《QUESTION 1》
The length of the side of a square is 50 cm and the breadth of a rectangle is 25 cm. If the areas of the square and the rectangle are equal, find the length of the rectangle.

《QUESTION 2》
A wire is in the shape of a rectangle with length 6 cm. It is bent to form a square whose side is 5 cm. Find the breadth of the rectangle. Also, calculate the areas of both the rectangle and the square and find which shape encloses more areas.​

Answers

Answer 1

The length of the rectangle is 100cm.

The breadth of the rectangle is 4cm.

The square encloses more area than the rectangle.

What is the length of the rectangle?

The first step is to determine the area of the square.

Area of a square = length² = 50² = 2500 cm²

Area of a rectangle = length x width

length = area / width

2500 / 25 = 100cm

What is the breadth of the rectangle?

The first step is to determine the perimeter of the square.

Perimeter = 4 x length

4 x 5 = 20cm

Perimeter of a rectangle = 2(length + width)

breadth = (perimeter / 2) - length

(20 / 2) - 6

10 - 6 = 4cm

Area of the square = 5 x 5 = 25

Area of the rectangle = 6 x 4 = 24

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Related Questions

square root of 12-square root of 8

Answers

Answer:

please tell me if im wrong!

Step-by-step explanation:

answer: 16 √ 3

Answer:

24√2

Step-by-step explanation:

if I'm correct the equation is

(√12)^2(√8)

we expand the surds

(√4x3)^2 (√4x2)

(2√3)^2 (2√2)

(4x3) (2√2)

12x2√2 =

24√2

Please help with the attached photo.

Answers

The solution to the equation r(1 - 2cosФ) = 1 is given as x² + y² - 4x√(x² + y²)  + 4x² = 1

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

In polar form:

r = √(x² + y²) and cosФ = x / √(x² + y²)

Hence:

r(1 - 2cosФ) = 1

√(x² + y²) [1 - 2(x / √(x² + y²))] = 1

√(x² + y²) - 2x = 1

Take square of both sides:

x² + y² - 4x√(x² + y²)  + 4x² = 1

The solution to the equation r(1 - 2cosФ) = 1 is given as x² + y² - 4x√(x² + y²)  + 4x² = 1

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Consider the set S of bit strings defined recursively by:

Answers

The correct option regarding the recursively defined strings is given by:

c) Both i) and ii).

Which of the strings belong to alphabet S?

First we start with string 101, we have that:

101 -> 1w -> 10w -> 101

Which belongs to alphabet S.

For string 001, we have that:

001 -> 0w -> 00w -> 001.

Which belongs to alphabet S.

Hence statement c is correct.

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Determine a, given that A = 63°, C = 49°, and c = 3. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect. a =

Answers

The value of a given that A = 63°, C = 49°, and c = 3 is 4 units

How to determine the value of a?

The given parameters are:

A = 63°, C = 49°, and c = 3

Using the law of sines, we have:

a/sin(A) = c/sin(C)

So, we have:

a/sin(63) = 3/sin(49)

Multiply both sides by sin(63)

a = sin(63) * 3/sin(49)

Evaluate the product

a = 4

Hence, the value of a is 4 units

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algebra 2 help needed urgent !!!

Answers

Answer:

  11, 7, 3, -1, -5

Step-by-step explanation:

The dependent variable y is often used interchangeably with the function value f(x). That is, we can usually presume that ...

  y = f(x)

__

evaluate the function

To find f(x), put the value of x everywhere x appears in the function definition, and do the arithmetic. A calculator or spreadsheet can relieve some of the boredom of repetition. Here are a couple of examples.

  f(-2) = -4(-2) +3 = 8 +3 = 11

  f(-1) = -4(-1) +3 = 4 +3 = 7

time saver

You may notice that each increase of 1 in the value of x causes a decrease of 4 in the value of y. That means we can simply subtract 4 from the previous value of y to find the next one:

  [tex]\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}-2&11\\\cline{1-2}-1&7\\\cline{1-2}0&3\\\cline{1-2}1&-1\\\cline{1-2}2&-5\\\cline{1-2}\end{array}[/tex]

__

Attached is an example of this table being filled by a calculator.

Give the domain and range. A relation. An arrow goes from negative 2 to 4, from 0 to 6, from 2 to 8. a. domain: {–2, 0, 2}, range: {4, 6, 8} b. domain: {0, 2}, range: {6, 8} c. domain: {4, 6, 8}, range: {–2, 0, 2} d. domain: { 6, 8}, range: {0, 2} Please select the best answer from the choices provided A B C D

Answers

Answer:

domain= (-2,0,2)

range= (0,4)

What is a necessary step for constructing perpendicular lines through a point off the line?

Answers

Answer:

Find another point on the perpendicular line.

Step-by-step explanation:

Given an original line "m", and a point off the line "Q", in order to construct a second line "p", meant to be perpendicular to "m" through the point "Q", fundamentally, the only truly necessary step to construct a perpendicular line through is to find another point on the yet-to-be-found perpendicular line.

Most often, this is accomplished by exploiting the fact that "p" is the set of all points that are equidistant from any pair of points that are symmetric about "p".

Since the symmetry must be about "p", and we don't even know where "p" is, one often finds two points on "m" that are equidistant from "Q".

This can be accomplished by adjusting a compass to a fixed radius (larger than the distance from "Q" to "m"), and making an arc that intersects "m" in two places.  Those two places will be equidistant from "Q", and are simultaneously on line "m".  Thus, these two points, "A" & "B" are symmetric about "p".

Since "A" & "B" are symmetric about "p", they are equidistant from "p", and are on "m".  One could try to find the point of intersection between "p" and "m" through construction, but this is unnecessary.  We need only find a second point (besides "Q") that is equidistant from "A" & "B", which will necessarily be a point on "p", to form the line perpendicular to "m".

To do this, fix the compass with any radius, and from "A" make a large arc generally in the direction of "B", and make the same radius arc from "B" in the direction of "A" such that the two arcs intersect at some point that isn't "Q".  This point of intersection we can call point "T", and the line QT is line "p", the line perpendicular to the original line, necessarily containing "Q".

Help needed on this composition math problem

Answers

Given that f(x) = x/(x - 3) and g(x) = 1/x and the application of function operators, f ° g (x) = 1/(1 - 3 · x) and the domain of the resulting function is any real number except x = 1/3.

How to analyze a composed function

Let be f and g functions. Composition is a binary function operation where the variable of the former function (f) is substituted by the latter function (g). If we know that f(x) = x/(x - 3) and g(x) = 1/x, then the composed function is:

[tex]f\,\circ\,g \,(x) = \frac{\frac{1}{x} }{\frac{1}{x}-3}[/tex]

[tex]f\,\circ\,g\,(x) = \frac{\frac{1}{x} }{\frac{1-3\cdot x}{x} }[/tex]

[tex]f\,\circ\,g\,(x) = \frac{1}{1-3\cdot x}[/tex]

The domain of the function is the set of x-values such that f ° g (x) exists. In the case of rational functions of the form p(x)/q(x), the domain is the set of x-values such that q(x) ≠ 0. Thus, the domain of f ° g (x) is [tex]\mathbb{R} - \{\frac{1}{3} \}[/tex].

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3x - [2 +3 (2-x) = S-(3-X)

Answers

What is the value of x?

NS,
Word problem on unit rates associated with ratios of whole...
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) Greg bought 16 pounds of sugar for $8.
C
How many dollars did he pay per pound of sugar?
dollars per pound
(b) It takes 76 pounds of seed to completely plant a 12-acre field.
How many pounds of seed are needed per acre?
pounds per acre
|||

Answers

Answer:

Define different tipes of discontuinity of a function .also,write the condition for increasing, decreasing and concave of function

Steve is ordering burgers and individual pizzas for $1000. He plans to buy not more than 80 items. The costs of each burger and each pizza are $7 and $4. Select the inequality that describes this situation. Use the given numbers and the following variables. x = the number of burgers. y = the number of pizzas.

Answers

[tex]x+y\leq 80[/tex]

[tex]7x+4y=1000[/tex]

The number of burgers = [tex]x[/tex]

the number of pizzas = [tex]y[/tex]

the cost of each burger = $[tex]7[/tex]

the cost of each pizza = $[tex]4[/tex]

not more than 80 items: [tex]x+y\leq 80[/tex]

total price =[tex]7x+4y=1000[/tex]

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Consider the equation below. "-2(5x+8)=14+6x" The equation was solved using the following steps.

Answers

The equation -2(5x+8) = 14+6x solved using step by step representation is x = -15/8.

Solving steps for the Equation

The equation to be considered as given in the task content is; -2(5x+8)=14+6x.

It follows from the task content that the steps for solving the equation are as follows;

-2(5x+8) = 14+6x

Step 1: opening parenthesis

-10x - 16 = 14 + 6x

Step 2: collect like terms

-10x - 6x = 14 + 16

Step 3: evaluate

-16x = 30

Step 4: Division

x = 30/-16

x = -15/8

Hence, the value of x upon solving the equation is; -15/8.

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NEED HELP ASAP !!!!

Which graphs represents the compound inequality x≤ 5 orx≥ 5?

Answers

Answer:

b

Step-by-step explanation:

B.

I assure you! Someone also has b put into it to. So, they are correct.

What are the coordinates of point P on the directed line
segment from A to B such that P is the length of the
line segment from A to B?

A. (-29/4 , -3/2)
B. (-13/4 , 1/2)
C. (-11/4 , -1/2)
D. (25/4 , -1/2)

Answers

The coordinate of the point P is (-11/4, -1/2) option (C) is correct because point (-29/4, -3/2) lies on the line.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line segment shown in the picture:

From the graph:

Point A( -5, -1) and B(4, 1)

The equation of the line passing through the points:

[tex]\rm (y -1 ) = \dfrac{1+1}{4+5}(x-4)[/tex]

9(y - 1) = 2(x - 4)

The above equation shows the straight-line passing through points A and B.

From the graph point (-11/4, -1/2) lies on the line the coordinate of the point P is (-29/4, -3/2)

Thus, the coordinate of the point P is (-11/4, -1/2) option (C) is correct because point (-29/4, -3/2) lies on the line.

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Need help ASAP, will mark brainliest if you can check my answer:

Answers

According to the compound interest model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61

How to determined all the variables associated with compound interest

Compound interest describes the capital gain in term of deposited capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:

C' = C · (1 + r/100)ˣ     (1)

Where:

C - Initial capitalC' - Current capital r - Interest rate, in percentage.t - Time, in years

The doubling time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):

x = (㏒ 2)/[㏒ (1 + r/100)]     (2)

Now we proceed to calculate each missing variable:

Case I - Doubling time

x = (㏒ 2)/[㏒ (1 + 6.2/100)]

x ≈ 11.5

Case I - Current capital

C' = 75000 · (1 + 6.2/100)⁵

C' = 101317.36

Case II - Interest rate

[tex]r = 100\cdot \left(\sqrt [5] {\frac{7130.90}{5000} }-1\right)[/tex]

r ≈ 7.4

Case II - Doubling time

x = (㏒ 2)/[㏒ (1 + 7.3/100)]

x ≈ 9.8

Case III - Initial capital

C = 11414.71/(1 + 8.4/100)⁵

C = 7626.38

Case III - Doubling time

x = (㏒ 2)/[㏒ (1 + 8.4/100)]

x ≈ 8.6

Case IV - Interest rate

[tex]r = 100\cdot \left(\sqrt [11] {2 }-1\right)[/tex]

r ≈ 6.5

Case IV - Initial capital

C = 17539.32/(1 + 6.5/100)⁵

C = 12801.61

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pls help me solve for x in this equation

Answers

Answer:

x = 9/2

Step-by-step explanation:

√2x + √2x = 6

2√2x = 6

2√2x/2 = 6/2

√2x = 3

(√2x)² =( 3)²

2x = 9

x = 9/2

Answer:

x = 4.5

Explanation:

[tex]\rightarrow \sf \sqrt{2x} + \sqrt{2x} = 6[/tex]

add following

[tex]\rightarrow \sf 2\sqrt{2x} = 6[/tex]

divide both sides by 2

[tex]\rightarrow \sf \sqrt{2x} = 3[/tex]

square both sides

[tex]\rightarrow \sf 2x = 3^2[/tex]

simplify the following

[tex]\rightarrow \sf 2x = 9[/tex]

divide both sides by 2

[tex]\rightarrow \sf x = 4.5[/tex]

Solve by completing the square:
x2 + 3x – 9 = 0

Answers

Answer:

[tex]x=\dfrac{-3\pm3\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]x^2+3x-9=0[/tex]

Completing the square

Move the constant to the right side by adding 9 to both sides:

[tex]\implies x^2+3x=9[/tex]

Add the square of half the coefficient of x to both sides:

[tex]\implies x^2+3x+\left(\dfrac{3}{2}\right)^2=9+\left(\dfrac{3}{2}\right)^2[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{45}{4}[/tex]

Factor the trinomial on the left side:

[tex]\implies \left(x+\dfrac{3}{2}\right)^2=\dfrac{45}{4}[/tex]

Square root both sides:

[tex]\implies x+\dfrac{3}{2}=\pm\sqrt{\dfrac{45}{4}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{45}}{\sqrt{4}}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{9 \cdot 5}}{2}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{9} \sqrt{5}}{2}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{3\sqrt{5}}{2}[/tex]

Subtract 3/2 from both sides:

[tex]\implies x=\pm\dfrac{3\sqrt{5}}{2}-\dfrac{3}{2}[/tex]

[tex]\implies x=\dfrac{-3\pm3\sqrt{5}}{2}[/tex]

Which solid could have exactly two planes of symmetry?
Square Prism
Cylinder
Pentagonal Pyramid
Triangular Prism

Answers

Answer:

Triangular Prism

Step-by-step explanation:

A plane of symmetry divides a three dimensional shape into two congruent halves that are mirror images of each other. An isosceles triangular based prism has 2 planes of symmetry. An isosceles triangular based prism has 2 planes of symmetry. An isosceles triangular based prism has 2 planes of symmetry.

(7 x 10 ^5) + (4 x 10 ^2)

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(7\times 10^5) + (4 \times 10^2)}\\\mathsf{= 7\times 10^5 + 4 \times 10^2}[/tex]

[tex]\large\textsf{Let's solve for the LEFT SIDE first}[/tex]

[tex]\mathsf{7\times 10^5}\\\\\mathsf{10^5}\\\mathsf{= 10\times10\times10\times10\times10}\\\mathsf{= 100 \times 100\times 10}\\\mathsf{= 10,000 \times 10}\\\mathsf{= 100,000}\\\\\mathsf{7\times100,000}\\\mathsf{= 700,000}[/tex]

[tex]\large\textsf{NEW EQUATION: }\bold{700,000} + {4}\times 10^2[/tex]

[tex]\large\textsf{Now, let's solve for the RIGHT SIDE last}[/tex]

[tex]\mathsf{4\times 10^2}\\\\\mathsf{10^2}\\\mathsf{= 10\times10}\\\mathsf{= 100}\\\\\mathsf{4\times100}\\\mathsf{= 400}[/tex]

[tex]\large\text{NEW EQUATION: 700,000 + \bf 400}[/tex]

[tex]\large\text{700,000 + 400}\\\\\large\text{SIMPLIFY IT!}\\\\\large\text{= 700,400}[/tex]

[tex]\huge\text{Therefore, the answer should be: \boxed{\mathsf{700,400}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Solve −x+5≤4 or 2x+3≥−1 and write the solution in interval notation.

Answers

Answer:

Step-by-step explanation:

[tex]\left \{ {{-x+5\leq 4} \atop {2x+3\geq -1}} \right.[/tex]   ⇒ [tex]x\geq 1\\2x\geq 4\\x\geq -2[/tex]

or

[tex]x \geq -2\\(-2,+ { \infty} )[/tex] (Answer)

Help me with this question please!! :)

Answers

Answer: 13/69

Step-by-step explanation:

13 students are female and got a B out of a total of 69 students, so the probability is 13/69

document attached. please help!!

Answers

Answer:

The answers to different parts for ratio are - 3:5,3:5,3:5,9:25,graph C respectively .

Step-by-step explanation:

A ratio is a relationship between two quantities, normally expressed as the quotient of one divided by the other, or the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

a) The ratio of the median weekly earnings of the holder of a high school diploma only to the median weekly earnings of the holder of a bachelor's degree - 750/1250 = 3:5

b) The ratio of the area of the red rectangle  to the area of the blue rectangle - 750 x 1 / 1250 x 1 = 3:5

c) The ratio of the area of the red square to the area of the blue square in graph B - 3:5

d) the ratio of the volume of the red cube to the volume of the blue cube in graph C - 750 x 750 /1250x 1250 =9:25

e) The most misleading graph is graph B  because the distribution of values , depth, and shapes differ.

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If the cost, C, for manufacturing x units of a certain product is given by C=x²-10x+65, find the number of units manufactured at a cost of $12,140.
There are_____manufactured at a cost of $12,140.

Answers

Answer:

115

Step-by-step explanation:

You solve this by factoring.

12140 = x^2-10x+65

0 = x^2-10x-12075

0=(x+105)(x-115)

The only positive solution is x=115

14 men and 10 women started a pie eating contest. At the second round, 2 men and 2 women dropped out of the contest. What is the percentage of women that proceeded to the next round?

Answers

Answer: 80%

Step-by-step explanation:

Since only 2 out of 10 women dropped out, 10 - 2 = 8

One woman = 10%, 8 x 10% = 80%

The percentage of the women who moved to the next stage is 80%.

What is the percentage?

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Women who moved to the next stage: 10 - 2 = 8

(8/10) x 100 = 80%

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What is the value of x in the figure below? In this diagram, AABD ~ ACAD.

Answers

The value of x in the right angle triangle is 45 / 4 units

How to find the side of a right triangle?

AB² = 20² - 15²

AB = √400 - 225

AB = √175

AB = √175 units

Hence, using similarity ratio,

x / 15 = 15 / 20

cross multiply

20x = 225

x = 225 / 20

x = 45 / 4

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On a number line, 6.87 would be located
6.87
A. To the right of 6.81
B. Between 6 and 6.5
C. Between 6.5 and 7
D. To the left of 6.81
Check all that apply.

Answers

A and C are the answers

evaluate 2/3 - 1/6 * 1/4​

Answers

Answer: 0.625

Step-by-step explanation:

x(x - 5) = -4

Solve the equation, using the quadratic formula.

Answers

1 and 4 are the answers!

evaluate 2b^3 where b = 3

Answers

Answer:

Answer=54

Step-by-step explanation:

Given:- b=3

2b³

Solution:-

2 x b³

2 x 3 x 3 x 3

6 x 9

54 (answer)

Hope this helps you

Have a good day.

Two dice are thrown. Determine the probability of obtaining a score of at least 4.

Answers

11/36 would be the probability of getting 4 , when two dice are thrown simultaneously.

As there are 6 faces of die,
So Probability of Not getting four in one dice = [tex]5/6[/tex]

As both events are mutually exclusive, the probability of not getting four in two dice = [tex](5/6) * (5/6) = 25/36[/tex]

So probability of getting at least one four is = [tex]1-(25/36) = 11/36[/tex]

So probability = [tex]11/36[/tex]

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