Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead, because she runs 25% faster than Bonnie. How many laps will Annie have run when she first passes Bonnie

The best option regarding the solutions of the trigonometric equation presented in this problem is given as follows:

A. 60º + n360º, 300º + n360º.

The trigonometric equation for this problem is defined as follows:

[tex]\cos{x} - \sqrt{1 - 3\cos^2{x}} = 0[/tex]

Then, isolating the cosine, we have that:

[tex]\cos{x} = \sqrt{1 - 3\cos^2{x}}[/tex]

Applying the square for both sides, we have that:

cos²(x) = 1 - 3cos²(x).

4cos²(x) = 1.

cos²(x) = 1/4

cos²(x) = 0.25.

Applying the square root to both sides, we have that:

cos(x) = 0.5.

Meaning that the angle measures of x with the cosine of 0.5 are given as follows:

x = 60º, x = 300º.

(as the cosine is positive on the first and fourth quadrant).

One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option a is correct.

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Answer:10

Step-by-step explanation:

got the same question

Most likely one of these unrelated factors that could possibly have an impact on how long it takes to finish the race is the environment

Therefore the correct option is a) Number of people the stadium can hold

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Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.

He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.

The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.

Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.

Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

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Answer:

60 × 40 = 2,400

I hope this helped.

Answer: 2400 people would come in 40 days

Step-by-step explanation:

If 60 people came on 1 day, that is the unit rate

60 to 1

So, just multiply 1 by 40 and 60 by 40

2400 to 40

Therefore, 2400 is the answer

Answer:

no

Step-by-step explanation:

Answer:

s = 11.cm

Θ = 2.2.radians

Step-by-step explanation:

The equation of a circle is (x+3)² + (y+5)² = 4² with a center at (-3,-5).

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

The center is approximated to lie at the position (-3,-5) in the graph below with the axes of symmetry. The points of intersection of the circle with any of the two axes (broken lines) provide a diameter of around 8 units, and so the radius is half the diameter, which is 4 units.

The equation of the circle whose graph is given below is:

(x+3)² + (y+5)² = 4²

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A right triangle is formed by the provided sides 6 cm, 10 cm, and 8 cm

Given that a triangle has sides measuring 6 cm, 10 cm, and 8 cm.

The question is whether a right triangle is formed by the specified sides.

The Pythagorean theorem states that the sum of the squares of the base and height is equal to the square of the hypotenuse.

Hypothesis 2 Equals Base 2 plus (Altitude)2

Make the hypotenuse 10 cm long.

Specify 6 cm for the base and 8 cm for the perpendicular.

(Hypotenuse)2 LHS (Hypotenuse)

RHS: (Base)2 + (Altitude)2 (Base)2 + (Altitude)2 = (6)2 + 2 = (10)2 = 100 (8)

LHS = RHS: 2 = 36 + 64 = 100

The sides provided meet the requirements for a right triangle.

As a result, a right triangle is formed by the provided sides.

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Therefore a quadratic function can be written in vertex form as

y = a(x - h)^2 + k.

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

A quadratic function can be written in vertex form as y = a(x - h)^2 + k

Where (h, k) is the vertex, and a is the leading coefficient.

y = ax^2 + bx + c (standard form)

y = a(x + b/2a)^2 + c - b^2/4a

y = a(x - h)^2 + k where h = -b/2a and k = c - b^2/4a

For example,when y = 3x^2 - 6x - 5

y = 3x^2 - 6x - 5

y = 3(x^2 - 2x) - 5

y = 3(x^2 - 2x + 1 - 1) - 5 = 3(x - 1)^2 - 8

So, the equation is in vertex form y = 3(x - 1)^2 - 8

Note that this only works for parabolas that opens upwards or downwards, if the parabola opens to the sides, the vertex form is y = a(x-h)^2 +k

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Answer:

I think it would be 10 inches but I am not sure

The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.

Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.

When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.

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We can solve this equation using the distributive property. First, we will use the distributive property to multiply the 3y by 2.

The distributive property is a mathematical rule that allows you to multiply a single number by a group of numbers by multiplying the single number by each number in the group individually. This rule can be expressed in two ways. The first way is a(b + c) = ab + ac. The second way is a(b - c) = ab - ac.

This will give us 2x * 3y = 2(3y). Then, we will subtract 6 from both sides of the equation, which gives us 2x * 3y - 6 = 2(3y) - 6. We can then divide both sides of the equation by 6, which gives us 2x * 3y / 6 = 2(3y) / 6. Finally, we can divide both sides of the equation by 3y, which gives us 2x = -2. Therefore, the solution to 2x 3y = -6 is 2x = -2.

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Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.

Subtracting two integers from each other is a type of subtraction.

The process for determining the difference between two decimals and two whole numbers is the same.

We only add a new step.

Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.

To give them all the same amount of decimal places, we must first convert each decimal.

7.2 becomes 7.200 as a result.

The computation may now be done as before:

8.967 - 7.200 = 1.767

Therefore, there is a 1.767 discrepancy between these figures.

In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.

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Answer:

Step-by-step explanation:

We know that : Percentage means 'divided by 100'

therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005

y = 0.25x + 50 and y = 0.3x + 40 will be the equation to find the cost to rent a car.

A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

Costs are the dollar amount spent on materials, labor, services, goods, equipment, and other items for use by a company or other accounting organization.

y = 0.25x + 50

y = 0.3x + 40

The equations will be written as y = mx + b, or slope-intercept form. You must determine what you have in order to determine what belongs where.

They receive $50 per day plus $0.25 per mile from Rent-A-Wreck. This indicates that the $0.25 per mile is the number that changes daily. Thus, y = 0.25x + 50 will be the equation.

They receive $40 per day with $0.30 per mile from Drive-A-Lemon. This indicates that the $0.30 per mile is the number that changes daily. y = 0.3x + 40 will be the formula.

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Answer: 35

Step-by-step explanation:

So first you plug 5 into the equation which is:

10(5)-15

which is 50-15

50-15 is 35

Answer:

35

Step-by-step explanation:

plug 5 in for x and u will get 35

The percentage increase in the population from 1965 to 2015 is 35 %.

To calculate the population growth rate (PG), take the difference (subtraction) between the original population and the population at time point 1, divide by the original population, and multiply by 100. The population growth rate (PGR) for that period (10 years) was 12%.

Given:

In the year 1965, the population of country A was 2714000.

In the year 2015, the population of country A was 3663900.

Percentage increase in population 50 years

                         = [tex]\frac{(3663900-2714000)}{2714000}[/tex] × 100

                         = 35 %

Thus, the percentage increase in the population from 1965 to 2015 , i.e, 50 years is 35%.

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The nature of the roots of the equation x^2 - 5x + 7 = 0 : no real roots

Consider given quadratic equation: x^2 - 5x + 7 = 0

Comparing given quadratic equation with the standard form of quadratic equation i.e., ax^2 + bx + c = 0

a = 1, b = -5, c = 7

First we find the discriminant:

D = b^2 - 4ac

D = (-5)^2 - 4(1)(7)

D = 25 - 4(7)

D = 25 - 28

D = -3

Since, the discriminant D < 0

Therefore, there are no real roots of this equation.

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The number of bracelets is 4.

The number of bracelets is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Number of bracelets = x

Number of necklaces = y

Amount of gold in each bracelet = 8 grams

Amount of gold in each necklace = 16 grams

Now,

x + y = 12 _____(1)

x = 12 - y ____(2)

8x + 16y = 160 ______(3)

Substituting (2) in (3) we get,

8(12 - y) + 16y = 160

96 - 8y + 16y = 160

96 + 8y = 160

8y = 160 - 96

8y = 64

y = 8

Now,

x = 12 - y

x = 12 - 8

x = 4

Thus,

The number of bracelets and necklaces that were made is 4 and 8.

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Answer:

Step-by-step explanation:

The mean of 4 5 6 7 8

there are 5 numbers in sequence, you can solve at a glance by looking at the number in the middle, or add the numbers and divide them by their number, in any case the answer will be 6

4 5 6 7 8    (6 is central)

or

(4 + 5 + 6 + 7 + 8) : 5 =

30 : 5 =

6

A domain has [-1, 1]

Now, According to the question:

Let's know:

How do you find the domain?

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.

A square root with a negative number under the root cannot produce a real number. This means that [tex]1-x^2[/tex] must be greater than or equal to zero.

Squaring a real number will always produce a positive number, so [tex]x^{2}[/tex]must be equal to or smaller than 1. This means x is between 0 and 1, giving the domain of [0,1].

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The complete question is this ;

What is the domain of [tex]\sqrt{1-x^2}[/tex]

Therefore, F = c * M1 * M2 / d^2 when the force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the distance between them using the C constant.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

Direction is characterized as the course that anything follows, the route that must be taken to go to a certain location, the direction in which something is beginning to take shape or the direction you are facing.

F = c * M1 * M2 / d^2

Where,

F is the force of attraction,

M1 and M2 are the weights of the two bodies,

d is the distance between the two bodies,

and c is the proportionality constant.

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Yes S lies as the perpendicular bisector as asked in the question .

The distance is calculated with the use of distance formula,

d = √( x2 - x1 )² + ( y2 - y1 )²

Now , we are suppose to calculate the distance between the points S and R, given their values are ,

S=(4,-2) and

R=(3,7)

Using distance formula ,

d = √( 3 - 4 )² + ( 7 - (-2))²

d =  √ 1 + 81

=  √82

Now, the distance between Q and S can be found as ,

Q=(-5,-1)

S=(4,-2)

d = d = √(4 + 5)² + ( -2 + 1)²

d =  √ 81 + 1

=  √82

As the distance between the two ends of the segment and the point S is the same, the point S must lie on the perpendicular bisector of QR, according to the perpendicular bisector theorem.

For question number 9 the distance between Q and S are,

Q=(-5,4)

S=(-2,-5)

d = √( -2 -5)² + ( 5 - 4)²

d =  √ 9 + 1

=  √10

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The standard deviation equation ( 1 + 6.8)% × 93000 > 202800

What is standard deviation?

Your dataset's standard deviation serves as a gauge of its degree of variability. It displays the typical difference between each outcome and the mean.

                            While a high standard deviation indicates that values are frequently distant from the mean, a low standard deviation indicates that values are typically grouped close to the mean.

( 1 + 6.8)% × 93000

= 202800

Then we get n ≈ 12,

the equation ( 1 + 6.8)% × 93000 > 202800

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Answer: HL

Step-by-step explanation:

HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

The fish is closer to sea level. Sea level is defined as the mean sea level, which is a fixed point of reference for measuring altitude.

The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.  To explain further, sea level altitude is a point of reference that is used to measure the altitude of other objects. Sea level altitude is defined as the mean sea level which is a fixed point.

Therefore, when trying to determine which animal is closer to sea level, it is important to look at the altitude of both the fish and the bird. The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.

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The percentage increase in project completion time is 26.85%.

Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

=(137-108)/108*100

=26.85%

The percentage increase in time to complete the project is 26.85%.

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The AROC is 3 for the interval 2 < x < 5, which is the correct answer that would be option (A).

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

The table is given in the question as follows:

x          y

0         -2

1         -3

2         0

3         3

4         6

5         9

We have to determine the Average Rate of Change in the table below for the interval 2 < x < 5

As per the given table, the required AROC would be as:

⇒ (9 - 3)/(5-3)

⇒ 6/2

Apply the division operation, and we get

⇒ 3

Hence, the correct answer would be option (A).

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Answer:

Step-by-step explanation:

1) 6.2

2)12.4

3) 18.6