Last year the chess club had 20 members. This year the club has 15 members. Find the percentage of change and state whether the percent of change is an increase or decrease

The questions are solved by setting up equations based on the information provided, and then solving. The equations help identify the larger integer, the denominator, and the positive integer in the various problems.

The first question talks about two integers, hence we can express them as x and y. It is stated that one is 3 less than the other, so we let y = x - 3. The sum of their squares is 185, so we can write this as x² + y² = 185. Replacing y in the equation, we get x² + (x - 3)² = 185. Solve this quadratic equation for its roots, one of which is the larger integer.

In the second question, the numerator of a fraction is described to be 1 more than twice its denominator. If the denominator is x, the numerator becomes 2x + 1. We're also told that when 4 is added to both, the fraction reduces to 1/2. Thus, we have: (2x + 1 + 4) / (x + 4) = 1/2. Solve this equation to find the denominator.

The third question talks about a positive integer and its inverse (1/x if x is the integer). It is mentioned that their difference is 1/4. Hence, we get the equation: x - 1/x = 1/4. Solving this equation gives the required integer.

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Answer:

Option D. 4 batches

Step-by-step explanation:

A potato chips manufacturing facility uses 1/6 barrel of oil in each batch and we have to find the batches of potato chips manufactured in 2/3 of a barrel.

We will use unitary method to solve this question.

∵ [tex]\frac{1}{6}[/tex] barrel is required to manufacture batch = 1

∴ 1 barrel is required to manufacture batches = 1 ÷ [tex]\frac{1}{6}[/tex]

∴ [tex]\frac{2}{3}[/tex] barrel is required to manufacture batches = [tex](\frac{1}{\frac{1}{6}})(\frac{2}{3})=(\frac{6}{1})(\frac{2}{3})=6.\frac{2}{3}=4[/tex]

Therefore Option D.4 is the correct option.

The expression 3x3x3x3x3x3x3 is equivalent to 3⁷.

Given that an expression 3x3x3x3x3x3x3, we need to write an equivalent expression to it,

The expression that is equivalent to 3x3x3x3x3x3x3 can be simplified using the exponentiation operation.

In mathematics, when you have a number or variable multiplied by itself multiple times, you can represent it using exponentiation.

In this case, we have the number 3 multiplied by itself 7 times. Using exponentiation, we can rewrite this expression as 3⁷.

The exponent 7 indicates that the base number, which is 3, should be multiplied by itself 7 times. So, 3⁷ means 3 multiplied by itself 7 times.

When we calculate 3⁷, we get the result 2187.

Therefore, the expression 3x3x3x3x3x3x3 is equivalent to 3⁷.

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Answer:

Perimeter of the rectangle is 30 cm.

Step-by-step explanation:

Kirby drew a quadrilateral with 4 right angles, a side that measures 9 centimeters and a side that measure 6 centimeters.

Since quadrilateral has all its sides equal to 90° and opposite side equal in size.

Therefore, the quadrilateral is a rectangle.

Perimeter of rectangle =  sum of all sides

                                      = [ 9 + 9 ] + [ 6 + 6 ]

                                      = [ 18 ] + [ 12 ]

                                      = 30

Perimeter of the rectangle is 30 cm.

 A = E = 25.02 feet

 B = D = 31.11 feet

 C = ║(37, 65) -(63, 39)║ = √((-26)² +26²) = √1352 ≈ 36.77 . . . feet

i litterly need just 49 points lol thank man XD

Tracy has the equivalent of 2 and 1/2 full boxes of tile left after tiling the bathroom, as each of the four boxes has 5/8 of tile remaining.

The question involves a scenario where Tracy is cleaning up after tiling a bathroom and assessing how much tile is remaining. With four open boxes of tile and each box containing 5/8 of tile remaining, we can calculate the total amount of tile left. To do this, we simply multiply the number of boxes by the fraction representing the remaining tiles in each box. This gives us:

4 boxes × 5/8 tile per box = 20/8 (or 2 and 1/2 boxes when simplified).

Therefore, Tracy has the equivalent of 2 and 1/2 full boxes of tile left after tiling the bathroom. The small gaps mentioned in another context are typically recommended to accommodate expansion and contraction of the tiles due to changes in temperature and humidity, which is an important concept in laying tile.

Final answer:

To find the width of the rectangular classroom, we divide the area, expressed as -3a - 21, by the length, expressed as a+3. Simplifying the trinomial by binomial division, we find that the width is represented by the expression (a - 7).

Explanation:

To find the expression for the width of the classroom, we need to divide the area of the rectangle by its length. The area of the rectangular classroom is given by the trinomial a - 4a - 21, which simplifies to -3a - 21. Since we are given that the length of the rectangle is a+3, we divide the area by the length to get the width.

Width = Area / Length

Width = (-3a - 21) / (a + 3)

Now, to divide the trinomial by the binomial, we look for a binomial that when multiplied by the length gives us the area. The factors of -21 that add up to -4 (the coefficient of 'a' in the area expression) are -7 and 3. So, the binomial that we seek can be written as (a - 7) because:

(a+3)(a-7) = a² - 7a + 3a - 21 = a² - 4a - 21

Which matches our area expression. Therefore, the expression for the width of the classroom is (a - 7).

The population of city A is 82% of the population of city B.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let y be the population of the city A.

and, x be the population of city B.

As, the population of city A is 18% less than the population of city B.

So, (100- 18) = 82% = 0.82

Thus, the relation is y= 0.82 x

Hence, The population of city A is 82% of the population of city B.

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Final answer:

City A's population is 82% of city B's population, which is calculated by subtracting the decrease percentage (18%) from 100%.

Explanation:

The question focuses on finding the percentage of city A's population relative to city B's population. Given that city A's population is 18% less than city B's population, it means that city A has 82% (100% - 18%) of the population of city B. Therefore, if city B is considered 100% in terms of population size, city A's population is 82% of city B's population. This is calculated by understanding that subtracting the percentage decrease from 100% gives us the remaining percentage.

Hence, City A's population is 82% of City B's population, indicating that City A's population is 82/100 or 0.82 times the population of City B.

Answer : the solution of c is 14.

Explanation :

Since we have given that

[tex]\frac{c-4}{c-2}=\frac{c-2}{c+2}-\frac{1}{2-c}\\\\\frac{c-4}{c-2}=\frac{c-2}{c+2}+\frac{1}{c-2}\\\\\frac{c-4}{c-2}=\frac{(c-2)^2+c+2}{(c+2)(c-2)}\\\\\frac{c-4}{c-2}=\frac{c^2+4-4c+c+2}{(c+2)(c-2)}\\\\(c-4)(c+2)=c^2+6-3c\\\\c^2-8-2c=c^2+6-3c\\\\-2c+3c=6+8\\\\c=14[/tex]

So, c = 14

So, the solution of c is 14.

There is no extraneous solution as if we put the value of c i.e. 14 in the equation it does not make the equation not defined . so by putting the value of c we get a defined value,

Hence , there is no extraneous solution.

Answer: The solution is C = 14

And there is zero extraneous solutions

Step-by-step explanation: Because I said so :-)

Answer:

  x = 6 cm

Step-by-step explanation:

The area is the product of length (x +2) and width (2x -5). It is 56 cm², so for all dimensions in cm, we can write ...

  (x +2)(2x -5) = 56

  2x² -x -66 = 0 . . . . . subtract 56 to put into standard form

  (x -6)(2x +11) = 0 . . . .  factor

Solutions to the equation are values of x that make the factors zero:

  x = 6, x = -11/2

The negative solution is extraneous, so the solution of interest is ...

  x = 6 cm