every nonzero real number has a reciprocal. zero does not have a reciprocal. therefore, zero is not a nonzero real number

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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Answer:

$4

Step-by-step explanation:

A 4:2 ratio is the same as a 2:1 ratio, so Ann receives double what Bob gets.

If Ann gets 8 dollars and Bob gets 4, then Ann would have $4 more than Bob, and it would follow the appropriate ratio.

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

No.

Step-by-step explanation:

An integer is defined as a whole number.

The number given, "1.765", is not a whole number, as it includes the decimal .765. 1.765, as implied by decimal point, is a decimal number.

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Answer:

Step-by-step explanation:

\(|x-7|+|1-x|>6\\\\\mathrm{For\:each\:absolute\:find\:positive\:and\:negative\:intervals}\\\\\mathrm{For\:}x\le \:1:\quad x<1\\\\\mathrm{For\:}1<x<7:\quad \mathrm{No\:Solution}\\\\\mathrm{For\:}x\ge \:7:\quad x>7\\\\\mathrm{Combine\:the\:intervals}\\\\<1\quad \mathrm{or}\quad \mathrm{No\:Solution}\quad \mathrm{or}\quad \:x>7\\\\x<1\quad \mathrm{or}\quad \:x>7\)

Answer:

y=2x-A

Step-by-step explanation:

The product of the expression (x-√7-3√8)(x√7-3√8) can be simplified as option B. 7x^2-12x√14+72

An identity equation is an equation that holds true for all values of the variable(s) involved. In other words, an identity equation is an equation that is always true, regardless of the values of the variables.

Given that (x-√7-3√8)(x√7-3√8), Using the identity equation which can be expressed as :  (a-b)² = a² +b² -2ab, we can aplly this as;

[(x√7-3√8)(x√7-3√8)] = [(x√7-3√8)² ]= [(x√7)²+(3√8)² -2(x√7)(3√8)]

   =[7x²+72 -6x√56]

   = [7x²+72-6x√(14×4)]

 =[ 7x²+72-12x√(14)]

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Answer:

  C = 1/5t +6

  slope: 1/5, (C) The additional charge per minute

Step-by-step explanation:

Before we can write the function, we need to know the slope of the line. Marked points are separated by 5 units horizontally (run=5) and 1 unit vertically (rise=1). The slope is ...

  m = rise/run = 1/5

The initial charge is the C-intercept: 6. The function can be written in slope-intercept form as ...

  C = 1/5t +6

__

As we saw above, the slope of the function is 1/5, which represents ...

  the additional charge per minute

Answer:

40%

Step-by-step explanation:

24/60 is 40%

Answer:

24 minutes is 2/5 of an hour, or 40%

Step-by-step explanation:

There are 60 minutes in one hour. Therefore, 24 minutes is equalto 24/60 x 100 = 40 percent of one hour. What is 24 minutes as a percent? 40% of an hour.

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Using the circles:

A circle with a radius of 8 inches has an area and circumference given by:

A = πr² = π(8²) ≈ 201.06 square inches

C = 2πr = 2π(8) ≈ 50.27 inches

Rounding to the nearest hundredth:

A ≈ 201.06 square inches

C ≈ 50.27 inches

Therefore, the area is approximately 201.06 square inches and the circumference is approximately 50.27 inches.

A circle with a diameter of 20 meters has a radius of 10 meters. The area and circumference are given by:

A = πr² = π(10²) ≈ 314.16 square meters

C = 2πr = 2π(10) ≈ 62.83 meters

Rounding to the nearest hundredth:

A ≈ 314.16 square meters

C ≈ 62.83 meters

Therefore, the area is approximately 314.16 square meters and the circumference is approximately 62.83 meters.

Using these relationships, find the measures of some of the angles:

a) mJKP = mJKN (by vertical angles) and mJKP + mPKL = 90° (by complementary angles), so mJKN + mPKL = 90°.

b) mJKN = mJKP (by vertical angles) and mJKN + mKNM = 90° (by complementary angles), so mJKP + mKNM = 90°.

c) mJLK = mMPL (by alternate interior angles) and mMPL = 63°, so mJLK = 63°.

d) mKNM = 90° - mJKN (by complementary angles). We cannot determine the measure of mJKN.

e) mJLK = mMPL (by alternate interior angles) and mJLR = mJLP (by vertical angles), so:

mJLK + mKLP + mPLJ + mJLP = 360° (by the sum of angles in a quadrilateral)

63° + 90° + mPLJ + mJLP = 360°

mPLJ + mJLP = 207°

f) mJLR = mJLP (by vertical angles) and mKPL = 90°, so:

mJLR + mJLP + mKPL = 180° (by the angles in a triangle)

mJLR + mJLP + 90° = 180°

mJLR + mJLP = 90°

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Image transcribed:

Use the circle below for questions 1-7.

1. Name a radius.

2. Name a diameter.

1.

2.

3.

R

3. Name a chord that is not a diameter.

P

4. Name a central angle.

4.

S

5. Name a minor arc.

5.

6. Name a major arc.

7.

7. Name a semicircle.

For questions 8 and 9, find the area and circumference. Round to the nearest hundredth.

8.

A =

C=

9.

A =

20 m

8 in

C=

10. If m∠MPL = 63°, find each measure.

K

a) mR= =

= m KNM d) 이이

=

b) - =

c) L

=

f) mJLR =

N

M

Gina Wilson (All Things Algebra, LLC), 201

Answer:

x= 17/8

Step-by-step explanation:

6x− 5/2=2x+6

Step 1: Simplify both sides of the equation.

6x+−5/2=2x+6

Step 2: Subtract 2x from both sides.

6x+−5/2−2x=2x+6−2x

4x+−5/2=6

Step 3: Add 5/2 to both sides.

4x+−5/2+5/2=6+5/2

4x=17/2

Step 4: Divide both sides by 4.

4x/4=17/2/4

x=17/8

Answer:

15 or 3 so B

Step-by-step explanation:

So 5/6 of 18 is 90/6. If you like, you can divide that to simplify and you get 15. Another way to do it is to divide 18 by 6 which gets you 3.

Answer: 149,150,151

Step-by-step explanation:

1.st solution

Let the smallest number is x.

So next consecutive number is x+1

So the third consecutive number is x+2

So the sum of these three numbers is:

x+x+1+x+2=450

3x+3=450

3x=447

x=149  - first number

Second number is 149+1=150

Third number is 150+1=151

2-nd solution

The sum of 3 numbers in row is 450. It means that average  number is 450:3=150 - is the number which is in the middle

So the first one number is 150-1=149 and the third number is 150+1=151

Answer: S=11

Step-by-step explanation:

to find the area of a square is height times length. The square root of a number is a number that when multiplied by itself equals the original number. 121 is a perfect square because x times x =121 is rational. 11x11=121. Hence, 11 is how long each side of the garden is.

hope this helps!

Answer:

Step-by-step explanation:

We would convert 20 minutes to hour.

60 minutes = 1 hour

20 minutes = 20/60 = 1/3 hour

Let x represent the number of calls received in 20 minutes or 1/3 hour

If the mean number of calls per hour is 5.4, then the number of calls received in 20 minutes is

5.4 × 1/3 = 1.8

The probability that there will be 2 or more calls is expressed as P(x ≥ 2)

From the Poisson distribution calculator,

P(x ≥ 2) = 0.54

Answer:

it's 7500

Step-by-step explanation:

20% of 7500 is 1500. General tip, commission is usually 25%

Answer:

Here:

Step-by-step explanation:

Repeating - 36.5365365...  

Non- repeating - 36.5  

Answer:

1.) ax2+Bx+c

2.) parabola

3.) I don't know

4.) I don't know

5.) maximum

6.) minimum

7/8)  The solutions of a quadratic equation are also called roots, zeroes, and x -intercepts.

I hope this kinda helped.

Answer:

1.) ax2+Bx+c

2.) parabola

3.) I don't know

4.) I don't know

5.) maximum

6.) minimum

7/8)  The solutions of a quadratic equation are also called roots, zeroes, and x -intercepts.

I hope this kinda helped.

Answer:

So you must first get the total of all the birds, which is going be a fraction of course , that being 14/14 birds in total, since there are only 3 black birds the probability of me getting a black one 3/14 because there are fourteen in total, and the probability for the green birds is 6/14.

The combined probability that the first bird is black and the second is green is 0.0918

Probability is the likeliness of an event to happen.

Total Blue birds = 5

Total Green birds = 6

Total Black birds = 3

Total birds = 14

The probability of selecting two birds such that the first bird is black and the second is green.

Probability = ( No. of the desired outcome )/( Total outcomes)

The probability of selecting black bird is 3/14

The probability of selecting green bird is 6/14

Therefore, the combined probability that the first bird is black and the second is green is

= (3/14) * (6/14)

= 18/196

= 0.0918

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To find f+g, we need to add f(x) and g(x):

f(x) + g(x) = (2x^(2) +5) + (1/2x)

f+g = 2x^(2) + (1/2)x + 5

To find f-g, we need to subtract g(x) from f(x):

f(x) - g(x) = (2x^(2) +5) - (1/2x)

f-g = 2x^(2) - (1/2)x + 5

To find fg, we need to multiply f(x) and g(x):

f(x) * g(x) = (2x^(2) +5) * (1/2x)

fg = x + (5/2)x^(-1)

To find f/g, we need to divide f(x) by g(x):

f(x) / g(x) = (2x^(2) +5) / (1/2x)

f/g = 4x + 10x^(-1)

Answer:

C. A loan finances the total purchase price of the car while a lease finances only the depreciated value and related fees

Step-by-step explanation:

He legit said it. (Just writing this for those who are blind)

One difference between obtaining a car with a lease or a loan is that: a loan finances the total purchase price of the car while a lease finances only the depreciated value and related fees.

A loan is suitable for a property that you wish to possess at the maturity date, i.e. anything with long-term worth.

On the other hand, a lease is ideal for items that deteriorate gradually and will not retain their worth beyond the period.

The interest on a loan is amortized throughout the period. i.e. your consumer pays more interest at the start and more principal in the end.

Although leasing is not free, the financing charges are predetermined all through the period and are not deducted from the borrowed amount.

From the information given:

One difference between obtaining a car with a lease or a loan is that: a loan finances the total purchase price of the car while a lease finances only the depreciated value and related fees.

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Answer:

=24x−30

Step-by-step explanation:

=(6)(4x+−5)

=(6)(4x)+(6)(−5)

=24x−30

Answer:

6 (4x - 5)

24x -30

i think question is not complete

Step-by-step explanation:

The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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The sum total by the given data is equals to $658,880.

We are given that;

Percent=15%

Amount= $98,880

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:

15% = 0.15

To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:

$98,880 / 0.15 = $98,880 x 1/0.15

To multiply by 100, we can move the decimal point two places to the right. This gives us:

$98,880 x 1/0.15 x 100 = $658,880

Therefore, by the percentage the answer will be $658,880.

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The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Answer:

B

Step-by-step explanation:

x must be a number between 60 and 57 and those numbers are 58 or 59

60 is greater than 59, and 59 is greater than 57

Answer:

x = 59

Step-by-step explanation:

The number must be less than 60 from the first inequality and greater than 57 from the second inequality

so the integers allowed are 58,59

Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer