = -3 + 3x - x²

c. Approximating the given quantity -1/1.06:

Substituting x = -1.06 in P₁(x) and P₂(x),

P₁(x) = x - 2

⇒ P₁(-1.06) = (-1.06) - 2 = -3.06

P₂(x) = -3 + 3x - x²

⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30

Therefore, the approximating polynomials are calculated by using Taylor polynomial series.

Disclaimer: The given question is incomplete. Here is the complete question.

Question:

a. Find the linear approximating polynomial for the following function centered at the given point a.

b. Find the quadratic approximating polynomial for the following function centered at the given point a.

c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.

f(x) = -1/x , a = 1; approximate -1/1.06

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If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026

Total orders both accurate and not accurate = 1131

Total orders from restaurant B (both accurate and not accurate) = 337

Probability of first order from B = 337/1131

Probability of second order from B = 336/1130

Probability of third order from B = 335/1129

Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129

Probability of the first three orders from B = 0.026

Complete question is;

Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A

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Using a linear function, we have that:

a) The fixed cost is of $10.

b) The equation is: C = 10 + 12d.

c) The cost of an 18 km trip is $226.

d) The distance traveled is of 20 km.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the slope is of m = 12. When d = 5, C(d) = 70, hence we find the fixed cost as follows:

C(d) = 12d + b

70 = 60 + b

b = 10.

Hence the equation is:

C(d) = 12d + 10.

For a trip of 18 km, d = 18, hence the cost is:

C(12) = 12 x 18 + 10 = $226.

When the cost is of $250, the distance is found as follows:

250 = 12d + 10

12d = 240

d = 240/12

d = 20 km.

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A pole vaulter have to run at 18m/s speed.

According to the statement

The typical pole for pole vaulting is 17 feet long

we use the formula

1/2 m(v)^2 = mgh

Now rearrange the terms

(v)^2 = 2gh

here g = 10 and h = 15 then

substitute the values

(v)^2 = 2*10*15

v = 17.32

So, A pole vaulter have to run at 18m/s speed.

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Answer:

Axis Of Symmetry = -2

Vertex = (1,-2)

Min (0,-2)

Domain = All Real #'s

Range =  Y is greater than or equal to -2

Step-by-step explanation:

what is the best definition of luminous

Step-by-step explanation:

[tex] - 32 + 45 = 13 \\ t_{n} = ( a_{1} + (n - 1)d) \\ \\ d = 13 \: \: a_{1} = - 45[/tex]

[tex] t_{n} = - 45 + (n - 1)13 = = = > \\ - 45 + 13n - 13 = = = > \\ t_{n} = 13n - 58[/tex]

and now

[tex]124 = 13n - 58 = = = > \\ 182 = 13n = = = > n = 14[/tex]

The number of terms in the sequence: –45, –32, –19, –6, ..., 124 = 9.

The common difference is -45 - (-32)= 13

                                                  d = 13.

AP is a sequence of numbers in order, in which the difference among any two consecutive numbers is a constant cost. it's also referred to as mathematics series.

using arithmetic progress:-

last term = (n-1)d

first term(a) = –45

    term = a + (n-1)d

there is a difference of 13, so the sequence will be

–45, –32, –19, –6,7, 20, 33, 46, 59, 72, 85, 98, 111, 124.

∴ number of terms = 9

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The values when the given numbers are multiplied will be:

230

78

3

91

1800

3. 5 × 23 × 2

It should be noted that the given information simply means that we should multiply 5 by 23 by 2. This will be:

= 5 × 23 × 2

= 230

5. 34 + 0 + 18 + 26

This information simply means that we should add thirty four, eighteen, and twenty six together. This will be:

34 + 0 + 18 + 26 = 78

7. (3 × 10 × 8) = ....... × (10 × 8)

(3 × 10 × 8) = 3 × (10 × 8)

9. 0 + ...... = 91

It simply means the number that will be added to zero that will give ninety one. This will be 91.

11. The total income for the theater will be:

= (20 × 18) × 5

= 1800

Therefore, the correct values based on the computation will be 730, 78, 3, 91, and 1800.

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The probability of drawing a red four and then a blue four is:

P = 1/100

We know that there are 10 cards in total, then the probability of drawing a red four (there is only one of these cards) is:

p = 1/10

Now we put the red four again, the probability of getting a red blue is computed in the same way:

q = 1/10

The probability for both events happening consecutively is:

P = p*q = (1/10)*(1/10) = 1/100

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Answer: 127

Step-by-step explanation:

angle b is 127 as well because they're vertical angles and vertical angles are equal to each other.

The exponent Marina should use for b is: D. 7.

When dividing, you subtract the exponents. I.e. [tex]a^m \div a^n = a^{m - n}[/tex].

Using the rule, we would also subtract the exponents of b in the simplified expression. Thus:

[tex]b^4 \div b^{-3}[/tex]

Subtract the exponents

4 -(-3) = 4 + 3 = 7.

Therefore, the Maria should use the exponent b = 7.

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Answer:  D

Step-by-step explanation:

Answer:

P = 16.4

Step-by-step explanation:

Given the equation PV = nRT and the values we know, we need to isolate P .

Thus, we have:

[tex]PV=nRT\\3P=2*0.0821*300\\P=49.26/3\\P=16.42=16.4[/tex]