What is the equation of the line –3x–2y=30 in slope-intercept form?



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Final answer:

To show that the differential equation M(x) + N(y)dy/dx=0 is separable, we must demonstrate that M and N can be expressed as functions of x and y respectively, without overlap, leading to an equation of the form f(y)dy/dx + g(x) = 0. Explanation of separable equations through specific cases and integration methods.

Explanation:

Separable equations involve the relationship M(x) + N(y)dy/dx = 0. To show this, you can use specific cases where M and N can be separated into functions of only x or y.

For example, if M/N can be expressed as f(y)/g(x), then the separable equation becomes f(y)(dy/dx) + g(x) = 0.

Integrating M(x, y) with respect to x can lead to finding a function f(x, y) that satisfies the given differential relationship.

Answer:

235 workers

Step-by-step explanation:

Factory operates on a standard work week shift for 5 days = 8 hours per day

In one week working hours are = 8 × 5 = 40 hours.

Company has an order for 7,500 new cars to be delivered in one week.

One car requires time to be fitted with a new hood ornament that requires to install = 1 hour and 15 minutes ( 1.25 hours )

In 40 hours (one week) cars will install with one worker = [tex]\frac{40}{1.25}[/tex] = 32 cars

To fulfill the order of 7,500 cars, Company needs workers = 7,500 ÷ 32 = 234.375 ≈ 235 workers.

235 workers must be assigned this job to meet the deadline.

-Line

Two adjacent, supplementary angles form a straight line

Answer: The number of successful throw made in that season in total is 30

Step-by-step explanation:

On average the player successfully made 5 out of 6 free throws .

Thus if number of free throws is x then number of successful throw will be [tex]\frac{5}{6}\times x[/tex] .

The basketball player attempted 36 free trials in a season .

Here x=36

Therefore No of successful throws [tex]=\frac{5}{6}\times 36=30[/tex]

Thus the number of successful throw made in that season in total is 30

To find out the number of toothpicks required to form 100 adjacent squares, one can use the formula 4 + 3(n - 1), resulting in 301 toothpicks.

To determine how many toothpicks are required to form 100 adjacent squares, we must first understand the pattern established by the initial set of squares. When forming three adjacent squares, 10 toothpicks are used. This is because the first square requires 4 toothpicks, and each subsequent square shares a side with the previous square, thus requiring only 3 additional toothpicks for each new square.

For n adjacent squares, the number of toothpicks required can be calculated with the formula: 4 + 3(n - 1), since the first square uses 4 toothpicks and each additional square uses 3 more toothpicks.

Now, let's apply this to 100 adjacent squares:

Therefore, 301 toothpicks are required to form 100 adjacent squares.

The relationship is that for each square, we need 4 toothpicks (1 new side for each square). So, for 100 adjacent squares, we require 400 toothpicks.

Let's analyze the pattern to determine the relationship between the number of squares and the toothpicks required. Consider the formation of 3 adjacent squares:

For the first square, we need 4 sides (4 toothpicks).

For the second square, we have 3 shared sides with the first square and 1 new side (3 + 1 = 4 toothpicks).

For the third square, we have 3 shared sides with the second square and 1 new side (3 + 1 = 4 toothpicks).

So, for 3 adjacent squares, we need a total of 12 toothpicks (4 + 4 + 4).

Now, let's generalize this pattern. For each additional square beyond the third, we are adding 4 toothpicks (1 new side for each square). Therefore, the toothpicks required to form n adjacent squares can be expressed as 4n.

For 100 adjacent squares:

Toothpicks=4×100=400

Hence, 400 toothpicks are required to form 100 adjacent squares.

The question probable may be:

To form 3 adjacent squares, 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?

1.D ,square root of 2

2.C, undefined

3. A

4. A, about -1

5. D, 12.3 feet

Answer:

ANswer is D on edgeunity

Step-by-step explanation:

Answer:

C just did this

Step-by-step explanation:

The number -9 is a rational number as it can be written as a fraction of two integers, specifically -9/1.

The number -9 is a rational number because it can be expressed as a fraction of two integers: -9/1 where -9 is the numerator and 1 is the denominator. By definition, rational numbers include all integers, as each integer can be written as a fraction with a denominator of 1. This is different from irrational numbers, which cannot be written as a simple fraction. An example of an irrational number is the square root of 2, which cannot be precisely expressed as a fraction of two integers.

Answer:

the answer is 16

The expression for adding 8 to the sum of 23 and 10 is (23 + 10) + 8. This is due to the commutative property of addition, which states that the order in which you add numbers does not change the result.

The question asks for an expression to calculate adding 8 to the sum of 23 and 10. The first step is to add 23 and 10 together, which equals 33. Then add 8 to that sum. You can represent this process mathematically as (23 + 10) + 8. So if you need to write an expression for adding 8 to the sum of 23 and 10, it would be (23 + 10) + 8. Remember, adding numbers together (a process called addition) is commutative, meaning you can add numbers in any order and still get the same result.

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Answer:

30 feet, 24 feet, 24 feet

Step-by-step explanation:

A kite is a quadrilateral with two pairs of congruent adjacent sides.

One of the longer sides measures 30 feet. According to the definition, the kite has two sides of length 30 feet. Let x feet be the length of another side.

The perimeter of the kite is

[tex]2\cdot 30+2\cdot x\ feet[/tex]

Since the kite has a perimeter of 108 feet, we have

[tex]2\cdot 30+2\cdot x=108\\ \\60+2x=108\\ \\2x=108-60\\ \\2x=48\\ \\x=24[/tex]

The length of two another sides is 24 feet. The kite has two sides of 30 feet and two sides of 24 feet.

Answer: Hello mate!

The kite has two equal-length long sides and two equal-length shorter sides. We also know that the perimeter is the addition of the four sides, where we have two long sides, L, and two short sides, S.

Then 2S + 2L = 108ft

S + L = 54 ft

if L = 30 feet

S + 30 ft = 54ft

S = 54ft - 30 ft = 24ft

Then the other long side also has 30ft length, and the two shorter sides have 24ft length.