A community builds a sandbox section and a playground section at one of the local parks. The area of the playground
section is 1,675 square feet. It is 100 square feet more than 4.5 times the area of the sandbox section.
• Write an equation that can be used to determine the area, A. of the sandbox section.
. What is the area of the sandbox section? Show all work.
Enter your equation, answer, and work in the box

Please help worth 25 points

solving factor by grouping, The final factored form of the expression is n(n + 3) - 10.

A factor is a number that divides into another number exactly with no remainder. For example, the factors of 8 are 1, 2, 4, and 8.

Factor by grouping is a method of factoring polynomials, which is used to find the common factors in an expression. The idea is to group the terms of the polynomial in such a way that the common factors can be factored out of them. In other words, it is a way to simplify an algebraic expression by finding common factors among the terms and then grouping them together. For example, the polynomial 2x^2 + 6x can be factored by grouping as (2x^2 + 6x) = 2x(x + 3). This is the most common way to factor a polynomial with four terms.

To solve the problem "factor by grouping" for the expression "n^2+3n-10", you can follow these steps:

Write the expression in the form of (n^2 + An + B) + (Cn + D)

(n^2 + 3n - 10) = (n^2 + 3n) + (-10)

Factor out the greatest common factor (GCF) of the terms in the first set of parentheses.

(n^2 + 3n) = n(n + 3)

Factor out the GCF of the terms in the second set of parentheses, if possible. In this case, there is no GCF.

Combine the factored expressions from step 2 and step 3 to get the final factored form.

n(n + 3) + (-10)

The final factored form of the expression is n(n + 3) - 10.

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Answer:

c 1

A F E 2

Step-by-step explanation:

Answer:

a) The rotational speed of the clay: 3.45 rad/s.

b) The value of A in the equation of motion: 0.15 m.

c) The value of ϕi: 90° or π/2 rad.

Given that;

Revolution per minute( rpm) is = 33( 1/3) =  100/3

The frequency ( f) is= 100 / 3(60) = 0.55 Hz

a) Rotational speed W = 2πf

we substitute

W = 2π × 0.55

W = 3.45 rad/s

So, the rotational speed of the clay is  3.45 rad/s.

b) given equation; y(t)=Asin(ωt+ϕi)

given that radius = 0.15 m

y(t)=(0.2)sin(ωt+ϕi)

So, the value of A in the equation of motion is 0.15 m.

c) since y(t) has the maximum value at t =0

so at t=0

y(0) = (0.15)sin(ω(0)+ϕi)

= 0.15sin(ϕi)

this gives maximum value when ϕi = 90°

so,

y(0) = (0.15)sin(ω(0)+ϕi)

= 0.15sin(90°)

= 0.15

So, the value of ϕi is 90° or π/2 rad.

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The complete question is:

You are standing next to a table and looking down at a record player sitting on the table. Take the spindle (axis of rotation) to be the center of your coordinate system and the y-axis to be perpendicular to the side of the player you are standing next to. Long-playing records revolve 33(1/3) times per minute. You put a small blob of clay at the edge of a record that has a radius of 0.15 m, positioning the clay such that it is at its greatest value of y at t = 0.

Equation of motion for the y component of the clay's position: y(t)=Asin(ωt+ϕi)

Required:

a. What is the rotational speed of the clay?

b. Determine the value of A in the equation of motion.

c. Determine the value of ϕi in the equation of motion. Suppose that −π<ϕi≤π

It is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 4 and 7

4 + 7 > 8

11 > 8

Now we add 7 and 8

7 + 8 > 4

15 > 4

Now we add 4 and 8

4 + 8 > 7

12 > 7

It is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm because the sum of two sides are greater than third sides.

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The expression for the quarters you take is (1 - 0.50) x 28

The money you have left is $3.50.

The expression that is used to represent the total number of quarters is:

Total number of quarters = number of quarters you have x ( 1 + percent you find/100)

Total number of quarters = 20 x (1 + 40/100)

Total number of quarters = 20 x 1.40 = 28 quarters

Number of quarters you have left = (1 - percentage spent/100) x number of quarters

= (1 - 50%/100) x 28

(1 - 0.50) x 28

0.50 x 28 = 14 quarters

Value of 14 quarters in dollars = 14 x 0.25 = $3.50

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Answer: Area: (100+75π/2)cm^2 Perimeter: (10+75π/2)cm

Step-by-step explanation:

Area of total shape

= square+3 semi-circles

=100cm^2 + 5*5πcm^2*3/2 = 100cm^2+75/2*πcm^2

= (100+75π/2)cm^2

Perimeter of shape

= 10cm + 25/2π*3cm

= (10+75π/2)cm

Step-by-step explanation:

in this figure you can observe 1 cube and 3 half cirles

the flield of the square would by using a formula a(lenght) * b(height)

in this case it would be 10m * 10m = 100m

and the formula for a cirle would be

A = pir^2

knowing that we can connect two of the halfs and make a cirle with a radius of 5

A= pi 5^2

A= pi 25

25pi approximatly equals to 78.53982m

knowing that information we can devide that value by 2 and get the value of the 3rd half cirlce

which is 39.26991m

than we add all the values we collected

39.26991m + 78.53982m + 100m = 217.80973 m

Answer:

The slope is -2/3 and the y-intercept is 5

The numbers in a function table follow a pattern and have inputs and outputs. By constructing an equation using variables .

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). the act of placing two or more items in a logical order. Chronological.

given

The numbers in a function table follow a pattern and have inputs and outputs.

By constructing an equation using variables, you may determine the rule. Make sure your rule is applicable to all possible combinations of inputs and outputs .

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Answer:

C) DF

Step-by-step explanation:

since the HF is the diameter of the top circle because the line is formed from the centre of the circle (c)

therefore,

the line made from the centre of (b), DF is the diameter

both DF and HF are congruent aswell as HD but thats not the option available in this question.

The definite integral is [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex][tex]=[/tex][tex]\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Here,

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]

Put [tex]$16+r^2=t^2$[/tex]

[tex]$2 r d r=2 t d t$\\[/tex]

[tex]$r d r=d t$[/tex][tex]$r=0 \Rightarrow t=4$[/tex]

[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} d t$[/tex]

[tex]$=\left[\frac{t^3}{3}-16 t\right]_t^{\sqrt{17}}$[/tex]

[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]

[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

Therefore, the evaluated integral is [tex]\frac{31 \sqrt{17}}{3}$[/tex].

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Answer:

Inverse most likely

Step-by-step explanation:

Answer: We can start solving this problem by using the information given in the equation 6b + 2r = 60. This equation represents the total cost of the bread and rolls sold, with 6b representing the cost of the bread (6 dollars per loaf) and 2r representing the cost of the rolls (2 dollars each). The goal is to find the value of b, the number of loaves of bread sold.

We can use the information that the baker sold 24 rolls. If we substitute this value into the equation, we get:

6b + 2(24) = 60

Next, we can simplify the equation by substituting in the value of 24 for r:

6b + 48 = 60

Now we can subtract 48 from both sides of the equation to find the value of b:

6b = 12

Finally, we can divide both sides of the equation by 6 to find the value of b:

b = 12/6 = 2

So the graph suggests that the baker must sell approximately 2 loaves of bread if 24 rolls are sold.

We can check this by substituting this value in the equation to make sure that it works and total cost of the bread and rolls sold is $60

6(2) + 2(24) = 60, which is true

It is important to note that this is an approximation based on the information given, and it is possible that the baker may have sold a different number of loaves of bread while selling 24 rolls.

Step-by-step explanation:

Step-by-step explanation:

[tex]4[/tex]

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

Answer:

85

Step-by-step explanation:

First, take your 400 and minus the 60 on the floor.
Then take your 340 and divide it by 4.
Which then leads to your final answer of 85 per box.

Answer:4x5

Step-by-step explanation:

Answer:

The area of the base of a cylinder is found by dividing the volume of the cylinder by its height.If the volume of the cylinder is represented by 5x2 +15x + 2 and the height is 5x, which expression represents the area of the base?x2 + 3x + 5x (5x2 + 15x + 2)x + 3 + x (x2 + 3x +2)

Step-by-step explanation:

x+3+x+2

variable X represent the number of colors in T-shirt. The equation of the

Total cost = 75 ( $3+$50 X)

It is a mathematical statement that shows the equality between two or more expressions. There are various types of equation such as linear, polynomial, quadratic, exponential and so on. By using equation, the value of unknown variable is determined.

Here,

What will be the equation that representing the given relationship?

given, number of T-shirt = number of members = 75

charges of each T-shirt = $ 3

$50 fee for each color printed in the shirt.

let, X be the number of colors on the T-shirt.

The equation that represents the total cost of the order.

75($3 + $50 X) = total cost

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Sine function relates side lengths of a right triangle to an acute angle.

In a right triangle, the side lengths are related to the acute angles through the trigonometric functions. The side opposite the acute angle is related to the angle through the sine function, the side adjacent to the acute angle is related to the angle through the cosine function, and the hypotenuse is related to the angle through the tangent function.

More specifically, if θ is an acute angle in a right triangle and a and b are the lengths of the side opposite and adjacent to the angle respectively, and c is the length of the hypotenuse, we have:

sin(θ) = a/c

cos(θ) = b/c

tan(θ) = a/b

Thus, we can use these functions to find the length of any side of the right triangle if we know the measure of one of the acute angles and the length of one of the other sides.

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The  equation of the line is y =  x + 6.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

= 1/-m  =1/ 4  

then,

y =  x/4 + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

hence, y =  x/4 + 6 ← equation of perpendicular line.

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The formula to find the position of an image is x = (width of the canvas - width of the image)/2 and y = (height of the canvas - height of the image)/2.

1. First, calculate the width of the canvas by subtracting the x-coordinate of the right side of the canvas from the x-coordinate of the left side.

2. Then, calculate the height of the canvas by subtracting the y-coordinate of the top side of the canvas from the y-coordinate of the bottom side.

3. Next, calculate the width of the image by subtracting the x-coordinate of the right side of the image from the x-coordinate of the left side.

4. Then, calculate the height of the image by subtracting the y-coordinate of the top side of the image from the y-coordinate of the bottom side.

5. Finally, calculate the x-coordinate of the position of the image by dividing the width of the canvas by two and subtracting the width of the image from that result.

6. Calculate the y-coordinate of the position of the image by dividing the height of the canvas by two and subtracting the height of the image from that result.

Therefore, the formula for finding the position of an image is x = (width of the canvas - width of the image)/2 and y = (height of the canvas - height of the image)/2.

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A term can be a number, a variable, a product of two or more variables, or a number and a variable product. A factor is anything that is multiplied by another item. A factor might be a number, a variable, a word, or a more complicated statement. The numbers or variables that are multiplied together to generate a word are referred to as its factors.

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the words 4m and 5 are separated by the arithmetic sign + and m is the variable of the provided expression.

Here,

A term can be a number, a variable, the product of two or more variables, or the product of a number and a variable. Anything that is multiplied by another object is referred to as a factor. A factor might be a number, a variable, a word, or a longer statement. The factors are the numbers or variables that are multiplied together to form a word.

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The term least common denominator (LCD) is used when referring to the denominators in fractions.

The smallest common denominator shared by two or more fractions is referred to as the least common denominator (LCD).

They are the same when the common denominator also happens to be the smallest common denominator. The least common denominator will always be smaller than the common denominator if this is not the case.

There are numerators and denominators in fractions. The fraction's top and bottom halves are called the numerator and denominator, respectively.

A common denominator is a denominator that is shared by two or more fractions. They all require common denominators before two or more fractions may be added together or subtracted.

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Barry mistakes that dividing 1,243 by 3 would yield 481. This is not the case, because 1243/3 = 414.33.

The mistake that Barry made is that he most likely used simple long division method, but forgot to carry over the decimal number.

Another mistake could be the misreading of the problem, thinking that the 1,243 is the quotient, while in reality it is the dividend.

The solution of the given equations 3x + 2y = 11 , 2x + 3y = 4 is given by :

option a. ( 5, -2 ).

As given in the question,

Given equations are written as :

3x + 2y = 11 ___(1)

2x + 3y = 4 ___(2)

Solve the given system of equations using the method of elimination we get,

Multiply (1) by 3 and (2) by 2 to eliminate y we have,

9x + 6y = 33

4x + 6y = 8

5x = 25

⇒ x = 5

Substitute the value x in (1) to get the value of y we have,

3(5) + 2y = 11

⇒2y = 11 - 15

⇒y = -4/2

⇒ y = -2

Therefore, the solution of the given equations  is given by :

option a. ( x ,y ) = (5,-2).

The above question is incomplete , the complete question is :

Which of the following is a solution of the equation ?

3x + 2y = 11

2x + 3y = 4.

a. ( 5, -2 )            b. ( 5, 2)          c. ( 2,5)         d. ( -2 ,-5)

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The y-intercept of y = 5x − 10 is -10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y = 5x - 10

m = 5 and c = -10

As we know the c is the y-intercept which is equal to -10.

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On the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.

What is the linear equation in one variable?

A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.

In the given problem, the rental cost of a mid-sized car from Eliana's Rentals can be represented by the equation:

y = 60 + 6x (where y is the total cost and x is the number of days)

The rental cost of a mid-sized car from Arcadia Rent-a-Car can be represented by the equation:

y = 30 + 12x (where y is the total cost and x is the number of days)

At some point, renting from either one of the companies would cost the customer the same amount, so we can set both equations equal to each other and solve for x:

60 + 6x = 30 + 12x

Solving for x:

30 = 6x

x = 5

Hence, on the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.

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By using the box method, the terms of the equation should be distributed and simplified as follows;

         3x            x²

1         3x            x²

6x      18x²         6x³

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would multiply both sides of the equation together in order to open the bracket as follows;

(3x + x²)(1 + 6x)

3x(1) + 3x(6x) + x²(1) + x²(6x)

3x + 18x² + x² + 6x³

By combining like terms and rearranging the equations, we have:

6x³ + 19x² + 3x.

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Therefore , the solution of the given problem of function comes out to  be f(x) =54 .

A mathematical formula known as a cost function is used to visualise how production costs will vary depending on the output level. In other words, given a specific quantity produced, it calculates the total cost of production.

Here,

f(x) =  -6x + 90

=> x =6

=>  f(x) = -6*6 + 90

=> f(x) = -36 + 90

=> f(x) = 54

thus , f(x) = 54 is the correct solution for finding the left amount of money

Therefore , the solution of the given problem of function comes out to  be f(x) =54 .

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Answer: e = 7.5*h

Step-by-step explanation: The relationship between Lisa's earnings, e, and the number of hours, h, that she works is proportional. This means that the ratio of e to h is constant. One way to represent this relationship is through an equation of the form:

e = k*h

where k is a constant of proportionality. In this case, we know that Lisa earns $30 for 4 hours of babysitting, so we can use this information to find the value of k:

30 = k*4

k = 30/4 = 7.5

So the equation that represents Lisa's earnings, e, relative to the number of hours, h, that she works is:

e = 7.5*h

Where e is the earnings and h is the number of hours and 7.5 is the constant of proportionality.

Alternatively, you can write the equation as e = 30/4 * h = 7.5 * h

This equation tells us that for every hour that Lisa babysits, she earns $7.5.

Answer:

7.5

Step-by-step explanation:

because I'm smart like that!

The triangle formed when the sides are 5, 12, 13 is a right-angled triangle. The Pythagorean theorem can be used to verify this.

From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angled triangle.

Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,

CA² = AB² + BC²

Now, let us check this rule for the above given sides of the triangle.

Longest side² = Sum of squares of other two sides

13² = 12² + 5²

169 = 144 + 25

169 = 169

Thus, the sides 5 cm, 12 cm and 13 cm can form a right-angled triangle.

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Hailey walked a total of 3.82 miles.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that,

Distance Hailey walked in the morning = 2.32 miles

Distance Hailey walked in the evening = 1.5 miles

Total distance she walked = 2.32 miles + 1.5 miles

                                            = 3.82 miles

Hence the distance Hailey walked in total is equal to 3.82 miles.

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