please answer it asap.

Answer: the radius of the circle is 14 cm. :)

Step-by-step explanation:

To find,

The radius of the circle.

Solution,

The radius of the circle will be 14 cm.

We can easily solve this problem by following the given steps.

According to the question,

Length of a rectangular wire = 32 cm

The breadth of a rectangular wire = 12 cm

This wire is bent into the shape of a circle.

So,

The perimeter of the rectangle = Circumference of the circle

We know the formula for the perimeter of a rectangle is as follows:

P = 2(Length+Breadth)

P = 2(32+12) cm

P = 2(44) cm

P = 88 cm

We know that the formula to find the circumference of the circle is given as follows:

C =

2πr = 88 cm

2×22r/7 = 88

44r/7 = 88

Using the cross multiplication method,

44r = (88×7)

r = (88×7)/44

r = (2×7) cm

r = 14 cm

Hence, the radius of the circle is 14 cm.

Answer:

14.01 cm

Step-by-step explanation:

The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:

When this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:

(let r = radius)

2 × π × r

So, we can write:

Solving for r, we get:

So, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.

Answer:

7,3

Step-by-step explanation:

its 7,3

the concept of a sequence of transformations is a fundamental one in many different fields, as it allows us to understand how complex systems or objects can be broken down into smaller, more manageable parts that can be manipulated or analyzed in a systematic way.

What is a sequence?

The sequence is an ordered list of elements or events that follow a particular pattern or rule. In mathematics, a sequence typically refers to a set of numbers that are arranged in a specific order, with each element in the sequence being defined by a mathematical formula or recurrence relation.

A sequence of transformations refers to a series of steps or operations that are performed in a specific order to change or manipulate a given object or system. These transformations can take many different forms, depending on the context in which they are used.

For example, in mathematics, a sequence of transformations might refer to a series of algebraic manipulations that are used to simplify or solve an equation. In computer science, a sequence of transformations might refer to a series of functions or algorithms that are applied to data in order to transform it into a different format or structure.

In other fields, such as physics or chemistry, a sequence of transformations might refer to a series of physical or chemical changes that occur in a system over time. These transformations could include changes in temperature, pressure, or chemical composition, among other factors.

Therefore , the concept of a sequence of transformations is a fundamental one in many different fields, as it allows us to understand how complex systems or objects can be broken down into smaller, more manageable parts that can be manipulated or analyzed in a systematic way.

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The tension in cable B is 400 N.

What is tension in cable ?

Tension is the force transmitted through a string, rope, cable, or wire when it is pulled taut by forces acting from opposite ends. It is the pulling force that exists between two objects that are connected by a rope or cable and is usually measured in newtons (N) or pounds (lbs). The tension in a cable or rope can be calculated using the principles of equilibrium, where the sum of the forces acting on the object is equal to zero. In other words, the tension in a cable is the force that must be applied to the cable in order to keep it taut and maintain its position or prevent it from breaking.

According to the question:
To solve this problem, we need to use the fact that the sum of the forces acting on the sign must be zero in order for the sign to be in equilibrium. We can break down the weight of the sign into its components parallel and perpendicular to the cables:

F_parallel = 800 N * sin(30°) = 400 N

F_perpendicular = 800 N * cos(30°) = 693.2 N

The tension in cable A must balance the perpendicular component of the weight of the sign, so we have:

Tension_A = 693.2 N

The tension in cable B must balance the horizontal component of the weight of the sign, so we have:

Tension_B = 400 N

Therefore, the tension in cable B is 400 N.

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In linear equation, -(x - 1) ( 5x² +  3) is the solution of equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

4) 2x⁵+4x³-6x²-12 ⇒  2(x² + 2) (x³ - 3)

5) 3x⁷ - 8x⁶-9x⁵+24x⁴   ⇒ x⁴(3x - 8) (x² - 3)

6)  -5x³ + 10x²- 3x + 6   ⇒  -(x - 1) ( 5x² +  3)

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You do not use lines to connect the dots.

Answer:

Since the vertex is (0,-3), we know that the equation of the parabola will have the form:

y = a(x - 0)^2 - 3

where "a" is the coefficient that determines whether the parabola opens up or down.

To find the value of "a", we can use the fact that the parabola passes through the point (4, -7):

-7 = a(4 - 0)^2 - 3

-7 + 3 = 16a

-4 = 16a

a = -1/4

Substituting this value of "a" into the equation for the vertex form, we get:

y = -(1/4)x^2 - 3

So the equation of the parabola in vertex form is y = -(1/4)x^2 - 3, with vertex (0, -3) and passing through (4, -7).

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we input 4 into g(x) = 3(x/2), we get:

g(4) = 3(4/2) = 3(2) = 6

Therefore, the output of g(4) is 6.

Answer: The surface area of the rectangular prism is 140 and 3/16 square centimeters.

Answer: $22 per shirt and $14 per sweater

Step-by-step explanation:

     Let x be shirts and y be sweaters.

     We will write equations for the given situation.

5x + 8y = $222

6x + 5y = $202

     Next, we will graph both of these equations. The point of intersection will give the prices of one shirt and one sweater.

(22, 14)

➜ $22 per shirt

➜ $14 per sweater

In the function k(x) = 3(2^(-8x)), the domain is all real numbers (-∞, +∞) and the range is all positive real numbers (0, +∞).

Hi! I'd be happy to help you find the domain and range of the function k(x) = 3(2^(-8x)). The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values) that the function can produce.

For k(x) = 3(2^(-8x)), the function is an exponential function, and exponential functions are defined for all real numbers. This means that you can input any real number value for x, and the function will produce a valid output. Therefore, the domain of k(x) is all real numbers, which can be represented as (-∞, +∞) or R.

To find the range, we need to consider the behavior of the exponential function as x increases and decreases. As x goes to negative infinity, 2^(-8x) approaches infinity, and thus 3(2^(-8x)) also approaches infinity. As x goes to positive infinity, 2^(-8x) approaches 0, but since we are multiplying by 3, the minimum value of k(x) is 0. However, the function never actually reaches 0, so the range is all positive real numbers, which can be represented as (0, +∞).

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Answer:

x=10

Step-by-step explanation:

or,-x+1+9

or,0= -x+10

or,x=10

The graphs of the exponential functions are introduced in the image attached below.

The solution to the system of two exponential functions is 35 representatives and 7.735 minutes of average wait time.

In this problem we must represent two exponential functions describing average wait time, in minutes, as a function of number of customer service representatives. The functions are described by:

A(x) = 15.7 · 0.98ˣ

B(x) = 11 · 0.99ˣ

Now we draw each of the two functions by the help of a graphing tool. The solution to the system of exponential functions is:

Number of Customer Service Representatives: 35

Average Wait Time: 7.735 minutes

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Answer: 188 messages

Step-by-step explanation:

We will set up and solve a proportion.

      [tex]\displaystyle \frac{9.75}{65} =\frac{28.2}{x}[/tex]

Now, we will cross-multiply.

      9.75 * x = 65 * 28.2

      9.75x = 1,833

Lastly, we will divide both sides of the equation by 9.75.

      x = 188 messages

The x-intercept of the equation is (16, 0), which means that after 16 hours of driving, Xavier will have used up all the gas in his tank.

To find the x-intercept of the equation G = 12 - 0.75t, we need to set G = 0 and solve for t:

0 = 12 - 0.75t

0.75t = 12

t = 16

As a result, the equation's x-intercept is (16, 0), indicating that Xavier will run out of gas after 16 hours of driving.

The x-intercept in the problem denotes the moment at which Xavier runs out of gas and his car comes to a complete stop. This is a crucial factor to take into account when organising a lengthy road trip because it shows how long Xavier can travel before needing to refuel. If the fuel efficiency of Xavier's vehicle is assumed to be constant, the x-intercept can also be used to determine how far he can go on a single tank of gas. So, for Xavier to plan his road trip and make sure that he doesn't run out of gas, it's imperative that he comprehend the x-intercept of the equation G = 12 - 0.75t.

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Answer: x = -1

Step-by-step explanation:

Step 1: Distribute. 6 + 3x - 2x = 11 + 4 + 10x

Step 2: Subtract like-terms. x + 6 = 10x + 15

Step 3: Leave x by itself. x + (6-6) = 10x + (15-6)

Step 4: Subtract 10x to x, and simplify. (x - 10x) = (10x - 10x) + 9

Step 5: Divide. -9x/9 = 9/9

The answer is x = -1. Hope this helps

The value of the numeric expression 1/3+1/4➗2/4 is given as follows:

5/6.

The numeric expression in the context of this problem is defined as follows:

1/3+1/4➗2/4.

The division operation takes precedence over the addition operation, hence:

(1/4)/(2/4) = 1/2 -> as we can simplify the denominator of 4 for both the factors, leaving with a quotient of 1/2.

Then the expression is given as follows:

1/3 + 1/2.

The least common factor of 2 and 3 is of six, hence the result of the sum is given as follows:

1/3 + 1/2 = (2 + 3)/6 = 5/6.

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Answer:

There are 121 tens in the figures.

Step-by-step explanation:

9- No tens

95- 9 tens

26- 2 tens

100- 10 tens

1000- 100 tens

If you add the number of tens up, you will get 121.

Answer:

D

Step-by-step explanation:

hopes this helps .........

The inverse of the graph of f is added as an attachment

To graph an inverse function from the a graph, follow these steps:

Using the above steps, we have the inverse graph added as an attachment

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An inequality which has solutions represented by the graph include the following: C. x > 4

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Next, we would determine the solution as follows;

5 - x > 4

-x > 4 - 5

x > 1 (False).

2x + 1 ≥ 9

2x ≥ 9 - 1

2x ≥ 8

x ≥ 4 (False).

2x - 5 > 3

2x > 3 + 5

2x > 8

x > 4 (True).

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The dimensions of each half rectangular brick are, length 15 cm, and height 10 cm.

Let the original dimensions of the rectangular brick be length L, breadth B, and height H.

According to the problem statement, each dimension of the original brick is 5 cm larger than the desired dimensions of each half brick.

Therefore, the dimensions of each half brick are;

(L-5)/2, (B-5)/2, and (H-5)/2.

Since the two half bricks have identical dimensions, we have:

(L-5)/2 = (B-5)/2 = (H-5)/2

Simplifying this equation, we get:

L-5 = B-5 = H-5

Therefore, L = B = H + 5.

Now, the volume of the original brick is L x B x H, and the volume of each half brick is [(L-5)/2] x [(B-5)/2] x [(H-5)/2].

Since the two half bricks have the same dimensions, their volumes are equal. Thus, we have:

(L-5)/2 x (B-5)/2 x (H-5)/2 = (L x B x H)/2

Substituting L = B = H + 5, we get:

(H+5-5)/2 x (H+5-5)/2 x (H-5)/2 = (H x H x (H+5))/2

Simplifying this equation, we get:

(H+5)/2 x (H-5)/2 x H/2 = (H x H x (H+5))/2

Cancelling out the factor of 1/2, we get:

(H+5)(H-5)H = H x H x (H+5)

Simplifying this equation, we get:

H³ - 125H = H³ + 5H²

Subtracting H³ from both sides, we get:

-125H = 5H²

Dividing both sides by 5H, we get:

H = -25 or H = 0

Since H represents the height of the brick, it must be positive. Therefore, we have H = 0, which implies that the original brick has zero height. This is not a valid solution, so we reject it.

Therefore, the only valid solution is:

H = 25 cm

Substituting this value of H in the equation L = B = H + 5, we get:

L = B = 30 cm

Therefore, the dimensions of the original brick are:

Length = L + 5 = 35 cm

Breadth = B + 5 = 35 cm

Height = H + 5 = 30 cm

And the dimensions of each half brick are:

Length = Breadth = 15 cm

Height = 10 cm

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Hence, there are 43.5 square inches accessible on the award for text engraving.

A square is a geometric figure with four equal sides and four right angles. It is a particular kind of rectangle with equal-length sides. It is also possible to describe it as a regular quadrilateral with equal-length sides and right-angled corners. By multiplying one side of a square by itself, the area of the square can be calculated. A = s2 is the formula for calculating the area of a square, where A stands for the area and s for the length of one side. The perimeter of a square is calculated similarly by adding the lengths of its four sides. P = 4s is the formula for calculating a square's perimeter, where P stands for the perimeter.

given

The plaque's available engraving space is equal to the plaque's surface area less the rhombus's area in the centre.

The plaque's location is:

Area plaque is equal to 7.5 x 10 inches, or 75 square inches.

The rhombus's surface area is:

(diagonal1 x diagonal2) / 2 = (7 x 9) / 2 = 31.5 square inches is the area of a rhombus.

Thus, the following is the engraving area:

Area available equals Area plaque minus Area rhombus, or 75 minus 31.5, or 43.5 square inches.

Hence, there are 43.5 square inches accessible on the award for text engraving.

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There are no equations in the form  [tex]a * b^{x}[/tex] that contains m = 3 and b=1  points.

The slope-intercept form can be used to determine the equation of a line that goes through two specific points:

y = mx + b

where m denotes the slope and b is its y-intercept.

It is possible to determine the slope of the line using the coordinates (0, 1) and (1, 4).

[tex]= \frac{y2 - y1}{x2 - x1} =\frac{4 - 1 }{1-0} \\= \frac{3}{1} \\= 3[/tex]

As a result, the line's equation can be expressed as:

y = 3x + b

We can use either location to determine b:

1 = 3(0) + b

b = 1

The line's solution is as follows:

y = 3x + 1

The following assertions can be evaluated using this equation:

1) These values can be found in only one equation with the form y = mx + b.

False. The formula y = 3x + 1 is expressed as y = mx + b rather than y = max + b.

2) These points are included in two equations of the type y = m + b.

False. These points are only present in one equation of the type y = mx + b.

3) These points do not appear in any equations of the type y = [tex]a * b^{x}[/tex].

True. The coordinates (0, 1) and cannot be passed through by any equations in this form. (1, 4).

4) These points are contained in precisely one equation with the form y = [tex]a * b^{x}[/tex].

False. For a line in two variables, the equation form y - a - b° is invalid.

5) These points can be found in multiple equations with the shape y = [tex]a * b^{x}[/tex].

False. For a line in two variables, the equation form y = [tex]a - b^{x}[/tex] is invalid.

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The coordinates of the image if triangle ABC is translated 4 units down would be: A′(1, -6), B′(9, -6), C′(5, -2)

To translate the triangle 4 units down, we need to subtract 4 from the y-coordinate of each vertex.

Vertex A has coordinates (1, -2), so its image A' after the translation is (1, -2 - 4) = (1, -6).

Vertex B has coordinates (9, -2), so its image B' after the translation is (9, -2 - 4) = (9, -6).

Vertex C has coordinates (5, 2), so its image C' after the translation is (5, 2 - 4) = (5, -2).

Therefore, the coordinates of the vertices of triangle ABC after it is translated 4 units down are A′(1, −6), B′(9, −6), and C′(5, −2).

So, the answer is option A: A′(1, −6), B′(9, −6), C′(5, −2)..

How can you use the coordinates of the vertices of a figure to determine its image after a translation?

To determine the image of a figure after a translation, you can add or subtract the same amount from the x- and/or y-coordinates of each vertex, depending on the direction and distance of the translation.

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There are 90 distinct arrangements of the letters in SPINNING.

In mathematics, permutation refers to the arrangement of objects in a specific order. A permutation of a set of objects is an ordered arrangement of those objects. For example, if we have a set of three objects {A, B, C}, then the permutations of this set would be {ABC, ACB, BAC, BCA, CAB, CBA}. The number of permutations of a set of n objects is denoted by n!. Permutations are commonly used in combinatorics, probability theory, and other areas of mathematics and science.

In the given question,

The word SPINNING has 8 letters, out of which two letters appear twice.

Let's first consider the distinct arrangements of the 6 unique letters (ignoring the repeated letters).

There are 6! ways to arrange these 6 letters in a row.

However, we need to adjust for the repeated letters. The letter "N" appears twice, so we divide by 2! to account for the fact that the two N's can be arranged in 2! = 2 ways without changing the arrangement of the other letters. Similarly, the letter "I" also appears twice, so we divide by another 2!.

Therefore, the total number of distinct arrangements of the letters in SPINNING is:

6! / (2! x 2!) = 360 / 4 = 90.

So there are 90 distinct arrangements of the letters in SPINNING.

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According to given equations, any value of x less than 15.6 will result in the shopkeeper spending less than $100 on electricity.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side and a right-hand side, separated by an equals sign (=). The left-hand side and the right-hand side of an equation may contain one or more variables, and the equation is true only for certain values of these variables.

Let E be the amount the shopkeeper spends on electricity. Then, we have:

Total monthly expenses = Rent + Electricity = 8x + 15

Rent = 3x - 7

Substituting the value of Rent in the equation of total monthly expenses, we get:

8x + 15 = (3x - 7) + E

Simplifying this equation, we get:

5x + 22 = E

Therefore, the shopkeeper spends 5x + 22 dollars on electricity.

To find the value(s) of x for which the shopkeeper spends less than $100 on electricity, we can set up an inequality:

5x + 22 < 100

Solving for x, we get:

5x < 78

x < 15.6

Therefore, for any value of x less than 15.6, the shopkeeper will spend less than $100 on electricity. To verify this, we can plug in a value of x less than 15.6 and see if the resulting amount spent on electricity is less than $100. For example, if we let x = 10, then:

5x + 22 = (5 * 10) + 22 = 72

Since 72 is less than $100, we have verified that any value of x less than 15.6 will result in the shopkeeper spending less than $100 on electricity.

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Answer:

[tex] { - 2x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]

Step-by-step explanation:

[tex] - 2(x - 1) \times ({1 + x})^{3} + 3(1 + x) \times ( {1 - x})^{2} = ( - 2x + 2) \times (1 + 3x + 3 {x}^{2} + {x}^{3} ) + (3 + 3x) \times (1 - 2x + {x}^{2} ) = ( - 2x - 6 {x}^{2} - 6 {x}^{3} - 2 {x}^{4} + 2 + 6x + 6 {x}^{2} + 2 {x}^{3} ) + (3 - 6x + 3 {x}^{2} + 3x - 6 {x}^{2} + 3 {x}^{3} ) = x - {x}^{3} - 2 {x}^{4} + 2 + 3 + 3 {x}^{2} - 6 {x}^{2} = x - {x}^{3} - 2 {x}^{4} + 5 - 3 {x}^{2} = - 2 {x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]

Answer:

[tex]h(0) = -16(0)^2 + 128[/tex]

[tex]= 128[/tex]

Therefore, the rocket goes to a maximum height of 128 feet.

4. The axis of symmetry of the parabolic path of the rocket is the vertical line that passes through the vertex of the parabola. Since the coefficient of [tex]t^2[/tex] is negative, the parabola opens downwards, and the vertex represents the maximum point of the path. As we found in question 2, the time at which the maximum height occurs is t = 0, so the axis of symmetry is the vertical line passing through t = 0.

5. To find when the rocket hits the ground, we need to find the time t at which h(t) = 0. Substituting [tex]h(t) = -16t^2 + 128[/tex], we get:

[tex]-16t^2 + 128 = 0[/tex]

Solving for t using the quadratic formula, we get:

t = (0 ± √(0^2 - 4(-16)(128))) / (2(-16))

= (±√8192) / (-32)

= ±8

Since time cannot be negative, the rocket hits the ground after approximately 8 seconds.

6. To find how high the rocket is at t = 2 seconds, we can substitute t = 2 into the equation h(t) = -16t^2 + 128:

h(2) = -16(2)^2 + 128

= -64 + 128

= 64 feet

Therefore, the rocket is at a height of 64 feet at 2 seconds.

7. To find when the rocket is at a height of 252 feet, we need to solve the equation [tex]-16t^2 + 128 = 252[/tex]. Rearranging and solving for t, we get:

[tex]-16t^2 + 128 = 252[/tex]

[tex]-16t^2 = 124[/tex]

[tex]t^2 = -124/-16[/tex]

t^2 = 7.75

t ≈ ±2.78 seconds

Since time cannot be negative, the rocket is at a height of 252 feet after approximately 2.78 seconds.

8. The graph coordinates of the rocket's path can be plotted using the function [tex]h(t) = -16t^2 + 128[/tex]. The x-axis represents time t in seconds and the y-axis represents the height of the rocket in feet. We can plot points on the graph by substituting different values of t into the equation and plotting the resulting height. For example, some common points to plot include the vertex at (0, 128), the point where the rocket hits the ground at approximately (8, 0), and the point where the rocket is at a height of 252 feet at approximately (2.78, 252). We can also plot other points by substituting different values of t into the equation and plotting the resulting height.