Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4 (picture provided)

Answer:

The weight of the parcel is approximately 6 kilograms.

Step-by-step explanation:

The weight of the parcel is  12 lbs and 8 oz.

1 lb = 16 oz

So,  8 oz =  lb.

That means,  12 lbs and 8 oz = (12 + 0.5) lbs = 12.5 lbs

Now, 1 lb = 454 g

So,  12.5 lbs = (12.5 × 454) g = 5675 g

As,  1 kilogram = 1000 g

That means, 1 g = 0.001 kilogram

So,  5675 g  kilograms. (Rounded to the nearest whole kilogram)

Thus, the weight of the parcel is approximately 6 kilograms.

For a system of 2 equations in 2 unknowns, there are 3 cases:

When slopes are different, the two lines intersect at one point, the solution.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence no solutions. If the lines are the same line, they intersect at all points, so there are infinitely many solutions.

Answer:

$96.93

Step-by-step explanation:

1. multipy the cost of the item (89.75) times the 8% tax.

    89.75 * 0.08 = 7.18 in tax

2. add the item cost plus tax

    89.75 + 7.18 = $96.93

Max will have to pay $ 96.93  in total for the DVD player.

An extra amount of money to be paid to the seller as tax on sales or on the receipt of sales is called sales tax.

According to the problem,

So, Max will have to pay $ { 89.75 + [tex](\frac{8}{100}) 89.75[/tex]}

                                   = $ 96.93

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The square root of 128, which is an irrational number, is approximately 11.304. Rounded to two decimal places, it becomes 11.30.

The process of simplifying the irrational number 128 involves finding a square root since irrational numbers are those that cannot be expressed as a simple fraction, such as roots that are not even. The square root of 128 is not a whole number, therefore it's an irrational number. Using a calculator, the square root of 128 is approximately 11.304. So to obtain the square root of 128 to two decimal places, you round 11.304 to 11.30.

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Answer:

false

Step-by-step explanation:

Add both the numerators and the denominators when adding fractions and mixed numbers - this statement is false.

To add fractions with  denominators, first find a common denominator. The least common denominator is easiest to use. The least common multiple can be used as the least common denominator. Adding mixed numbers involves adding the fractional parts, adding the whole numbers, and then recombining them as a mixed number.

1. Add the whole numbers together.

2. Find the lowest common denominator of both fractions.

3. Convert the fractions to have the LCD as their denominator.

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Answer:

f(x)=x^2+4x-5

Step-by-step explanation:

Quadratic functions are second-order polynomials. To solve a quadratic equation, set the function equal to zero, and use the quadratic formula. The corresponding polynomial function in this case is f(x) = x² + 5x - 1.

Quadratic functions are second-order polynomials. They are of the form f(x) = ax² + bx + c, where a, b, and c are constants. To solve a quadratic equation, set the function equal to zero, and use the quadratic formula: x = (-b ± √(b²-4ac))/(2a). The discriminant, b²-4ac, determines the number and nature of the solutions. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution (a perfect square). If it is negative, there are no real solutions, but there are two complex solutions.

In this case, the corresponding polynomial function is f(x) = x² + 5x - 1.

Answer:

Part 1) Greta's right, the triangle is incorrect.

Part 2) [tex]34,203\ ft[/tex]

Part 3) The height of the tree is [tex]23.3\ ft[/tex], Trey’s house is not at risk

Step-by-step explanation:

Part 1) we know that

In the right triangle of the figure

[tex]sin(30\°)=\frac{1}{2}[/tex]

[tex]sin(30\°)=\frac{6\sqrt{3}}{12}=\frac{\sqrt{3}}{2}[/tex]

Compare

[tex]\frac{1}{2}\neq\frac{\sqrt{3}}{2}[/tex]

therefore

The triangle is not correct

Because

The side adjacent to the 30 degree angle should be [tex]6\sqrt{3}[/tex] and the side opposite the 30 degree angle should be [tex]6[/tex]

Part 2)

Let

x--------> the distance from the airplane to the SCCA (hypotenuse of the right triangle)

we know that

[tex]sin(17\°)=\frac{10,000}{x}[/tex]

[tex]x=\frac{10,000}{sin(17\°)}[/tex]

[tex]x=34,203\ ft[/tex]

Part 3)

Let

x-------->  the height of the tree

we know that

[tex]tan(43\°)=\frac{h}{25}[/tex]

[tex]h=tan(43\°)(25)=23.3\ ft[/tex]

[tex]23.3\ ft< 25\ ft[/tex]

therefore

Trey’s house is not at risk

Answer:

addition, subtraction, and multiplication only

Step-by-step explanation:

There are a couple of reasons why polynomials are not closed under division:

1. the set of polynomials includes zero, and division by zero is undefined.

2. division by a polynomial can give rise to terms that are not non-negative powers of the variable, 1/x, for example. These terms are not included in the set of polynomials.

Answer:

Addition, Subtraction, and Multiplication

Step-by-step explanation:

For this case we must find the area of a scalene triangle (different sides) by means of Heron's formula:

[tex]S = \sqrt {p (p-a) (p-b) (p-c)}[/tex]

Where:

S: It's the area

p: It is the semiperimeter

a, b, c: They are the sides:

[tex]p = \frac {a + b + c} {2}\\p = \frac {25 + 13 + 17} {2}\\p = 27.5 \ units[/tex]

So:

[tex]S = \sqrt {27.5 (27.5-25) (27.5-13) (27.5-17)}\\S = \sqrt {10467.1875}\\S = 102.309 \ units ^ 2[/tex]

ANswer:

Option D

Answer:

There are 162 students in the school.

Step-by-step explanation:

10% do not like purple.   x is the number of students in the school.  We have 162 students that do not like purple.

x*.10 = 162

Divide each side by .10

x = 162/.10

x =1620

There are 162 students in the school.

The discount is $37.50 and the sale price of the table is $212.50.

We have to calculate the discount and sale price

Discount

Discount amount =

Original price * Discount percentage

Discount amount = $250 * 15%

= $250 * 0.15

= $37.50

Sale price

Sale price = Original price - Discount amount

Sale price = $250 - $37.50

= $212.50

Answer:

E, B, A,

Step-by-step explanation:

C is wrong because it isn't decreasing

D is wrong because if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning y goes lower than 5

F is wrong because  if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning the y intercept is 2 not 5

Answer:

[tex]\Large \boxed{\mathrm{A , \ B, \ and \ E}}[/tex]

Step-by-step explanation:

[tex]F(x)=2 \cdot 5^x[/tex]

There are no restrictions on x. The domain is all real numbers.

To find the y-intercept, we set the x value to 0. The y-intercept of the function is (0, 2).

The function is increasing, because as the value of the input increases, the value of the output increases as well.

There are 360° in a circle and this circle is divided into 8 equal parts. 360/8 = 45 which means that each angle is 45°. The central angle subtended by minor arc BC is 2 portions of the circle, or 45 * 2 which is 90°. The answer is B.

Answer:

The answer should be B, 90.

Step-by-step explanation:

The circle is broken up into 8, 45 degree angles. the subtended of arc BC should be 90, tell me if i'm wrong.

Mark brainliest plz thanks!

To calculate the volume of the triangular prism, first find the area of the right triangle that forms the base and then multiply it by the height of the prism.

The question involves finding the volume of a triangular prism whose base is a right triangle with sides measuring 7 inches, 24 inches, and 25 inches, where 25 inches is the hypotenuse. The height of the prism is given as 3 inches. To find the volume of the prism, we use the formula for the volume of a triangular prism, which is the area of the triangular base times the height of the prism.

First, we find the area of the triangular base using the formula for the area of a right triangle, which is (1/2) × base × height. For this triangle, the base and height are the perpendicular sides, which are 7 inches and 24 inches respectively. Thus, the area of the base triangle is (1/2) × 7 × 24 square inches.

Next, we multiply the area of the base by the height of the prism to get the volume. The height of the prism is 3 inches, so the volume will be the area of the base triangle times 3 inches.

Answer:

m∠A = 9.1°

m∠B = 10.9°

c = 54.2

The answer is (d)

Step-by-step explanation:

∵ a = 25

∵ b = 30

∵ m∠C = 160°

∴ c² = a² + b² - 2 × ab × cos(C)

∴ c² = 25² + 30² - 2(25)(30) × cos(160) = 2934.5389

∴ c = 54.2

∵ a/sin(A) = b/sin(B) = c/sin(C)

∵ 25/sin(A) = 54.2/sin(160)

∴ sin(A) = (25 × sin(160)) ÷ 54.2 = 0.1577584

∴ m∠A = 9.1°

∵ 30/sin(B) = 54.2/sin(160)

∴ sin(B) = (30 × sin(160)) ÷ 54.2 = 0.18931

∴ m∠B = 10.9°

Answer:

(a) 0.48

(b) 0.20

(c) it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the​ casino.

Step-by-step explanation:

​(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino. ​

The probability that a radomly selected resident opposes the casino and strongly opposes the cassino is the product of the two probabilities, that a resident opposes the casino and that it strongly opposes the casino (once it is in the first group) as it is shown below.

Use this notation:

i) Determine the probability that a radomly selected resident opposes the casino, P(A)

Probability = number of favorable outcomes / number of possible outcomes

ii) Next, determine,the probability that a resident who opposes the casino strongly opposes it, P(B/A):

iii) You want the probability of both events, which is the joint probability or  intersection: P(A∩B).

So, you can use the definition of conditional probability:

iv) From which you can solve for P(A∩B)

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

In this case, you just want the complement of the probability that a radomly selected resident who opposes the casino does strongly oppose the casino, which is 1 - P(B/A) = 1 - 8/10 = 1 - 0.8 = 0.2.

​(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the​ casino?

You are being asked about the joint probability (PA∩B), which you found in the part (a) and it is 0.48.

That is almost 0.50 or half of the population, so you conclude it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the​ casino.

Answer:

40 feet

Step-by-step explanation:

The perimeter of a triangle is the distance around the triangle. It can be found by adding all the sides together. First, find the amount each side is by substituting x = 4 and simplifying.

3x - 4 = 3(4) - 4 = 12 - 4 = 8

x² -1 = (4)² - 1 = 16 - 1 = 15

2x² - 15 = 2(4)² - 15 = 32 - 15 = 17

Add the sides together, 8 + 15 + 17 = 40 feet

Answer:

She bought .9 ton of compost.

Step-by-step explanation:

Take the amount of bags she bought and multiply it by the weight of each bag.

40*50=2,000

Then divide it by the amount a ton is.

2,000/2,204=0.90718474

Round it to the nearest tenth.

=.9

Then that's you're answer.

1. Answer: a. -7

Step-by-step explanation:

[tex]f(x)=\dfrac{7}{x}\implies f(x)=7x^{-1}\\\\f'(x)=-1\cdot 7x^{-1-1}\\.\qquad =-7x^{-2}\\\\.\qquad =-\dfrac{7}{x^2}\\\\f'(1)=-\dfrac{7}{1^2}\\\\.\qquad =\large\boxed{-7}[/tex]

2. Answer: a. 4

Step-by-step explanation:

[tex]f(x)=4x+7\\f'(x)=1\cdot4x^{1-1}+0\cdot7\\.\qquad=4\\\\f'(5)=\large\boxed{4}[/tex]

3. Answer: d. 224

Step-by-step explanation:

[tex]f(x)=12x^2+8x\\f'(x)=2\cdot12x^{2-1}+1\cdot8x^{1-1}\\.\qquad=24x+8\\\\f'(9)=24(9)+8\\.\qquad=216+8\\.\qquad=\large\boxed{224}[/tex]

4. Answer: d. 11/81

Step-by-step explanation:

[tex]f(x)=\dfrac{-11}{x}\implies f(x)=-11x^{-1}\\\\f'(x)=-1\cdot -11x^{-1-1}\\\\.\qquad=11x^{-2}\\\\.\qquad=\dfrac{11}{x^2}\\\\f'(9)=\dfrac{11}{9^2}\\\\.\qquad=\large\boxed{\dfrac{11}{81}}[/tex]

5. Answer: -10

Step-by-step explanation:

s(t) = 1 - 10t

v = s'(t) = -10

     s'(10) = -10

A full circle is 360 degrees.

The circle is separated into 8 parts, so each arc is 1/8 of a circle, which equals: 360/8 = 45 degrees.

There are 2 45 degree arcs between B and C, so the arc from B to C = 45 x 2 = 90 degrees.

The answer is B.

Answer:

262,440

Step-by-step explanation:

Multiply the population (243000) times 8% (0.08)

   243000*0.08 = 19,440

Add the 8% to the total population

   19,440 + 243,000 = 262,440

The new population of City A after one year with an 8% of the increasing rate will be 262,440.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The number of inhabitants in City A was roughly 243000 individuals, and it expanded by 8% in one year.

The new population of City A after one year with an 8% of the increasing rate is given as,

⇒ (1 + 0.08) x 243,000

⇒ 1.08 x 243,000

⇒ 262,440

The new population of City A after one year with an 8% of the increasing rate will be 262,440.

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Answer:

nevermind

Step-by-step explanation:

Answer:

4.66667

Step-by-step explanation:

Answer: 6 outcomes

Step-by-step explanation: Since the first outcome is 2 and the second is 4 2 times 3 is ix since it is multiplying by 2 (2,4,6,8)

Final answer:

To find the total number of experimental outcomes for the entire experiment, multiply the number of outcomes for each step together, resulting in 24 total experimental outcomes.

Explanation:

The total number of experimental outcomes for the entire experiment can be calculated by multiplying the number of outcomes for each step together:

Number of outcomes for the first step: 3

Number of outcomes for the second step: 2

Number of outcomes for the third step: 4

Multiplying these numbers: 3 outcomes x 2 outcomes x 4 outcomes = 24 total experimental outcomes.

Answer: t=5 , t=8 on PLATO

Step-by-step explanation:

In the context of the problem, the zeros of the function represent the points in time when the roller coaster is at ground level. Specifically, the roller coaster goes underground at t = 5 seconds and comes back above ground at t = 8 seconds.

In the function f(t) = (t^2 − 13t + 40)(t^2 − 2t + 3), which models the height of the roller coaster above the ground, the zeros represent the points in time when the roller coaster is at ground level. In other words, when f(t) = 0, the height of the roller coaster is zero, implying it is at ground level. In your case, the zeros you found signify that the coaster is on the ground at the time instances t = 5 and t = 8 seconds since passing point A.

The values t = 5 and t = 8 seconds are the time instances when the roller coaster enters and exits the underground portion of the track respectively. It's crucial to comprehend the physical significance of mathematical solutions, particularly in real-world scenarios.

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Answer:

The perimeter would also be multiplied by 6.

Step-by-step explanation:

The perimeter would also be multiplied by 6. Suppose the sides are 5 and 10. The perimeter would be the sum of the side lengths or 5 + 5 + 10 + 10 = 30.

Multiply each side length so 5*6 = 30 and 10*6 = 60. Find the perimeter by finding their sum, 30 + 30 + 60 + 60 = 180.

Divide the new perimeter by the old perimeter to find a scale factor.

180/30 = 6.

The new perimeter is exactly 6 times bigger since 6*30 = 180.

Answer:

The perimeter is multiplied by 6.

Step-by-step explanation:

[tex]Domain: x\in\mathbb{R}[/tex]

Answer:

It's B.   f(x) = (x + 3(^2 + 1.

Step-by-step explanation:

f(x) ---- > f(x + 3)   is a translation of 3 units to the left.

The correct function that includes a 3 unit leftward translation is f(x) = [tex](x-3)^2+1.[/tex]

The correct function that includes a translation of 3 units to the left is option D, f(x) = [tex](x-3)^2+1.[/tex]

When we translate a function to the left by a certain number of units, we subtract that number from the x-values. In this case, subtracting 3 units from x would result in a translation to the left. The function f(x) = [tex](x-3)^2+1.[/tex] represents this translation. The x-3 part shifts the graph horizontally to the left by 3 units.

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Answer:

D

Step-by-step explanation:

If there is a 2x2 matrix as  [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

The determinant is given by  [tex]\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]

Now, if we calculate the value of "ad - bc", we see that:

[tex](-4)(-12)-(8)(6)=0[/tex]

We can't calculate the inverse, the inverse doesn't exist. The answer is D.

Answer:

A = 25π ft² or A = 78.5398 ft²

Step-by-step explanation:

The formula for area of a circle is

A = πr² where r is the radius

We are given a diameter of 10, the radius is half of the diameter, so for our problem r = 5.  Plug that in and evaluate

A = π(5²)

 A = 25π

or

A = 78.5398 if you multiply out pi