How to find the difference of the area of a square which the area is 98.01 inside a circle?

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Answer:

C

Step-by-step explanation:

The volume of a box (rectangular prism) is given by:

\(\displaystyle V = \ell wh\)

We are given that the desired volume is 540 cubic inches. The width is three inches longer than the length and the height is four inches longer than the length. Substitute:

\(\displaystyle (540) = \ell(\ell + 3)(\ell + 4)\)

Solve for the length. Expand:

\(\displaystyle \begin{aligned} 540 &= \ell (\ell^2 + 7\ell +12) \\ 540&= \ell ^3 + 7\ell^2 +12\ell \\ \ell^3 + 7\ell ^2 +12\ell -540 &= 0\end{aligned}\)

We cannot solve by grouping, so we can consider using the Rational Root Theorem. Our possible roots are:

±1, ±2, ±3, ±4, ±5, ±6, ±9, ±10, ±12, ±15, ±18, ±20, ±27, ±30, ±36, ±45, ±54, ±60, ±90, ±108, ±135, ±180, ±270, and/or ±540.

(If you are allowed a graphing calculator, this is not necessary.)

Testing values, we see that:

\(\displaystyle (6)^3 +7(6)^2 + 12(6) -540 \stackrel{\checkmark}{=} 0\)

Hence, one factor is (x - 6).

By synthetic division (shown below), we can see that:

\(\displaystyle \ell^3 + 7\ell^2 +12\ell -540 =(\ell -6)(\ell ^2 + 13\ell +90)\)

The second factor has no real solutions. Hence, our only solution is that l = 6.

In conclusion, our answer is C.

Answer:

6 inches

Step-by-step explanation:

I just took the test

You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.

Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.

The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:

Cost of bananas = AED 7.35 * 1.4 = AED 10.29

The total cost of apples is given by the equation:

Cost of apples = $10.20 * x

The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:

Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15

Substituting the known values, we have:

(10.29 + 10.20 * x) / (1.4 + x) = 8.15

Cross-multiplying and simplifying, we get:

10.29 + 10.20 * x = 8.15 * (1.4 + x)

Expanding the equation, we have:

10.29 + 10.20 * x = 11.41 + 8.15 * x

Rearranging the equation, we get:

10.20 * x - 8.15 * x = 11.41 - 10.29

1.05 * x = 1.12

Dividing both sides by 1.05, we find:

x = 1.12 / 1.05

x ≈ 1.067

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Answer:

Step-by-step explanation:

You want the area of the composite figure consisting of a rectangle and a triangle.

The area of the rectangle is ...

  A = LW

  A = (5 ft)(6 ft) = 30 ft² . . . . rectangle area

The base of the triangle is the difference in length of the horizontal segments:

  b = 9 ft -5 ft = 4 ft

The area is given by the formula ...

  A = 1/2bh

  A = 1/2(4 ft)(6 ft) = 12 ft² . . . . triangle area

The area of the figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 30 ft² +12 ft²

  total area = 42 ft²

__

Additional comment

The area of this trapezoid can also be found using the trapezoid formula:

  A = 1/2(b1 +b2)h

  A = 1/2(9 ft +5 ft)(6 ft) = 42 ft²

The rectangle is shown in the figure as 5 ft wide and 6 ft tall. It does not matter which of these dimensions you call the length and which you call the width. Their product is the same either way.

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The diagram is showing the length of each line segment.

• NM has length 110 + 4x

• ML has length x + 103 (this is the one you have to find)

• LK has length 70

• NK has length x + 243

The segment NK has length equal to the sum of the lengths of NM, ML, and LK. So we have

x + 243 = (110 + 4x) + (x + 103) + 70

Solve this equation for x :

x + 243 = (110 + 103 + 70) + (4x + x)

x + 243 = 283 + 5x

x - 5x = 283 - 243

-4x = 40

x = 40/(-4)

x = -10

Now solve for x + 103 by adding 103 to this result:

x + 103 = -10 + 103 = 93

So ML has length 93.

Answer:

Well the volume is 1570.8 cubed. but i don't know what it would be in your range of answers.

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

2 1/3 is equal to 7/3 and 2 goes into 7, 3.5 times.

Answer:

there are 3   2/3 in 2 1/3  with 1/3 left over

Step-by-step explanation:

Hope this helps.

Have a nice day :)

Can you give me brainliest plz :)

The area of the shaded segment is 100/3π square centimeter

What is a area?

Area is nothing but the surface bounded by the object in 2D.

What is a segment?

A part of a line or curve between two points In circle we can say segment is nothing but a region or area cutoff from the circle by chord.

What is a segment area?

Area bounded by a segment. Area of segment has a formula (θ/360°)πr²

According to the question

θ=120°

radius =10cm

area of segment = (120°/360°)π(10²)

120°/360° =0.333

10²=100

0.333×π×100

33.3π or (100/3)π

Thus area of the shaded segment is 33.3π or (100/3)π square centimeters

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Answer:

Since all views look like a circle, the solid would be a ball, which is also called a sphere.

The answer is Sphere

The geometrical name of the solid given is Sphere.

The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

................................

What plus Ten equals thirty two is equivalent to

x + 10 = 32

10 is adding on the left, then it will subtract on the right

x = 32 - 10

x = 22

Answer:

600,000

Step-by-step explanation:

this is just like a free point though

Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

Slope m = (y2 - y1)/(x2 - x1)

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

Maddy monthly pay is $3958 and her bi-weekly salary is $1827

An equation is an expression used to show the relationship between two or more variables and numbers.

Maddy found a job with an annual salary of $47.5K ($47500). There are 12 months in a year. Hence:

Maddy monthly pay = $47500 / 12 = $3958

Maddy found a job with an annual salary of $47.5K ($47500). There are 52 weeks in a year. Hence:

Maddy bi-weekly salary = ($47500 / 52) * 2 = $1827

Maddy monthly pay is $3958 and her bi-weekly salary is $1827.

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The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.

In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.

Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:

sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x

Step 2 - Divide each side of the formula by cos² x:

sin² x / cos² x + cos² x / cos² x = 1 / cos² x

(sin x / cos x)² + 1 = (1 / cos x)²

Step 3 - Use the definition of the two trigonometric functions:

tan² x + 1 = sec² x

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Answer:

Hello!

_____________________

Your answer would be ( 68% ).

Step-by-step explanation: To find percentage, we need to find an equivalent number with denominator 100. Multiply both numerator & denominator by 100

\(\frac{17}{25} . \frac{100}{100}\)

\(= ( \frac{17 . 100}{25} ) . \frac{1}{100} = \frac{68}{100}\)

Therefore, the answer is 68%

If you are using a calculator, simply enter 17÷25×100 which will give you 68 as the answer.

Hope this helped you!

The solution after change into percentage is, 68%

We have to change 17 out of 25 to a percentage.

Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We can change it as,

⇒ 17/25

⇒ (17/25) × 100%

⇒ 1700/25

⇒ 68%

Therefore, The solution after change into percentage is, 68%

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Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:

200

Step-by-step explanation:

You can simply just graph it and see where the points intersect, or you can do it algebraically.

0.45x+29.99=0.40x+39.99 subtract 29.99 both sides

0.45x=0.40x+10.00 subtract .40x both sides

0.05x=10.00 divide both sides by 0.05

x=200

Answer:

Use the following Financial Ratios to measure financial performance against standards. In addition, analysts compare these ratios to industry averages (benchmarking), industry standards or rules of thumbs and against internal trends (trends analysis). Furthermore the most useful comparison when performing financial ratio analysis is trend analysis They are derived from thethree following financial

statements:

⚫Balance Sheet

•Income Statement

⚫Statement of Cash Flows

.5 Categories

The five (5) major categori in the financial ratios list include the following:

•Liquidity Ratios

•Activity Ratios

•Debt Ratios

•Profitability Ratios

•Market Ratios

Step-by-step explanation:

Sana makatulong

Ratios dealing with short-term debts are Liquidity Ratios; those gauging efficiency in using assets for sales are Activity Ratios, and those scrutinizing long-term debt handling are Leverage Ratios. Along with the calculations, observations and identification of trends and their driving factors are also necessary.

In finance and business, ratio analysis is a tool used for conducting quantitative analysis on a company's financial statements. It involves the calculation and interpretation of various financial ratios. The following are the answers to the question's blanks:

However, only calculating ratios is not enough; you must also observe and identify trends suggested by the analysis, as well as identify the factors that drive these trends. These additional steps provide context and deeper insights into the company's financial performance.

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Answer:

He would need to buy 39 more. 25 plus 36 is 61. 100 minus 61 is 39. therefore, he needs to buy 39 more i hope this helped if it did could i have brainliest thanks!

Answer:

Step-by-step explanation:

hello :

 f(x) = √(2x)

g(x) = √(8x)

(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/

x ≥ 0: /x/ = x        (f g)(x) = 4x......(answer : A)

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

she had 27 students after 5 students left her class.

Her present number of student = 27

Initial number of student before 5 left the class = 27 + 5 = 32

number of student in his class before the 5 student left can be represented as follows

where

b = number of student before 5 student left his class

b - 5 = 27