The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rate of change of

(i) the perimeter.

(ii) area of rectangle.

Answer:

Step-by-step explanation:

Answer:38cm2

Step-by-step explanation:

The area of right angle triangle is 36 sq.cm. Whose base 9, Height 8 .

Base is 9 cm.

8 centimeters tall.

Triangle area equals 1/2 x base x height

Triangle's area is 1/2 x 9 x 8 = 36 square centimeters.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

The surface inside a flat figure is measured by its area. Squares are used to measure area. To obtain the square units, multiply the length by the width.

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On solving the provided question, we can say that - the value of the following polynomial will be 3x^2 = 5 => x^2 = 5/3

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

here,

[tex]3x^{-2}-5[/tex]

3x^2 = 5

x^2 = 5/3

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Answer:

  x = 3

Step-by-step explanation:

You want to know the value of x, given that NM = 5x-1 and QP = 3x+5 in congruent triangles NMQ and QPN.

Corresponding parts of congruent triangles are congruent, so we have ...

  NM = QP

  5x -1 = 3x +5

  2x = 6 . . . . . . . . . . add 1-3x

  x = 3 . . . . . . . . . . divide by 2

Total Liabilities  + Equity = $220,000.

Total Assets = $220,000.

What is Ratio Analysis and Balance Sheet?

The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.

One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.

Here we are given in the Question,

Assets

Cash = $45,000

Inventory = $41,000

Property = $134,000

Liabilities

Notes  = $55,000

Wages  = $56,000

and

Equity

Stock = $50,000

Investment = $59,000

Total Liabilities  + Equity = ( Notes + wages ) + (stock + Investment)

Total Liabilities  + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)

Total Liabilities  + Equity = $220,000.

Total Assets = Cash + Inventory + Property

Total Assets = $45,000 + $41,000 + $134,000

Total Assets = $220,000

Therefore,

Total Liabilities  + Equity = Total Assets.

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Based on the the information provided above, Ashley's and Saskia's numbers are equal to 22 and 7 respectively.

In order to write a system of equations to describe this situation, we would assign variables to Ashley's number and Saskia's number respectively, and then translate the word problem into an algebraic equation as follows:

Translating the word problem into an algebraic equation, we have the following:

x - 1 = 3y                   .....equation 1.

4x + y = 95              .......equation 2.

Making x the subject of formula in equation 1, we have:

x = 3y + 1      .......equation 3.

Substituting equation 3 into equation 2, we have:

4(3y + 1) + y = 95

12y + 4 + y = 95

13y = 95 - 4

13y = 91

y = 91/13

y = 7.

For the value of x, we have:

x = 3y + 1

x = 3(7) + 1

x = 21 + 1

x =22.

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Answer:

350,000.00

Step-by-step explanation:

420,000.00 - 20% = 350,000.00
Increase percentage: 70,000.00

Luca's average trip will be 58 miles per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

In this case, it took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, Luca's average trip will be:

= Distance / Time

= 464 / 8

= 58 miles per hour.

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The given statement in the form of inequality is given as -

(x ÷ 4) ≥ 26.

inequality : An inequality is used to make unequal comparisons between two expressions or numbers.

expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

equation : A mathematical equation is used to equate two expressions.

Given is the statement as -

"quotient of x and 4 is at least 26"

We can write the inequality as -

(x ÷ 4) ≥ 26

Therefore, the given statement in the form of inequality is given as -

(x ÷ 4) ≥ 26.

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The correct factorization of 33³ × 39 × 4¹¹ = 2²² × 3⁴ × 11³ × 13

Factorization is the collecting together of the common terms of an expression so as to have it in simpler form.

To find  the correct factorization of 33³ × 39 × 4¹¹, we write out each term in terms of its common factors.

so, we have that the factorization of the first term is 33³ = (3 × 11)³ = 3³ × 11³

Also, we have that the factorization of the second term is 39 = 3 × 13

Finally, we have that the factorization of the last term is 4¹¹ = (2²)¹¹ = 2²²

So, we have that 33³ × 39 × 4¹¹ = 3³ × 11³ × 3 × 13 × 2²²

= 3³ × 3 × 13 × 11³  × 2²²

= 2²² × 3⁴ × 11³ × 13  

So, the correct factorization is 2²² × 3⁴ × 11³ × 13

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The height of the building can be  649.44 ft

What is angle of elevation ?

angle of elevation states that the angle which is formed between line of sight and horizontal line.

Given,  the base of the triangle is 1.75 mile. The angle opposite of the tall side, x, is 4 degrees.

height of the building is an unknown variable (x) .

tan(angle) = opposite length /adjacent length.

Opposite length is x, adjacent length is 1.75 mile, angle is 4 degrees.

tan(4º) = x / 1.75

rearrange for x

x = 1.75*tan(4º) = ~1.75*0.0699  miles.

x = ~0.123

Now to get feet, just multiply by 5,280 ft in one mile

Height of the building is 0.123 miles * 5280 ft/mile = 649.44 ft

Hence , The height of the building can be  649.44 ft .

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A line has a slope of 5. it passes through the points (-5, -1) and (x,9) than the value of x is -3

We are going to use the fact that when a line passes through two points : [tex](x1,y1) and (x2,y2)[/tex]

the slope is given by the following formula:

[tex]slope=y2-y1/x2-x1[/tex]

In the present case, the slope is 5 and the points are (-5, -1) and (x, 9)

Hence,

[tex]5=9-(-1)/x-(-5)[/tex]

[tex]5=10/x+5\\x+5=10/5\\x+5=2\\x=-3[/tex]

Thus, the value of x is -3 when it travels between the coordinates (-5, -1) and (x, 9).

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By solving the interval  : [0,2pi] 4 csc x +6=-2 is  7pi/6 , 11pi/6

[tex]& 4 \csc x+6=-2 \\[/tex]

[tex]& 4 \csc x=-8 \\[/tex]

Simplifying,

[tex]& \csc x=-2 \\[/tex]

[tex]& \frac{1}{\sin x}=-2 \\[/tex]

[tex]& \sin x=-\frac{1}{2} \\[/tex]

We get,

[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]

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Answer:

245 miles

Step-by-step explanation:

210 = 6 gallons

210/6 = how far you can travel with one gallon

210/6 = 35

7*35 = how far you can travel with 7 gallons

7*35 = 245

Answer:

Ann drove 245 miles during her drive last weekend.

Step-by-step explanation:

If Ann used 7 gallons of gas during her drive last weekend, we can use the car's MPG to find out how far she drove by multiplying the number of gallons used by the MPG:

7 gallons * 35 miles/gallon = 245 miles

According to the question the angle between right angle triangle hence the   M∠1 = [tex]90^{0}[/tex] .

90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.

Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees (they are complementary).

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The measure of decimal number is 2 tenths + 5 thousandths is 0.205.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given expression

2 x 0.1 + 5 x 0.001

the expanded form is 2 tenths + 5 thousandths

= 2/10 + 5/1000

multiply and divide by 100 in 2/10

we get 200/1000

now 200/1000 + 5/1000 = 205/1000 = 0.205

Hence value of expression is 0.205.

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The value of fraction will be;

⇒ 101/24

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 7/8+ (-2/3) - (-4)

Now,

Since, The expression is,

⇒ 7/8+ (-2/3) - (-4)

Simplify as;

⇒ 7/8 - 2/3 + 4

⇒ (21 - 16)/24 + 4

⇒ 5/24 + 4

⇒ (5 + 96) / 24

⇒ 101/24

Thus, The solution is,

⇒ 101/24

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Answer:i think A

Step-by-step explanation:

Start with any random elements of sets and compute LHS and RHS individually.

a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.

b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.

Therefore, S = {1, 2, 3} and T = {1, 4, 5}.

Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.

Hence,  f(S ∪ T)=f(S) ∪ f(T).

Now, f(S ∩ T) = {1} and  f(S) ∩ f(T) =  {1, 2, 3} ∩ {1, 4, 5} = {1}.

Therefore,  f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)

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The solution to the equation 8z = 4x - 32 is z = -4 and x = 8.

An equation is a mathematical statement that states that two expressions are equal. It consists of an equals sign and two expressions, one on each side of the equals sign. Equations are used to solve for the value of the unknown expressions, and can be used to solve problems in various fields such as physics, chemistry, engineering, and mathematics.

1. Start by isolating the z variable by subtracting 4x from both sides of the equation. This will give us: 8z = -32.
2. Divide both sides of the equation by 8. This will give us: z = -4.
3. Finally, substitute z = -4 into the original equation and solve for x. This will give us: 4x = 32, so x = 8.

Therefore, the solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
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Complete questions as follows-
8z = 4x - 32
Please explain step by step how to solve 8z = 4x - 32.

You need 2 tablespoons of vinegar for every 1 tablespoon of oil.

What are a ratio and proportions?

A ratio is a way of comparing two or more values by division. A ratio expresses a relationship between two or more quantities. It is a comparison of one quantity to another. For example, the ratio of 3:2, 3 is being compared to 2.

A proportion is an equation that states that two ratios are equal. It can be written as:

a/b = c/d or a:b = c:d, where a,b,c,d are numerical values.

The ratio of tablespoons of vinegar to tablespoons of oil in the salad dressing is given by the ratio of the number of tablespoons of vinegar to the number of tablespoons of oil.

In this case, the ratio is 22 tablespoons of vinegar to 11 tablespoons of oil, or 22/11.

You can simplify this ratio by dividing both numerator and denominator by their greatest common divisor, that is 11

So the ratio of tablespoons of vinegar to tablespoons of oil is 2:1

Another way to express this is that for every 1 tablespoon of oil, 2 tablespoons of vinegar are needed.

So, If you want to know how many tablespoons of vinegar are needed for every tablespoon of oil you can use the proportion:

vinegar/oil = 22/11 = 2/1

Hence, you need 2 tablespoons of vinegar for every 1 tablespoon of oil.

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Find time needed to drive 200 miles:

50 miles = 1 hour

1 mile = 1/50 hour

200 miles = 1/50 x 200 = 4 hours

Find time of arrival:

7:00am + 4 hours = 11am

Answer: She will arrive at 11am

Answer:

The woman will arrive at New York City at 11 am.

Step-by-step explanation:

At an average speed of 50 miles per hour, it will take the woman 4 hours to reach New York City. If she leaves at 7 am, she will arrive at 11 am. Here's the math:

200 miles / 50 miles per hour = <<200/50=4>>4 hours

7 am + 4 hours = 11 am

So the woman will arrive at New York City at 11 am.

Answer:

124 degrees

Step-by-step explanation:

Since they are congruent the corresponding angles will be equal. There is only one obtuse in each triangle, Angles Y and N. N is measured to be 124 degrees so Y is also 124 degrees.

Number of Hours the band can record there music is 10hrs

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Word issues, also known as narrative problems, may be found in both daily life and the Common Core State Standards for every school level, from K to 12. For everything from counting pennies to calculating a gratuity, you can utilize the three primary forms of word problems: part-part whole, separate and join, and multiply and divide.

Total money the band has after selling the merch is = $375 + 200 = $575.

Rate for studio is $75 per day.

Total money left = $575 - 75 = $ 500

So number of Hours the band can record there music is= 500/50 = 10hrs.

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The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;

[tex]\bar {x}[/tex] ≈ 13.05

Median = 13.60

The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.

The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.

The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;

The number of data points = 28

The sum of the data is;  (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5

The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05

The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;

2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2

The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;

Median = (12.6 + 14.6)/2 = 13.60

The median is 13.60

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Answer: To solve a quadratic equation of the form ax^2 + bx + c = 0, there are several steps that Inga could use. Here are three options:

She could complete the square to rewrite the equation in the form (x + p)^2 = q.

She could use the quadratic formula: x = (-b +/- √(b^2 - 4ac)) / (2a).

She could factor the equation to rewrite it in the form (x + r)(x + s) = 0.

Option 1: Completing the square

To complete the square, Inga could add and subtract (b/2)^2 to the equation to get:

a(x^2 + bx + (b/2)^2) - (b/2)^2 = 0

Then, she could rewrite the equation in the form:

a(x + (b/2))^2 = (b/2)^2

Option 2: Using the quadratic formula

To use the quadratic formula, Inga could substitute the values of a, b, and c into the formula to get:

x = (-12 +/- √(12^2 - 4 * 2 * -3)) / (2 * 2)

= (-12 +/- √(144 + 24)) / 4

= (-

Step-by-step explanation: