Roy ia training for a race. He swims 1/4 lap in 3/5 minute. At that rate,how many minutes does it take roy to swin each lap?

The perimeter of a rectangle is an application of the Distributive property is shown below.

The dividing Property it is necessary to multiply each of the two integers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two words.

This property can be stated symbolically as: A ( B+ C) = AB + AC.

Given:

As, we know the perimeter of a rectangle is twice the sum of its length and width.

let length of rectangle be 'l' unit and width of rectangle is 'w' unit.

So, the Perimeter of rectangle =2L+2W

                                                   =  2(L+W)

Here, 2 is distributed over length of width in parenthesis.

Learn more about Distributive Property here:

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To factor out -1/3 from 1/3y - 3/2, distribute the negative sign to both terms resulting in -1/9y + 1/2.

To factor out -1/3 from the expression 1/3y - 3/2, we can distribute the negative sign to both terms. This results in -1/3(1/3y) + (-1/3)(-3/2). Simplifying this further, we get -1/9y + 1/2.

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Final answer:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, isolate the sine function and find the values of θ that satisfy the equation by taking the inverse sine of both sides. The solutions are θ = -π/6 and θ = 5π/6.

Explanation:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, we can start by isolating the sine function. Subtracting 1/2 from both sides of the equation, we get -sin θ = -1/2. Next, we can find the values of θ that satisfy this equation on the given interval by taking the inverse sine (sin⁻¹) of both sides. This gives us θ = sin⁻¹(-1/2).

Using the unit circle or a calculator, we can find the values of θ that satisfy this equation. Let's first find the value of θ in the first quadrant. Here, sin θ = -1/2, so θ = sin⁻¹(-1/2) = -π/6.

Since we are looking for solutions on the interval 0 ≤ θ < 2π, we need to find the other solution that lies in the second quadrant. In the second quadrant, sin θ is also negative, but the angle is measured from the positive x-axis in the clockwise direction. Therefore, θ = -π + π/6 = 5π/6 is the other solution.

Final answer:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, you can isolate the sine function and apply the inverse sine function to find the solutions.

Explanation:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, we can start by isolating the sine function. Subtracting 1/2 from both sides of the equation, we get -sin θ = -1/2.

Next, we can apply the inverse sine function to both sides. This will give us two possible values for θ within the given interval: θ = π/6 and θ = 5π/6.

Therefore, the solutions to the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π are θ = π/6 and θ = 5π/6.

Answer:

How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?

⇒ 1 triangle(s)

How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?

⇒ 0 triangle(s)

Answer:

The first one is 1. The second one is 0.

Step-by-step explanation:

I just did it and got it right.

The difference in quotients arises because dividing by smaller numbers results in larger quotients. For example, 80,000 divided by 2,000 equals 40, while dividing by 200 equals 400, and by 20 equals 4,000.

To understand this, let's calculate each quotient step-by-step:

The differences in results are due to the different divisors. As you divide by smaller numbers, the quotient increases because each division breaks the total into more parts.

Division and multiplication are closely related; dividing by a number is the same as multiplying by its reciprocal.

Summary

The fundamental concept here is that dividing by a larger number results in a smaller quotient, whereas dividing by a smaller number results in a larger quotient. This difference is evident when comparing the quotients of 80,000 divided by 2,000 (40), 200 (400), and 20 (4,000).

Answer: It’s C

Step-by-step explanation:

Lynn's method of multiplying 4 by 305 and doubling the result will not give her the correct answer to 44 x 305. This method is equivalent to multiplying by 8, not 44.

Lynn's method will not give her the correct answer. When Lynn multiplies 4 by 305 and then doubles the product, she is effectively multiplying 305 by 8, not by 44. To show this, consider the mathematical operations: when we multiply 4 by 305 we get 1220, and when we then double 1220 we get 2440. This is different from the result of multiplying 44 by 305, which is 13420. Therefore, the correct answer is C. Lynn's method will not be correct. Therefore, multiplying by 4 and then doubling the product is the same as multiplying by 8, not 44.

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To estimate the height of a mountain using angles of elevation from two points, set up a system of trigonometric equations based on right triangles and solve for the height using algebra.

To estimate the height of a mountain given two angles of elevation at different points, we use trigonometric concepts. At the first point, the angle of elevation is 32°, and at a point 1000 feet closer, the angle is 35°. To solve this, we can set up two right triangles that share the same height (the mountain) but have different base lengths. Denote the height of the mountain as h, the distance from the first observation point to the base of the mountain as d, and use the trigonometric tangent function:

Tan(32°) = h / d

Tan(35°) = h / (d - 1000)

This creates a system of two equations with two variables. We solve for h by manipulating the equations to isolate h and substituting into one of the equations. We can use trigonometric tables or a calculator to find the values for Tan(32°) and Tan(35°), and then solve for the distance d, which subsequently allows us to find the height h by simple algebraic rearrangement.

To find the number of student and adult tickets sold at a baseball game, we can set up a system of equations using the given information. Solving the system of equations will give us the values of the variables. In this case, 150 student tickets and 250 adult tickets were sold.

Let's assume that the number of student tickets sold is 'x' and the number of adult tickets sold is 'y'.

According to the information given, the total attendance was 400 people, so we can write the equation: x + y = 400.

The total ticket sales were $1050, so we can write another equation: 2x + 3y = 1050.

Now we have a system of equations that we can solve to find the values of x and y.

Using substitution or elimination method, we find that x = 150 and y = 250.

Therefore, 150 student tickets and 250 adult tickets were sold.

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To determine if a pair of numbers is relatively prime, we need to find their greatest common divisor (GCD). If the GCD is 1, then the numbers are relatively prime. The pair 14 and 81 is relatively prime.

For two numbers to be relatively prime, their greatest common divisor (GCD) must be 1.

We can find the GCD by finding the prime factors of each number and determining if they have any common factors.

Let's take a look at each pair of numbers:

Therefore, the pair of numbers that is relatively prime is 14 and 81.

Answer:

Correct answers of Logan is 19.

Step-by-step explanation:

Since, Logan didn't answered one problem.

Thus, total problem he attempt is 24.

Let the number of correct answer = x

and, Number of wrong answer = y

Then x + y = 24

And since it is given that,

He earned 4 points for correct answer and deduct 2 points for wrong answer. and he got score 66.

Thus we get equation,

4x - 2y = 66

Solving these two equation we get,

x = 19 and y = 6

Thus, Correct answers of Logan is 19.