A toy rocket is shot vertically into the air from a launching pad 8 feet above the ground with an initial velocity of 136 feet per second. The height​ h, in​ feet, of the rocket above the ground at t seconds after launch is given by the function h=-16t^2+136t+8 . How long will it take the rocket to reach its maximum​ height? What is the maximum​ height? Simplify your answer.

Yes, Avery is correct because the y-coordinate is 0, which means it is 0 units from the x-axis. Therefore, point A is on the x-axis.

Answer: Spinner 1 = 1/2, Spinner 2 = 1/3

Step-by-step explanation:

I don't know what the answer choices are telling you to do... but

spinner 1 has 4 total parts, 2 of which are odd. So there's a 2 out of 4 chance that the arrow will land on an odd number. Simplified, it will reduce from 2/4 to 1/2. Spinner 2 has 3 total parts (denominator) one of which is a vowel, a. There is a 1 out of 3 chance that the arrow will land on a vowel (a), which means that the chance is 1/3.

If you add 1/2 and 1/3, the result is 5/6.

If you multiply 1/2 and 1/3, the result is 1/6. (A)

If you subtract 1/2 and 1/3, the result is 1/6. (A)

If you divide 1/2 and 1/3, the result is 3/2

The linear scale factor is found by comparing the volumes of the two jars and taking the cube root of the ratio, resulting in a scale factor of approximately 1.89. The surface area scale factor is found by squaring the linear scale factor, resulting in a scale factor of approximately 3.57.

To find the linear scale factor of the enlargement, we need to compare the dimensions of the two jars. Since volume is a cubic measure, we can find the ratio of the volumes and then take the cube root to get the linear scale factor:

Volume of first jar = 87 cm³

Volume of second jar = 0.58 L = 580 cm³

Ratio of volumes = 580/87 ≈ 6.67

Linear scale factor = cube root of ratio of volumes = cube root of 6.67 ≈ 1.89 (rounded to the nearest hundredth)

Therefore, the linear scale factor of the enlargement is approximately 1.89.

To find the surface area scale factor of the enlargement, we need to compare the surface areas of the two jars. Since the jars are similar (i.e. they have the same shape), the surface area scale factor is equal to the linear scale factor squared:

Linear scale factor = 1.89

Surface area scale factor = (1.89)² = 3.57 (rounded to the nearest hundredth)

Therefore, the surface area scale factor of the enlargement is approximately 3.57.

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Answer:

The number is 6.

Step-by-step explanation:

[tex]3x + 4 = 22[/tex]

[tex]3x = 18[/tex]

[tex]x = 6[/tex]

The number which is thought is 6.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

a number multiply it by 3 add 4 and get 22.

Let the unknown number be x.

First multiply the given number by 3.

It becomes 3x.

Add 4 to it.

It becomes 3x + 4.

The equation we get is,

3x + 4 = 22

Subtracting both sides by 4,

3x = 18

Dividing both sides by 3,

x = 6

Hence the value of x is 6.

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Nοah will be 6 years οld when the accοunt reaches $17000.

The interest charged οn a debt οr depοsit is knοwn as cοmpοund interest. It is the idea that we use the mοst frequently οn a regular basis. Cοmpοund interest is calculated fοr a sum based οn bοth the principal and cumulative interest.

Tο sοlve this prοblem, we can use the fοrmula fοr cοmpοund interest:

A = [tex]P(1 + r/n)^{(nt)[/tex]

Where: A = the final amοunt (in this case, $17000)P = the principal amοunt (in this case, $10900)r = the annual interest rate (in this case, 3% οr 0.03 as a decimal)n = the number οf times interest is cοmpοunded per year (in this case, assuming it's cοmpοunded annually, n = 1)t = the number οf years

Plugging in the values we have:

[tex]17000 = 10900(1 + 0.03/1)^{(1*t)[/tex]

Simplifying further:

[tex]17000/10900 = (1.03)^{t1.55963303} = (1.03){^t[/tex]

Nοw we can take the natural lοg οf bοth sides tο sοlve fοr t:

[tex]ln(1.55963303) = ln((1.03)^t)t * ln(1.03) = ln(1.55963303)t = ln(1.55963303) / ln(1.03)[/tex]

Using a calculatοr, we can find that it is apprοximately 6.156 years.

Since Nοah's age will be rοunded dοwn tο the nearest whοle number,

Nοah will be 6 years οld when the accοunt reaches $17000.

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From given ratio of boys and girls, the total number of students at the school is 1240.

What exactly is a ratio?

A ratio is a comparison of two quantities or values by division. It is commonly used to express the relationship between two numbers, such as the ratio of the number of boys to the number of girls in a classroom.

The ratio of two numbers a and b can be expressed as a/b or as the fraction a:b. For example, if there are 20 boys and 30 girls in a classroom, the ratio of boys to girls is 20/30, which can be simplified to 2/3 or written as the fraction 2:3.

Now,

Let's represent the number of boys as 11x and the number of girls as 9x, where x is a common factor.

From the given information, we know that:

11x = 9x + 124

Simplifying

11x - 9x = 124

2x = 124

x = 62

Now,

Number of boys = 11x = 11(62) = 682

Number of girls = 9x = 9(62) = 558

Therefore, the total number of students at the school is:

Total number of students = Number of boys + Number of girls = 682 + 558 = 1240

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Step-by-step explanation:

We can use the simple interest formula:

R = P(1 + rt)

where R is the balance, P is the principal, r is the interest rate, and t is the time.

For Investment R, we have:

R = 1,500(1 + 0.0275*8)

R = 1,980

For Investment S, we can use the formula:

R = P(1 + r)^t

R = 900(1 + 0.0275)^8

R = 1,116.92

a. The difference between the balance of the two investments after 8 years is:

1,980 - 1,116.92 = 863.08

b. The interest earned for Investment R is:

I = Prt

I = 1,500*0.0275*8

I = 330

For Investment S, we can calculate the interest using:

I = R - P

I = 1,116.92 - 900

I = 216.92

The difference between the interest earned on the two investments is:

330 - 216.92 = 113.08

c. To compare the return on investment, we can use the concept of compound interest.

For Investment R, the total value after 8 years is:

R = 1,500(1 + 0.0275*8)

R = 1,980

For Investment S, we can calculate the effective annual rate:

EAR = (1 + r/n)^n - 1

EAR = (1 + 0.0275/1)^1 - 1

EAR = 0.0275

The total value after 8 years is:

R = 900(1 + 0.0275)^8

R = 1,116.92

The return on investment for Investment R is:

ROI = (1 + r/n)^nt - 1

ROI = (1 + 0.0275/1)^1*8 - 1

ROI = 0.2229

The return on investment for Investment S is:

ROI = (1 + EAR)^t - 1

ROI = (1 + 0.0275)^8 - 1

ROI = 0.2329

Therefore, Investment S had the better return on investment.

Answer:

1/6 chance

Step-by-step explanation:

The only number on a six sided die that's a multiple of 6, is 6

There's 6 numbers, and 6 is one of those 6 numbers. So, 1/6 chance that she rolls a 6, unlikely.

Answer:

2144.66058485 in³

Step-by-step explanation:

If the area is 64π in², and A = πr², then 64π=πr²

r = √64

r = 8 in

V = 4/3×π×r³

V = 4/3×π×8³

V = 2144.66 in³

The required area of the shape is 2014.88 sq units.

Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.

Given shape consist of a square and four half circles.

Radius of circle = 14 units, side length of the square is 28 units

Area of the shape = are of square + area of four half circles

= 28×28 + 4(π(14)²)/2

= 784 + 2π(14)²

= 784 + 1230.88

= 2014.88 sq units

Thus, required area of the shape is 2014.88 sq units.

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Dave sold 38 bags of popcorn. This can be answered by the concept of Selling price.

Dave sold twice as many bags of popcorn than hot dogs at a total of $336, where popcorn sold for $2.50 and hot dogs sold for $2 each. The question asks how many bags of popcorn Dave sold.

Let's start by assigning variables to the unknown quantities. Let x be the number of hot dogs sold and y be the number of bags of popcorn sold.

We know that Dave sold a total of $336 worth of both popcorn and hot dogs, so we can write an equation:

2.5y + 2x = 336

We also know that Dave sold twice as many bags of popcorn than hot dogs, so we can write another equation:

y = 2x

Substituting y in the first equation with 2x, we get:

2.5(2x) + 2x = 336

5x + 2x = 336/2.5

7x = 134.4

x = 19.2

Now that we know the value of x, we can use the second equation to find y:

y = 2x = 2(19.2) = 38.4

However, y represents the number of bags of popcorn sold, which must be a whole number. Since Dave cannot sell 0.4 of a bag of popcorn, we need to round down to the nearest whole number. Therefore, Dave sold 38 bags of popcorn.

Therefore, Dave sold 38 bags of popcorn.

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Answer:

x ≤ 7

Step-by-step explanation:

$56 (her budget) divided by $8 (which is the cost per pound) will equal x.  Since we do not know the actual answer of the number of pounds she will buy due to the fact she will spend less than $56, which is also making her open to buying a total of $56.   Since the question is asking for the possible numbers of pounds she will buy, we will use the identity for pounds to be x.  We don't know the actual amount she will buy so the answer is x ≤ 7.  She will buy either less than or exactly 7 pounds of candy.

Potentially hazardous cold food that requires time and temperature control for safety (TCS food) should not be kept at a temperature above 41°F (5°C) for more than 6 hours total time, according to the FDA Food Code.

According to the U.S. Food and Drug Administration (FDA) Food Code, potentially hazardous cold food that requires time and temperature control for safety (TCS food) should not be kept at a temperature above 41°F (5°C) for more than 6 hours total time.

After that, the food must be thrown out to prevent the growth of harmful bacteria. These food are harmful to the health of consumer.

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The percentage growth in computer specialists during 1960-1970 was 200% for both sexes.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the percentage growth, we need to know the initial number of computer specialists and the number of computer specialists after the growth period.

Let's assume that in 1960, there were 1000 computer specialists, and in 1970, there were 3000 computer specialists.

The growth in computer specialists during this period can be calculated as follows:

Growth = Final number - Initial number

Growth = 3000 - 1000

Growth = 2000

To calculate the percentage growth, we divide the growth by the initial number and multiply by 100:

Percentage Growth = (Growth / Initial number) * 100

Percentage Growth = (2000 / 1000) * 100

Percentage Growth = 200%

Therefore, the percentage growth in computer specialists during 1960-1970 was 200% for both sexes.

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Answer:

-------------------------------------

Using triangle inequality theorem, we get two options:

1) x is the longest side, then:

2) x is the shortest side, then:

Combine the two options to get, x is between 2 and 22, or:

This is the first choice.

The p-value for the test of the claims is roughly 0.004.

To test the claim of the bulb patron, we can use a thesis test with the following null and indispensable suppositions.

We can use the binomial distribution to calculate the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. This probability is the p-value of the test.

To calculate the p-value, we need to use the binomial distribution and find the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. Using a binomial calculator or statistical software, we can find that the probability of observing 1050 or further imperfect bulbs is roughly 0.004.

Since this p-value is lower than the significant position of 0.05, we can reject the null thesis and conclude that the imperfect rate of the bulbs is more advanced than 0.01.

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The probability that Liz has two boys given that she has at least one boy who is taller is approximately 0.2841

Let's first consider all possible gender combinations of Liz's two children:

Boy, boy (BB)

Boy, girl (BG)

Girl, boy (GB)

Girl, girl (GG)

We know that Liz has at least one boy, which rules out the GG combination. That leaves us with three possible combinations: BB, BG, and GB.

From the given information, we know that in 76% of families consisting of one son and one daughter, the son is taller than the daughter. This means that in the BB combination, the probability that the taller child is a boy is 1 (since both children are boys), and in the BG and GB combinations, the probability is 0.76 (since there is one boy and one girl, and we know the boy is taller).

So, let's calculate the probability that Liz has two boys (BB) given that she has at least one boy who is taller. We can use Bayes' theorem for this

P(BB | taller child is a boy) = P(taller child is a boy | BB) × P(BB) / P(taller child is a boy)

where P(taller child is a boy | BB) = 1 (as both children are boys), P(BB) = 1/4 (since there are four possible gender combinations), and P(taller child is a boy) = P(taller child is a boy | BB) × P(BB) + P(taller child is a boy | BG) × P(BG) + P(taller child is a boy | GB) × P(GB) = 1 × 1/4 + 0.76 × 1/2 + 0.76 × 1/2 = 0.88.

Substituting these values into Bayes' theorem, we get

P(BB | taller child is a boy) = 1 × 1/4 / 0.88 = 0.2841

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Each of the expressions has been simplified and solved by using properties of exponents as shown below.

In Mathematics and Geometry, an exponent is a mathematical operation that is written as an algebraic expression, so as to raise a quantity to the power of another.

Therefore, an exponent can be modeled by the following mathematical expression;

bⁿ

Where:

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷

12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴

5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵

6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶

9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸

1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶

(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴

3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷

9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵

3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶

1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.

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Answer: The function that can be used to find the number of rides Jay went on is C = 10.50 + 4.50r, where C is the total cost and r is the number of rides. In this case, we know that Jay spent a total of $46.50 on entrance fees and rides, so we can plug this value into the equation and solve for r:

46.50 = 10.50 + 4.50r

Subtracting 10.50 from both sides, we get:

36 = 4.50r

Dividing both sides by 4.50, we find that Jay went on r = 8 rides.

Answer:

the value for p will be 162

The recursive and explicit formulae of the given arithmetic expression are:

Recursive formular = [tex]a_{n+1} = a_{n-13}[/tex]

Explicit formular is Tn = 75 - 13n

You can determine the value of any term in a series by using an explicit formula. The integers are divided into the natural numbers, which are 1, 2, 3, 4, and so on. If you know the value of the (n-1)th term in a sequence, you may use a recursive formula to determine the value of the nth term in the sequence. Recursive formulas give the value of a specific phrase depending on the previous term, whereas explicit formulas give the value of a specific term based on the position.

Given:

a1 = 52

a2 = 75 = 52 - 13 = a1 - 13

Recursive formular = [tex]a_{n+1} = a_{n-13}[/tex]

a = 52, d = -13

F(11) = a + (n - 1)d = 52 + (n - 1)-13 = 52 - 13n + 13 = 75 - 13n

Explicit formular is Tn = 75 - 13n

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The arithmetic sequence has a common difference of 23, recursive rule of this sequence is xₙ = [tex]x_{n-1}[/tex] + 23 and explicit rule is xₙ = 23n + 29. The 11th term is 282.

An arithmetic sequence is a mathematical progression in which each term is generated by adding a constant value to the preceding term, with the exception of the first term. This constant value is known as the common difference, and it governs the pattern of the sequence. There are two types of arithmetic sequences, one is an increasing sequence and the other is a decreasing sequence. Increasing sequence is obtained if the common difference is a positive number. Decreasing sequence is obtained if the common difference is a negative number.

The general format of the recursive rule is xₙ = [tex]x_{n-1}[/tex] + d, where xₙ is the nth term, [tex]x_{n-1}[/tex] is the (n-1)th term and d is the common difference of the arithmetic sequence.

In the given sequence x₁ = 52 and x₂ = 75

Common difference can be calculated by subtracting first term from second term = x₂ - x₁ = 75 - 52 = 23

Hence recursive rule for this sequence is xₙ = [tex]x_{n-1}[/tex] + 23

The general format of explicit rule is xₙ = x₁ + (n-1) × d.

For this sequence it is xₙ = x₁ + (n-1) × 23 = 52 + 23n - 23 = 23n + 29

To find f(11) we can use the explicit rule

f(11) = 23 × 11 + 29 = 282

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Let Ramanujan pick a complex number $a+bi$, where $a$ and $b$ are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:

(

�

+

�

�

)

(

5

+

3

�

)

=

5

�

+

3

�

�

+

5

�

�

+

3

�

�

2

=

(

5

�

+

3

�

)

+

(

5

�

+

3

�

)

�

−

3

�

(a+bi)(5+3i)=5a+3ai+5bi+3bi

2

=(5a+3b)+(5b+3a)i−3b

We want this product to be equal to $32-8i$. Equating the real and imaginary parts gives us two equations:

5

�

+

3

�

=

32

(1)

5a+3b=32(1)

5

�

+

3

�

=

−

8

(2)

5b+3a=−8(2)

We can solve this system of equations to find $a$ and $b$. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:

15

�

+

9

�

−

25

�

−

15

�

=

−

96

15a+9b−25b−15a=−96

Simplifying:

−

16

�

=

−

96

−16b=−96

Therefore, $b=6$. Substituting $b=6$ into equation (1) gives:

5

�

+

18

=

32

5a+18=32

Therefore, $a=2$. Thus, Ramanujan picked the complex number $2+6i$.

Based on the given conditions and informations provided, the complex number that was picked by thr Ramanujan is calculated to be  2+6i.

Let Ramanujan pick a complex number a+bi, where a and b are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:

(a+bi)(5+3i) = 5a+3ai+5bi+3bi² = (5a+3b)+(5b+3a)i-3b

We want this product to be equal to 32-8i. Equating the real and imaginary parts gives us two equations:

5a+3b=32 (1)

5b+3a=-8 (2)

We can solve this system of equations to find a and b. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:

15a+9b-25b-15a=-96

Simplifying:

-16b=-96

Therefore, b=6. Substituting b=6 into equation (1) gives:

5a+18=32

Therefore, a=2. Thus, Ramanujan picked the complex number 2+6i.

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The value of the given inequality is x≥16.

A connection in mathematics that compares two numbers or other mathematical expressions unequally is known as an inequality. [1] It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are used:

A less than symbol (a b) indicates that an is less than b.

A bigger value than b is indicated by the notation a > b.

In either scenario, a and b are not equal. In these relationships, an is strictly less than or strictly greater than b, which is known as a strict inequality[1]. Comparability is not included.

Two kinds of inequality relations are looser than strict inequalities:

We have inequality

x-4≥12

add 4 on both sides

x-4+4≥12+4

x≥16

Hence,

The value of the given inequality is x≥16.

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Answer: Let's call the length of the slide "x". From the problem, we know that Kenji walks 5 feet after he slides down and climbs 8 feet to get to the top of the slide again. This means that the total vertical distance he traveled (height of the slide) is equal to 5 + 8 = 13 feet.

Using the Pythagorean theorem, we can find the length of the slide:

x^2 = 13^2 + h^2

where h is the height of the slide.

We know that h = 13 feet, so we can substitute that into the equation:

x^2 = 13^2 + 13^2

x^2 = 338

x ≈ 18.4 feet

Therefore, the length of the slide is approximately 18.4 feet. Rounded to the nearest tenth, this is 18.4 feet.

Step-by-step explanation:

Answer:

Enlargement

Step-by-step explanation:

If it gets bigger is enlargement if it gets smaller its reduction

(a) To solve for the probability, we can use the Poisson distribution. Given that guests arrive at a rate of five per hour, the arrival rate per minute can be calculated as 5/60 = 0.0833 guests per minute.

Let X be the number of guests that arrive in a 2-minute interval. We can model X using a Poisson distribution with parameter [tex]λ = 0.1667[/tex] (0.0833 guests per minute * 2 minutes). Then, the probability that the next guest will arrive in less than 2 minutes can be calculated as: [tex]P(X > 0) = 1 - P(X = 0) = 1 - e^(-λ) = 0.1535[/tex]  

(b) To solve for the probability, we can use the same Poisson distribution as before. Let Y be the time between the arrivals of the tenth and eleventh guests. We can model Y using an exponential distribution with parameter [tex]λ = 0.0833[/tex](the arrival rate per minute). Then, the probability that Y is less than or equal to 2 minutes can be calculated as:

[tex]P(Y < = 2) = 1 - e^(-λ*2) = 0.1573[/tex]

Therefore, the probability that from the arrival of the tenth to the arrival of the eleventh guest takes no more than 2 minutes is 0.1573. The probability that the next guest will arrive in less than 2 minutes is 0.1535.

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The two angles in degrees from 0° ≤ θ < 360° are 240° and 300°, and the two angles in radians from 0 ≤ θ < 2π are 4π/3 and 5π/3.

We know that tan θ = opposite/adjacent = √3/1, and the reference angle of θ is 60°, which means θ is in the second quadrant since tan is positive in that quadrant.

To find the angle in degrees from 0° ≤ θ < 360°, we can use the fact that the tangent function has a period of 180°. Therefore, we can add 180° to the reference angle of 60° to get the angle in the second quadrant:

θ = 180° + 60° = 240°

We can also find the angle in the fourth quadrant by subtracting the reference angle from 360°:

θ = 360° - 60° = 300°

To find the angles in radians from 0 ≤ θ < 2π, we can use the fact that π radians is equal to 180°. Therefore, we can convert the angles in degrees to radians:

θ = 240° * π/180 = 4π/3

θ = 300° * π/180 = 5π/3

Therefore, the two angles in degrees from 0° ≤ θ < 360° are 240° and 300°, and the two angles in radians from 0 ≤ θ < 2π are 4π/3 and 5π/3.

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For the point (5, 4) to the directrix, the distance to the directrix is equal to the distance to the focus. For the other points on the list, the distance to the directrix is equal to the distance to the focus. The distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.

A perfect, U-shaped curve is referred to by the term parabola in mathematics. It is described as the collection of all plane points that are equidistant from a focus and a fixed broadband (the directrix). The point where the parabola's curve changes direction is known as its vertex, and the line that runs through it and is perpendicular toward the directrix is known as its axis of symmetry. The behavior of electromagnetic waves, projectile motion, reflector and antenna forms, and other real-world phenomena are frequently modelled using parabolas.

To determine whether a point is on a parabola with a given focus and directrix, we can use the definition of a parabola: a parabola is the set of all points that are equidistant to the focus and the directrix.

In this case, the focus is the point (0, 2) and the directrix is the line y = -2.

Let's first consider the point (5, 4). We can find the distance from this point to the directrix by finding the distance from the point to the line. The formula for the distance from a point (x1, y1) to a line [tex]Ax + By + C = 0[/tex] is:

[tex]|Ax1 + By1 + C| / \sqrt(A^2 + B^2)[/tex]

In this case, A = 0, B = 1, and C = -2, so the equation of the directrix is y = -2, which can be written as [tex]0x + 1y - 2 = 0.[/tex] Plugging in (5, 4), we get:

[tex]|0(5) + 1(4) - 2| / \sqrt(0^2 + 1^2) = 6[/tex]

So the distance from (5, 4) to the directrix is 6.

Next, we can find the distance from (5, 4) to the focus (0, 2):

[tex]\sqrt((5-0)^2 + (4-2)^2) = \sqrt(29)[/tex]

Since the distance from (5, 4) to the directrix is not equal to the distance from (5, 4) to the focus, we can conclude that (5, 4) is not on the parabola.

We can repeat this process for each point on the list. For the point (-1, 5), we get:

Distance to directrix: |-1 - 2| / 1 = 3

Distance to focus: [tex]\sqrt((-1-0)^2 + (5-2)^2) = \sqrt(26)[/tex]

Since the distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.

Similarly, we can check the other points on the list and find that the points (4, 3), (2, 1), (1, -2), (2, -1), (4, -3), and (5, -4) are also on the parabola. The points (3, 5), (6, 7), (8, 0), and (0, 8) are not on the parabola.

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Answer:

right angles

Step-by-step explanation: