Please Solve this Lines and angles question

Answer:

Its 67.9 but technically its 67.912 *hope this helps

Step-by-step explanation:

Right scalene triangle.

Sides: a = 66   b = 16   c = 67.912

Area: T = 528

Perimeter: p = 149.912

Semiperimeter: s = 74.956

Angle ∠ A = α = 76.373° = 76°22'23″ = 1.333 rad

Angle ∠ B = β = 13.627° = 13°37'37″ = 0.238 rad

Angle ∠ C = γ = 90° = 1.571 rad

Height: ha = 16

Height: hb = 66

Height: hc = 15.55

Median: ma = 36.674

Median: mb = 66.483

Median: mc = 33.956

Inradius: r = 7.044

Circumradius: R = 33.956

Vertex coordinates: A[67.912; 0] B[0; 0] C[64.142; 15.55]

Centroid: CG[44.018; 5.183]

Coordinates of the circumscribed circle: U[33.956; 0]

Coordinates of the inscribed circle: I[58.956; 7.044]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 103.627° = 103°37'37″ = 1.333 rad

∠ B' = β' = 166.373° = 166°22'23″ = 0.238 rad

∠ C' = γ' = 90° = 1.571 rad

Answer:

the cone holds only 1/3 as much water as the cylinder, which comes to 29 gallons

Step-by-step explanation:

Let the radius in both cases be r and the height in both cases h.

Cylinder volume is (area of base)(height), and

Cone volume is (1/3)(area of base)(height).

Thus, the cone holds only 1/3 as much water as the cylinder, which comes to 29 gallons.

Answer:

353340 + x + 33

Step-by-step explanation:

real life sum situation

refer the attachment for your answer !!

Answer:

1.8 inches

Step-by-step explanation:

1. find the # of inches that represents 1 foot.

3/25 = 0.12in

2. to find the length of the line segment that represents 15 feet, multiply 0.12 inches by 15.

0.12*15 = 1.8in

Management is one of the most important factor in commiting fraud.

For publicly traded companies, the Sarbanes-Oxley Act of 2002 mandated strict financial and auditing rules. Legislators passed the Act to help protect shareholders, employees, and the general public from accounting errors and dishonest financial activities.

The Sarbanes Oxley Act mandates an Internal Controls Report for all financial reporting. This shows that adequate safeguards are in place to ensure the accuracy of a company's financial data. Year-end financial disclosure reports are also essential.

Sarbanes-Oxley is important because it tightens corporate oversight. In order to deter firms from committing similar actions, the legislation was passed in reaction to many high-profile corporate fraud instances.

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To simplify the expression 5√8 + √3, we can simplify each radical term separately and then combine them.

First, let's simplify the radical terms:

√8 can be simplified as 2√2 because 8 can be factored into 4 * 2, and √4 is equal to 2.

√3 cannot be simplified further since 3 is a prime number.

Now, let's substitute the simplified radical terms back into the expression:

5√8 + √3 becomes 5(2√2) + √3.

Next, we can multiply the coefficients outside the radicals:

5(2√2) is equal to 10√2.

Putting it all together, the simplified expression is:

10√2 + √3.

So, 5√8 + √3 simplifies to 10√2 + √3.

Therefore , the solution of the given problem of expression comes out to be 794.0481.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

Here,

3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Given : 5 +

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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On solving the provided question, we can say that a rectangle ABCD on a coordinate plane, point A is in Quadrant Il with coordinates (-a, b), the distance from point A to point B is 3a

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

a rectangle ABCD on a coordinate plane,

point A is in Quadrant Il with coordinates (-a, b).

the distance from point A to point B is 3a

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Answer:

Costs $2.75

Step-by-step explanation:

Set up:

\(\frac{12}{1.50} = \frac{22}{x}\)

Cross Multiply:

12x = 33

Divide by 12:

x = $2.75

Answer:

£2.74

Step-by-step explanation:

hioe this helps!

have a good day :)

the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Congress decides to allocate funds for a new road system, resulting in reduced spending on education and defense for the next two years. This prioritization reflects a trade-off between infrastructure development and investments in other critical sectors.

When Congress decides to prioritize funding for a new road system, it means that resources will be redirected from other areas, such as education and defense. This decision reflects a trade-off where the government chooses to invest in infrastructure development at the expense of reducing expenditures in education and defense sectors.

The impact of reduced education spending can have implications for schools, students, and educational programs. It may result in fewer resources for schools, leading to potential cuts in staff, curriculum, and extracurricular activities. Reduced funding for education can hinder educational opportunities and initiatives aimed at improving student outcomes and educational equity. Likewise, the reduction in defense spending can have consequences for national security and military capabilities. It may limit the resources available for military readiness, training, equipment modernization, and research and development. This reduction in defense spending could potentially impact the military's ability to respond effectively to security threats and maintain a strong defense posture.

Overall, the decision to fund a new road system at the expense of education and defense spending reflects a prioritization of infrastructure development. While investing in infrastructure is important, it is essential to carefully consider the potential consequences and seek a balanced approach that addresses the needs of various sectors for the overall well-being and progress of the country

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The correct option is \(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\).\) The function that has a range of \(\(\{y | y \leq 5\}\)\) is option \(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\).\)

To determine this, let's analyze the options:

\(\(a.\)  \(f(x) = \frac{{(x - 4)^2}}{5}\)\): This function will have a range of  \(\(y\)\)-values greater

than or equal to 0, so it does not have a range of \(\(\{y | y \leq 5\}\).\)

\(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\)\) : This function is a downward-opening parabola, and when we substitute various values of \(\(x\)\) , we get \(\(y\)\)-values less than or equal to 5. Therefore, this function has a range of \(\(\{y | y \leq 5\}\).\)

\(\(c.\)   \(f(x) = \frac{{(x - 5)^2}}{4}\)\): This function is an upward-opening parabola, and its

range will be  \(\(y\)\)-values greater than or equal to 0, so it does not have a

range of \(\(\{y | y \leq 5\}\).\)

\(\(d.\)   \(f(x) = -\frac{{(x - 5)^2}}{4}\)\): This function is a downward-opening parabola, and its range will be \(\(y\)\)-values less than or equal to 0, so it

does not have a range of \(\(\{y | y \leq 5\}\).\)

Therefore, the correct option is \(\(b. f(x) = -\frac{{(x - 4)^2}}{5}\).\)

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The height of a rectangular prism is 8.3 cm.

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.

We have,

Surface Area = 288 square cm

Base length = 4 cm and width = 9 cm

So, SA of rectangular prism

288 = 2(lw+ wh + lh)

144 = (36 + 9h + 4h)

13h = 144- 36

13h = 108

h = 8.30 cm

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To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Step-by-step explanation:

F = ka, where k is a real constant.

When a = 9, F = 36.

=> (36) = k(9), k = 4.

Therefore when a = 4,

F = (4)(4) = 16.

The value of F is 16 when a is 4.

Answer:

the answer is 68km.

Step-by-step explanation:

Answer:

42.5 miles is about 68km

multiply 42.5 by 8/5 and you have your answer

By multiplying half of the product of the lengths of two sides by the sine of the angle between them, you can calculate the area of the triangle using trigonometry

To find the area of triangle ΔABC using trigonometry, you can use the formula:

Area = (1/2) * a * b * sin(C)

In this formula:

- 'a' represents the length of side AB,

- 'b' represents the length of side BC,

- 'C' represents the angle between sides AB and BC.

By multiplying half of the product of the lengths of two sides by the sine of the angle between them, you can calculate the area of the triangle using trigonometry.

Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles, particularly right triangles. It focuses on the study of the angles and sides of triangles and how they are related through trigonometric functions.

Trigonometry primarily involves six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions relate the ratios of the sides of a right triangle to its angles.

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Answer:

d=7.4

d= =square 1.

Step-by-step explanation:

Answer:

7.4 meters

Step-by-step explanation:

Solve for the radius:

\(A=\pi r^2\)

\(42.71=\pi r^2\)

\(\frac{42.71}{\pi}=r^2\)

\(\sqrt{\frac{42.71}{\pi}}=r\)

Solve for the diameter:

\(d=2r\)

\(d=2\sqrt{\frac{42.71}{\pi}}\)

\(d\approx7.4\)

Therefore, the diameter of the circle is about 7.4 meters

Answer:

The U.S. pays $630,000,000 (or six hundred thirty million dollars) in FUTA taxes annually.

Step-by-step explanation:

First, we must find 6% of $7,000 to find the annual taxes per employee.

7,000 x 0.06 = $420

Therefore, each employee gets $420 in taxes per year.

Since there are 1.5 million employees, we need to multiply $420 by 1.5 million.

1,500,000 x 420 = $630,000,000

Therefore, the U.S. pays $630,000,000 in FUTA taxes annually.

Hope this helps! :D

Tax paid to FUTA annually by 1.5 million employee is $630000000.

Percent is the ratio or a fraction in which the whole is always taken as 100.

To convert a percentage to decimal, we follow the following step

According to the given question

Tax 6.0% on the first $7,000 an employee earn each year.

⇒ 6% of $7000 = \(\frac{6}{100}\)× $7,000 = $420

⇒ The tax of $420 an employee pay each year.

Therefore, the tax paid by 1.5 million of employees = 1500000 ×$420 = $630000000.  (1million = 1000000)

Hence, tax paid to FUTA annually by the 1.5 million employee will be $630000000.

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Answer:

1) b 2)d

Step-by-step explanation:

To find an equation that is perpendicular to a certain equation, find the reciprocal of the slope and switch the sign. For parallel, find an equation with the same slope and the same sign. Disregard the y-intercept if you're just trying to find the perpendicular or parallel equation

Slope=-1/4

#1

Perpendicular lines hAve slopes negative reciprocal to each other

So

equation is

c is y intercept

#2

Parallel lines have equal slopes

Option D

The authors of both passages agree that King’s "I Have a Dream" speech: had a profound impact on many Americans (Option C).

In a comprehension passage, some questions are given that follow the passage. The questions are to be answered by using the data given in the passage, even if it differs from real-life facts.

Now,

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Answer:

-8

Step-by-step explanation:

-3x+7x-8=34+9x-2

we move the x's to the left and the numbers to the right

4x-9x=32+8

-5x=40

x=-40/5

x=-8

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

the correct answer is except 3:x=8:32

When a prism is cut by a plane parallel to its bases and perpendicular to its height h, the shape of the intersection will be a rectangle. It is important to note that the rectangle may have different side lengths depending on the specific dimensions of the prism.

If a prism is cut by a plane that is parallel to the bases of the prism and perpendicular to its height h, the shape of the intersection between the prism and the plane would be a rectangle.

When a plane intersects a prism parallel to its bases, it creates cross-sections that are congruent to the bases. This means that the resulting shape of the intersection will have the same outline as the original bases of the prism.

Since the bases of a prism are typically quadrilaterals with right angles, such as rectangles or squares, the intersection shape will also have those characteristics. In this case, since the prism is cut by a plane parallel to its bases, the intersections will be congruent to the bases and have the same shape.

A rectangle is a quadrilateral with four right angles, and its opposite sides are equal in length. When a prism is cut by a plane parallel to its bases, the resulting intersection shape will maintain these properties and be a rectangle.

Therefore, when a prism is cut by a plane parallel to its bases and perpendicular to its height h, the shape of the intersection will be a rectangle. It is important to note that the rectangle may have different side lengths depending on the specific dimensions of the prism.

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

(2, 7)

Step-by-step explanation:

hope this helps :)

( 1 ) Find by using a formula of (-b/2a, (4ac-b²)/4a)

\((\frac{-b}{2a},\frac{4ac-b^2}{4a})\\(\frac{-12}{2(-3)}),(\frac{4(-3)(-5)-(12)^2}{4(-3)})\\(\frac{-12}{-6}),(\frac{60-144}{-12})\\(2,\frac{-84}{-12})\\(2,7)\)

The vertex is at (2,7)

( 2 ) Find by using a derivative (Calculus)

You can also find a vertex by using a calculus. Using a derivative

\(y'=-3x^2+12x-5\\y'=-6x+12\\\\\)

Then substitute y' = 0 to get a vertex.

\(y'=-6x+12\\0=-6x+12\\-12=-6x\\2=x\)

Then substitute x = 2 in the equation of y = -3x²+12x-5

\(y=-3x^2+12x-5\\y=-3(2)^2+12(2)-5\\y=-3(4)+24-5\\y=-12+24-5\\y=-17+24\\y=7\)

x = 2 and y = 7, therefore. The vertex is (2,7)

Answer: B. x = 16/3

3/5x + 1/2 = 3/4x -3/10

minus 3/4x on both sides

-3/20x + 1/2 = -3/10

minus 1/2 on both sides

-3/20x = -3/10

multiply both sides by 20/-3

x = 16/3

Answer:

B) \(x=\frac{16}{3}\)

Step-by-step explanation:

\(\frac{3}{5}x+\frac{1}{2}=\frac{3}{4}x-\frac{3}{10}\)

\(\frac{12}{20}x+\frac{10}{20}=\frac{15}{20}x-\frac{6}{20}\)

\(\frac{10}{20}=\frac{3}{20}x-\frac{6}{20}\)

\(\frac{16}{20}=\frac{3}{20}x\)

\(16=3x\)

\(\frac{16}{3}=x\)

Therefore, your answer is B) \(x=\frac{16}{3}\)

According to the question 35 can be accurately placed between 5 and 6, but it is notably closer to 6 on the number line.

The number 35 would be plotted on the number line between 5 and 6, but closer to 6. When considering the interval between 5 and 6 as a whole, 35 falls closer to the 6 side. It is not exactly midway between the two numbers, but its proximity leans towards 6.

This positioning indicates that 35 aligns more closely with the value of 6 rather than 5. Visually, if we were to divide the distance between 5 and 6 into equal parts, the point representing 35 would be located at a distance closer to 6.

Therefore, 35 can be accurately placed between 5 and 6, but it is notably closer to 6 on the number line.

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