The perimeter of a rectangle is 172 meters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.

On solving the provided question, we cam say that - by unitary method the answer is 4/5

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here, construction worker = 2/3 pounds

he has = 1/2

so the answer is 4/5

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The values sinθ=-5/√34, cosθ=-3/√34, tanθ = 5/3, cotθ = 3/5, secθ = -√34/3 and cscθ = -√34/5

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−3,−5) on its terminal side

r=√9+25

=√34

sinθ=y/r

sinθ=-5/√34

cosθ=x/r

cosθ=-3/√34

tanθ = y/x

tanθ = 5/3

cotθ = x/y

cotθ = 3/5

secθ = r/x

secθ = -√34/3

cscθ = r/y

cscθ = -√34/5

Hence, values sinθ=-5/√34, cosθ=-3/√34, tanθ = 5/3, cotθ = 3/5, secθ = -√34/3 and cscθ = -√34/5

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Answer:

Step-by-step explanation:

Answer:

$4.50 each

Step-by-step explanation:

27/6=4.50

Expression [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex] is equal to [tex]x^{2/7} /y^{-3/7}[/tex]

The correct option is 1.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Examples:

3x + 4y – 7,  4x – 10, etc.

Given expression is

[tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex]

⇒[tex]x^{2.1/7} /y^{3.1/5}[/tex]

⇒[tex]x^{2/7} /y^{3/5}[/tex]

⇒[tex]x^{2/7} . y^{-3/5}[/tex]

Hence [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex]  is equivalent to      [tex]x^{2/7} /y^{-3/7}[/tex].

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Each side length of an equilateral triangle is (6x³+9x)/3  units

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

An equilateral triangle has all the sides equal in length

Let each side be y

Perimeter is the sum of all sides

So, Perimeter = y+y+y = 3y

Given, Perimeter = 6x³+9x

=> 3y= 6x³+9x

=> y= (6x³+9x)/3  

Thus, each side length of an  equilateral triangle is (6x³+9x)/3  units

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The participant received a head start of 4 meters. The 4 in the equation represents the initial position of the participant.

The participant's rate of speed of the participant is 3 meters per second.

a. The participant received a head start of 4 meters.

The 4 in the equation represents the initial position (y-intercept, c) of the participant, so this is the head start that the participant received.

b. The participant's rate of speed of the participant is 3 meters per second.

This means that for every 1 second (represented by x in the equation), the participant covers a distance of 3 meters. So the participant's rate of speed is 3 meters per x second

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The T10 of the sequence is

T10 =-10.00

Generally, To determine the T10 of a geometric sequence, you will need to know the common ratio of the sequence.

If T2=-10 and

T6=-160, we can use these terms to find the common ratio.

The formula for any term in a geometric sequence is:

Tn = a * r^(n-1)

Where

We can use the terms you provided to find the common ratio:

-160 = -10 * r^(6-1)

-160 = -10 * r^5

r = (-160/-10)^(1/5)

Now that we know the common ratio, we can find T10:

T10 = a * r^(10-1)

T10 = -10 * r^9

So the T10 of the geometric sequence is

T10= -10 * (-160/-10)^(1/5)^9

T10 =-10.00

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The volume of the solid generated when R is rotated about the horizontal line y=-2 is 98.868.

The volume of the solid:3.574

The equation involving integral expressions:

[tex]\int\limits^k_0 {(4-f(x))} \, dx =\int\limits^2_0 {(4-f(x))} \, dx[/tex]

The given equation is f(x)=x^4-2.3x^3+4

f(x)=4 ⇒x=0,x=2.3

Now, substitute the values in the equation:

⇒ Volume=  [tex]\pi \int\limits^2_0 {(4-(-2)^2)} \, dx -(f(x)-(-2)^2)dx[/tex]

By solving the equation we get:

volume=98.868

b) consider the point r in the graph which is perpendicular to the x-axis that an isosceles right triangle with a leg in r.

Area of cross-section:

A=1/2(leg)(leg)=1/2(4-f(x))^2

Volume=∫(1/2(4-f(x))^2)dx     ∴with limits (0 to 2.3)

Solving the function we get:

Volume=3.574

c)given the vertical line x=k divides R into two regions with equal areas.

∫(4-f(x))dx=∫(4-f(x))dx

2∫(4-f(x))dx=∫(4-f(x))dx            ∴with limits 0 to 2.3 and 0 to k

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The triangle QRS and TUS are congruent.

In mathematics, a postulate is a statement that is considered exactly true without showing any proof on it.

The quadrilateral whose opposite sides are equal in length and parallel to each other is called parallelogram. The parallelogram that has four right angles is called rectangle. One of the main properties of parallelogram is that the diagonals bisect at a point.

In the given question, two diagonals QU and RT intersect at point S.

If we join the point Q with T and R with U, RQTU parallelogram is formed.

QU and RT are the diagonals of the parallelogram.

According to the properties of parallelogram, RQ = TU and QT =RU

As the diagonals intersect at S, we can discuss about two triangle RQS and TUS

we find side length QS = side length SU and side length RS = side ST

On the other hand, ∠QSR =∠UST because the diagonals bisect at S

Finally, the triangle RQS and TUS has two equal side length and one equal angles. Besides, other side and remaining angles are also similar.

So, ΔRQS≅ΔTUS

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The height of the doctor's office is solved using similar triangles to give

When the corresponding sides of two triangles are proportionate and their corresponding angles are congruent, The triangles are said to be similar.

As a result, the triangle's side should be proportionate if its corresponding angles are congruent.

Examining the descriptions shows that pair of equivalent sides are

height of tree and shadow of tree,

height of doctor's office and shadow's of doctor's office

The solution is worked out

height of tree / shadow of tree = height of doctor's office / shadow's of doctor's office

7 / 3 = height of doctor's office / 21

cross multiplying

3 * height of doctor's office = 7 * 21

height of doctor's office = 7 * 21 / 3

height of doctor's office = 49 feet

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An event that will have a sample space of S = {g, b} include the following: C. Flipping a two-sided coin with one side green and the other side blue.

In Mathematics and statistics, a sample space can be defined as a set or collection of possible outcomes (results or outputs) that are obtainable from a random experiment. Mathematically, a sample space is represented or denoted by using the symbol, "S."

Additionally, a sample space may contain a number of outcomes (results or outputs) that depends on the experiment. Generally speaking, the subset of possible outcomes (results or outputs) of that are obtainable from an experiment is typically referred to as events.

In this context, we can reasonably infer and logically deduce that "Flipping a two-sided coin with one side green and the other side blue" is an event which would have a sample space that is modeled by this mathematical expression;

S = {g, b}

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Answer: C: Flipping a two-sided coin with one side green and the other side blue.

Chelsea is sewing handmade scarves she has 7 1/2 yards of material and needs 2 1/4 yards of material for each scarf, so the number of scarves can she make with the existing material = 3. This can be solved using the concept of fractions.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Total material = [tex]7\frac{1}{2}[/tex] yards

[tex]= 7\frac{1}{2} = 7 + \frac{1}{2} = \frac{15}{2}[/tex] yards

Materials required for each scarf = [tex]2\frac{1}{4}[/tex] yards

Number of scarfs she make with the existing material

= Total Material ÷ Material required for each scarf

= [tex]\frac{15}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]

= [tex]\frac{15}{2}[/tex] × [tex]\frac{4}{9}[/tex]

= [tex]\frac{10}{3}[/tex]

= [tex]3\frac{1}{3}[/tex] ≈ 3

Hence, the number of scarves can she make with the existing material = 3.

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Answer:

1. 1/3 or 1 red paint : 3 yellow paint

2. 3/1 or 3 or 3 yellow paint: 1 red paint

Step-by-step explanation:

Answer:

a) 35 degrees

b) 98 degrees

Step-by-step explanation:

Complementary angles measure up to 90 degrees. So if one angle measures 55 degrees, the other would have to be 35 degrees as

55 + 35 = 90

Supplementary angles measure up to 180 degrees. So if one angle measures 82 degrees, the other would have to be 98 degrees as

82 + 98 = 180

The distance covered by the car in 8 seconds of the journey is 100 meters.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

Velocity (m/s) = 20, 15, 10, 5, 0

Calculate the distance as shown below,

[tex]Distance = velocity \times time[/tex]

Distance = 0 × 20 + 15 × 2 + 10 × 4 + 5 × 6 + 0 × 8

Distance = 0 + 30 + 40 + 30 + 0

Distance = 100 meter

Thus, the distance covered by the car is 100 meters.

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Diameter of Lawn = 28 cm

Length of rope tied at the centre of lawn = 7cm.

As the cow, tied to the rope grazes the lawn it forms a circle with radius 7cm.

Area of lawn grazed by cow

= pi*7^2. ( pi = 3.14)

= 3.14 * 49

= 153.86 sq. cm

Area of the lawn with radius 14 cm

= pi * 14^2. (pi = 3.14)

= 3.14 * 14^2

= 615.44 sq cm

Remaining area = Area of the Lawn - Area of the lawn grazed by cow

= 615.44 - 153.86

= 461.58 sq cm

The equation of line passes through the points (-3, -1) and (5, -1) will be;

⇒ y = - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-3, -1) and (5, -1).

Now,

Since, The equation of line passes through the points (-3, -1) and (5, -1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-1)) / (5 - (-3))

m = 0/8

m = 0

Thus, The equation of line with slope 0 is,

⇒ y - (-1)= 0 (x - (-3))

⇒ y + 1 = 0

⇒ y = - 1

Therefore, The equation of line passes through the points (-3, -1) and       (5, -1) in slope intercept form is,

⇒ y = - 1

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a) The values of c and d are 7 and 58.

b) The coordinates of the turning point of the curve y = -x² - 14x + 9 is,

⇒ (- 7, 58)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The expression is,

⇒ - x² - 14x + 9

Now, Simplify the expression to change in the form of -(x + c)² + d as;

⇒ - x² - 14x + 9

⇒ - (x² + 14x) + 9

⇒ - (x² + 14x) - 49 + 49 + 9

⇒ - (x² + 14x + 49) + 49 + 9

⇒ - (x + 7)² + 58

By comparing, we get;

The values of c and d are,

⇒ c = 7

⇒ d = 58

And. To find the coordinates of the turning point of the curve

y = -x² - 14x + 9, we can differentiate it with respect to x and equate it to zero.

⇒ y = -x² - 14x + 9

⇒ dy/dx = - 2x - 14 = 0

⇒ - 2x = 14

⇒ x = - 7

And,

⇒ y = -x² - 14x + 9

⇒ y = - (-7)² - 14×- 7 + 9

⇒ y = - 49 + 98 + 9

⇒ y = 58

Thus, The coordinates of the turning point of the curve y = -x² - 14x + 9 is,

⇒ (- 7, 58)

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The total sales required to earn the desired income of $2800 is calculated to be $6,375.

Sale is a business transaction involving the exchange of goods or services for money. It can refer to the act of selling, or the thing that is sold. Sales are typically the main source of revenue for businesses. The process of selling involves finding potential customers, negotiating a price, and delivering the product or service. The ultimate goal is to make a profit.

In order to earn a monthly income of $2800, a local salesman would need to sell $6,375 worth of goods in a month. This is calculated by subtracting the base salary of $875 from the desired income of $2800, which leaves $2,925. Then, 6% of $1450 is $87, so the remaining $2,838 must be made up of 6% of the sales above $1450. By dividing this amount by 6%, the total sales required to earn the desired income of $2800 is calculated to be $6,375.

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Answer: both are proportional

Step-by-step explanation:

Both. ..............................

Using strategic thinking, the solutions to the following questions are:

Strategic thinking involves using rational thought processes to focus on workable solutions to business problems.

Strategic thinking concentrates on the future based on its changing environments.

In this situation, 50% of a number represents one-half of the given value.  We can divide each number by 2 to find the solutions.

a) 50% of 10 liters of milk = 5 liters (10 x 50%)

b) 50% of 2,000 kilometers = 1,000 kilometers (2,000 x 50%)

c) 50% of 24 hours = 12 hours (24 x 50%)

Thus, strategically thinking, half of each value represents its 50%.

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The number of boxes of programs that she needed will be 5.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

Ivanna needs 201 programs for the school play on Thursday. If each box contains 46 programs.

Then the number of boxes of programs that she needed will be given as,

⇒ 201 / 46

⇒ 4.369

The number of boxes cannot be in decimal form. Then the number of boxes will be 5.

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The volume of the balloon is 1441.64cm³.

To calculate the volume these are few ways

The radius of the balloon is given as 7 cm. Also, the equation to calculate the volume is given as c³/6π²

The circumference c will be:

= 2πr = 2 × 22/7 × 7

= 44

The volume will be:

= c³/6π²

= 44³/(6 × 3.14²)

= 85284/(59.1576)

= 1441.64

Therefore, volume of the balloon will be 1441.64 cm³.

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Comparing the two sets of rainfall data for two different time periods in the same location, it can be concluded that the amount of rainfall in Period 1 was fairly constant whereas the amount of rainfall in Period 2 varied greatly.

The rainfall data for two different time periods in the same location provides information about the pattern of rainfall over the time periods.

The rainfall data over the period did not vary widely apart. The data shows that the amount of rainfall did not change too much.

However, for Period 2, the amount of rainfall had very different values.

Hence, it seems rainfall was more precise in frequency in Period 1 than in Period 2.

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The slope of the straight line equation as required to be determined in the task content is; 1.

The y-intercept of the straight line equation as represented in the task content is; 273.15.

It follows from the task content that the values which correctly represents the slope and y-intercept of the given equation be determined.

Since the given equation is;

K = ºC + 273.15

By comparison with the slope-intercept equation of a straight line; y = mx + c where y = K and x = °C.

It follows that the slope, m = 1 and the y-intercept, c = 273.15.

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The line graph of the inequality is represented by an open circle at x = - 9 going towards negative infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is x + 3 < - 6.

x < - 6 - 3.

x < - 9.

The line graph of the inequality will be represented as an open circle at

x = - 9 extending towards negative infinity because x is strictly smaller

than 9.

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Answer:

420 millimeters

Step-by-step explanation:

If the scale factor of the enlargement is 70, and the body length of the insect is 6 millimeters, then the body length of the insect under the microscope is 6 millimeters * 70, which is 420 millimeters. So the correct answer is 420 millimeters.