How do you find the sum of cube ?

The question focuses on Mathematics, specifically Geometry and Calculus. It requires calculating the area of geometric figures especially circles and disks in terms of π, often via the formula A=πr² or integration.

From the question, we are required to find the area of shaded parts, which essentially associates with geometric figures and their properties in Mathematics. Specifically, this question appears to focus on areas related to circles and spheres, as it mentions calculations in terms of π, radius (r) and certain formulas like A=πr², which is the formula for the area of a circle.

When asked to express something in terms of π, it typically means leaving the answer as multiples of π, rather than using its decimal equivalent. So for instance, if we calculated the area of a circle with a radius of 3 using A=πr², we would say that the area is 9π.

Another crucial information that surfaced in the materials provided is the area calculation using integration, which involves adding up the individual areas of 'thin rings' from r=0 to r=R where R is the total radius of the disk or circle. This is an important aspect of finding areas under curves or finding areas enclosed by curves in Calculus.

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The area of the shaded regions is [tex]\(8\pi - 8\)[/tex] square centimeters.

To find the area of the shaded regions in the circle with the inscribed triangle, we'll follow these steps:

1. Calculate the Area of Sector AOC:

  - The sector's central angle is 90° because triangle AOC is right-angled at C.

  - The area of a sector is [tex]\( \frac{\theta}{360} \times \pi \times r^2 \)[/tex], where [tex]\( \theta \)[/tex] is the central angle and [tex]\( r \)[/tex] is the radius.

  - Here, [tex]\( r = 4 \) cm and \( \theta = 90° \).[/tex]

  - So, the area of sector AOC is [tex]\( \frac{90}{360} \times \pi \times 4^2 = \pi \times 4 \) cm^2.[/tex]

2. Calculate the Area of Triangle AOC:

  - The area of a triangle is [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \).[/tex]

  - For triangle AOC, the base and height are both equal to the radius, which is 4 cm.

  - So, the area of triangle AOC is [tex]\( \frac{1}{2} \times 4 \times 4 = 8 \)[/tex] cm².

3. Calculate the Area of the Shaded Segment on the Opposite Side:

  - Subtract the area of triangle AOC from the area of sector AOC.

  - This gives us the area of the shaded segment: [tex]\( \pi \times 4 - 8 \)[/tex] cm².

Combining both shaded areas, the total area of the shaded regions is [tex]\( \pi \times 4 + (\pi \times 4 - 8) \)[/tex] cm², which simplifies to [tex]\( 8\pi - 8 \)[/tex] cm². Therefore, the area of the shaded regions is [tex]\( 8\pi - 8 \)[/tex] cm².

Answer:

To build a computer, you need to buy a motherboard for 120 dollars, a CPU for 100 dollars, RAM memory for 45 dollars, storage for 30 dollars, a case for 15 dollars, and a power supply for 50 dollars. What is the cost of building 10 computers? Hope this helps, if so then please mark brainliest.

The distributive property allows for the distribution of multiplication over addition within an expression and is key in algebra and vector operations.

The distributive property is a fundamental algebraic property used in mathematics, especially when dealing with expressions containing variables and constants. This property allows one to distribute multiplication over addition within an expression, helping simplify and solve equations. For example, using the distributive law, the expression A(A + B) can be expanded to AA + AB. Due to the idempotency theorem, which states that A times A is equal to A (AA = A), the result simplifies to A + AB = A. Furthermore, the distributive property is also a key concept in vector operations, such as the cross product, and is critical for proving various mathematical axioms and properties, such as the associative and commutative laws.

Answer:

x=-6, y=-8. (-6, -8).

Step-by-step explanation:

8x-5y=-8

-7x-5y=82

---------------

-(8x-5y)=-(-8)

-7x-5y=82

---------------------

-8x+5y=8

-7x-5y=82

---------------

-15x=90

x=90/-15

x=-6

8(-6)-5y=-8

-48-5y=-8

5y=-48-(-8)

5y=-48+8

5y=-40

y=-40/5

y=-8

Answer:

$102.30

Step-by-step explanation:

Carlos: 19.80

Shag: 19.80 x 5/6 = 16.5

Deontae: 16.5 x 4 = 66.0

Total: 19.80 + 16.50 + 66.00 = 102.30

The total amount saved by Carlos, Shaq, and Deontae is $102.30.

To find the total amount saved by Carlos, Shaq, and Deontae, we first need to understand how much each of them saved individually. Carlos saved $19.80. Shaq saved 5/6 of the amount that Carlos saved, which we can calculate as (5/6) * $19.80 = $16.50. Deontae saved 4 times as much as Shaq, which we can calculate as 4 * $16.50 = $66. Finally, we add all these amounts together to get the total saved amount.

So, the total saved amount of all three is $19.80 (Carlos) + $16.50 (Shaq) + $66 (Deontae) = $102.30

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Answer:  The required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]

Step-by-step explanation:  Given that two perpendicular lines have opposite y-intercept and the equation of one of the lines is

[tex]y=mx+b.[/tex]

We are to express the x-coordinate of the intersection point of the lines in terms of m and b.

Let the slope and y-intercept of the other line be s and c respectively.

Since the product of the slopes of two perpendicular lines is -1 and -b is the opposite of b, so we have

[tex]ms=-1~~~\Rightarrow s=-\dfrac{1}{m}[/tex]

and c = -b.

That is, the equation of the other line is

[tex]y=sx+c\\\\\Rightarrow y=-\dfrac{1}{m}-b.[/tex]

Comparing the equations of both the lines, we get

[tex]mx+b=-\dfrac{1}{m}x-b\\\\\\\Rightarrow mx+\dfrac{1}{m}x=-2b\\\\\\\Rightarrow \dfrac{m^2+1}{m}x=-2b\\\\\\\Rightarrow x=-\dfrac{2bm}{m^2+1}.[/tex]

Thus, the required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]

Final answer:

The x-coordinate of the intersection point for two perpendicular lines with opposite y-intercepts can be expressed as x = -2b/(m + 1/m), where m is the slope and b is the y-intercept of one of the lines.

Explanation:

When we have two perpendicular lines with opposite y-intercepts, and one of the lines has the equation y = mx + b, we can find the x-coordinate of the intersection point by expressing the other line's equation.

Since the other line is perpendicular, its slope will be the negative reciprocal of m. Therefore, if the first line's slope is m, the second line's slope will be -1/m. Also, if the y-intercept of the first line is b, the y-intercept of the second line will be -b, given that they are opposite.

The equation of the second line will then be y = (-1/m)x - b. To find the intersection point, we set the y-values of both equations equal to each other:

mx + b = (-1/m)x - b

Now, let's solve for x:

mx + (1/m)x = -2b

x(m + 1/m) = -2b

x = -2b/(m + 1/m)

Thus, the x-coordinate of the intersection point in terms of m and b is x = -2b/(m + 1/m).

Answer:

The total area of Tony's vegetable garden is 124 square feet

Step-by-step explanation:

The total area of Tony's vegetable garden is composed by three rectangles.

1st rectangle

Length = 10 feet

Width = 6 feet (14 - 8)

Area = 6 * 10 = 60 square feet

2nd and 3rd rectangles are equals

Length = 4 feet

Width = 8 feet (14 - 6)

Area = 2 * 4 * 8 = 2 * 32 = 64 square feet

Total area

Area of the three rectangles

60 + 64 = 124 square feet

The total area of the vegetable garden is 124 ft.

A rectangle is a quadrilateral in which opposite sides are parallel and congruent to each other.

The area of a rectangle is the product of its length and width. It is given by:

Area = length * width

Area of the vegetable garden = (8 ft * 4 ft) + (8 ft * 4 ft) + (10 ft * (14 - 8)ft)

Area of the vegetable garden = 32 ft + 32 ft + 60 ft = 124 ft.

Therefore the total area of the vegetable garden is 124 ft.

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Answer:

You would know what people would say by saying that because they mean that you were to match up the letters into a shape in that order

Step-by-step explanation:

Hopefully this helps, give me a brainliest

Answer:

The given angles are

[tex]\angle BOA\\\angle AOC[/tex]

When we write down angles, we have different notations to do it.

In this case, we have angles with three letter, each one indicates a specific element.

The first letter indicate the initial point where the angle starts, for example, [tex]\angle BOA[/tex], beginas at point B, the middle letter indicates the vertex where the angle is at, so [tex]\angle BOA[/tex] indicates is at vertex O, at last, the third letter A indicates the final point where the angle goes.

Having said that, [tex]\angle BOA[/tex] is the opening from point B, then goes to vertex O and finally goes to point A, in the image attached you can see this angle highlighted.

Using the same reasoning, we have that [tex]\angle AOC[/tex] starts at points A, goes to vertex O, and ends at point C. Refer to the image attached.

The amount of sheet tin needed to make the roof of the farm silo is approximately 25132.74125 square feet.

The roof of the farm silo is in the shape of a hemisphere, which means it is like half of a sphere. The diameter of the silo is given as 126.5 feet. To find the amount of sheet tin needed to make the roof, we need to calculate the surface area of the hemisphere.

The surface area of a hemisphere can be calculated using the formula: SA = 2πr^2, where SA is the surface area and r is the radius of the hemisphere.

Since the diameter is given, we can find the radius by dividing the diameter by 2. So, the radius is 126.5/2 = 63.25 feet. Plugging this value into the formula, we get:

SA = 2π(63.25^2)

Using a calculator to find the surface area, we get:

SA ≈ 2π(4005.0625) ≈ 25132.74125 square feet

Therefore, approximately 25132.74125 square feet of sheet tin is needed to make the roof of the farm silo.

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The amount of sheet tin needed to make the roof of a farm silo, in the shape of a hemisphere, with a diameter of 126.5 feet is approximately 25,132.741 square feet.

To calculate the sheet tin needed to make the roof of a farm silo shaped like a hemisphere, we need to find the hemisphere's surface area. The surface area of a hemisphere is given by the formula 2πr2, where r is the radius of the hemisphere.

The diameter of the silo provided is 126.5 feet, meaning the radius, r, would be half of the diameter, or 63.25 feet.

Now, substitute 63.25 feet into the formula:

2 * π * (63.25)2 = 2 * π * 3996.0625.

The total sheet tin needed to make the roof is approximately 25,132.741 square feet.

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Answer:390 miles

Step-by-step explanation:

speed*time=distance (keep that in mind)

8 2/3 is also equal to 26/3

take that number and multiply that by 45 min

45*26/3

that equall 390 miles

(I tried my best, I might be wrong)

Answer:

13/2

Step-by-step explanation:

Keep in mind that speed*time=distance

ok so, if you convert 8 2/3 in to a improper fraction you'll get 26/3. Now we have to turn 45 minutes into a fraction so it's easier to multiply, that would be 45/60 because 1 hour has 60 minutes. Now, we would multiply 26/3 and 45/60 and get 78/12. Simplify that and get 13/2

Answer:

Velocity equation

[tex]v=\frac{d}{t}[/tex]

Step-by-step explanation:

Given:

Velocity of the car v = 4 units

and time t = 2 seconds

Let d = distance

Find the velocity equation.

The equation of the velocity is given below.

[tex]velocity=\frac{distance\ travelted}{time\ to\ distance\ travel}\ unit/sec[/tex]

[tex]v=\frac{d}{t}[/tex]

The above equation says, the distance travelled in t times is called velocity.

The unknown value in given question is distance. so, we find distance by given value.

[tex]d = v\times t[/tex]

[tex]d = 4\times 2[/tex]

[tex]d = 8\ units[/tex]

Therefore, the distance travelled by car is 8 units.

Formula for velocity: V = d/t

V = velocity

d = distance

t = time traveled

We are given the variables t = 2 and v = 2.

Substitute these values into the formula.

4 = d/2

Solve for d (d = distance).

4 = d/2

4 * 2 = d/2 * 2

8 = d

Therefore, the car traveled a distance of 8 units.

Best of Luck!

Answer:

252 different combinations

Step-by-step explanation:

There are 12 men who may be elected to the council. If there are only 5 members of the council (the order doesn't matter), then there are

[tex]C^{10}_5\\ \\=\dfrac{10!}{5!(10-5)!}\\ \\=\dfrac{10!}{5!\cdot 5!}\\ \\=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10}{5!\cdot 5!}\\ \\=\dfrac{6\cdot 7\cdot 8\cdot 9\cdot10}{1\cdot 2\cdot 3\cdot 4\cdot 5}\\ \\=7\cdot 4\cdot 9\\ \\=252[/tex]

different combinations of council members.

Answer:

3

Step-by-step explanation:

From the given indices

(3a^n)^3 X (1/3a^n)^3

We can rewrite the equation to be

(3a^n)^3 X (3a^-n) ^3

We father simplify;

3a^3n X 3a^-3n

Since we have same base, we add their relative powers, we solve thus,

3a^(3n-3n)

= 3a^0

= 3 X a^0 = 3 X 1

=1

Answer:

265 Fahrenheit.

Step-by-step explanation:

It is given that,

Highest temperature ever recorded on earth = 136 Fahrenheit

Lowest temperature = -129 Fahrenheit

We need to plot these temperature as an integer on a number line.

136 is a positive integer. So, it lies 136 units on the right side of zero.

-129 is a negative integer. So, it lies 129 units on the left side of zero.

According to absolute values, |x|=|-x|=x.

Absolute value of 136 and -129 are

[tex]|136|=136[/tex]

[tex]|-129|=129[/tex]

The difference between he two temperatures is

[tex]|136-(-129)|=|136+129|=265[/tex]

Therefore, the difference between he two temperatures is 265 Fahrenheit .

Answer:

16

Step-by-step explanation:

let "x" be the number of correct questions and 37-x be the wrong questions,

4x-1(37-x)=44

4x-37+x=44

5x=81

x=16.2

hence,16 is the answer

The minimum number of correct answers obtained is 17.

In this mathematics competition, each correct answer is awarded 4 marks, while a wrong answer incurs a deduction of 1 mark. If a question is not attempted, no marks are awarded or deducted.

Let's use "c" to represent the number of correct answers and "w" to represent the number of wrong answers. Since there are 30 multiple-choice questions in total, we can express the number of attempted questions as c + w = 30.

Now, we know that the student skipped 3 questions, so the number of attempted questions is 30 - 3 = 27. Since no marks are awarded or deducted for questions not attempted, the number of correct answers will be c = 27 - w.

Next, let's consider the score of the student. Each correct answer earns 4 marks, and each wrong answer incurs a deduction of 1 mark. So, the total score can be expressed as 4c - w.

The problem states that the score is more than 44. Therefore, we have the inequality 4c - w > 44.

Now, we need to find the minimum value of "c" that satisfies this inequality. To do this, let's substitute c = 27 - w into the inequality:

4(27 - w) - w > 44

Simplify the equation:

108 - 4w - w > 44

Combine like terms:

108 - 5w > 44

Now, isolate "w" by moving constants to the other side:

-5w > 44 - 108

-5w > -64

Finally, divide both sides by -5 (remember to reverse the inequality when dividing by a negative number):

w < 64/5

w < 12.8

Since "w" represents the number of wrong answers, it must be a whole number. The largest integer less than 12.8 is 12, so the minimum number of wrong answers is 12.

Now, let's find the corresponding value of "c":

c = 27 - w

c = 27 - 12

c = 15

So, the minimum number of correct answers obtained is 15. However, the question asks for the minimum number of correct answers to achieve a score *more than* 44. Let's check the score:

4c - w = 4 * 15 - 12 = 48 - 12 = 36

The student's score is 36, which is less than 44, meaning they need more correct answers to exceed 44.

Let's try c = 16:

4c - w = 4 * 16 - 12 = 64 - 12 = 52

Now, the student's score is 52, which is greater than 44. Thus, the minimum number of correct answers obtained is 16.

However, the question states that the student *skipped* 3 questions, meaning they did not attempt them. So, we need to subtract these skipped questions from the total:

Total attempted questions = c + w = 16 + 12 = 28

Skipped questions = 3

Total questions = Total attempted questions + Skipped questions = 28 + 3 = 31

Since there are only 30 questions in the competition, the maximum number of attempted questions should be 30. Therefore, the minimum number of correct answers obtained is 16 - 3 = 13.

But remember, the question asks for the minimum number of correct answers obtained, so we need to find the smallest possible number of correct answers. Since the student skipped 3 questions, the actual number of attempted questions must be 27.

Let's try c = 17:

4c - w = 4 * 17 - 12 = 68 - 12 = 56

The student's score is 56, which is greater than 44. Therefore, the minimum number of correct answers obtained is 17.

In conclusion, the minimum number of correct answers obtained is 17.

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Answer:

BC/YZ=6/3

Step-by-step explanation:

Doing the quiz rn

The similarities of triangles can be proved using SSS theorem.

The missing mathematical statement is: [tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]

Because the similarities of both triangles is being proved using SSS, then only the sides would be compared

Sides AB, AC, XY and XZ have already been compared.

So, the missing mathematical statement is the ratio of sides BC and YZ

From the question, we have:

[tex]\mathbf{BC = 6}[/tex]

[tex]\mathbf{YZ = 3}[/tex]

So, the missing statement is:

[tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]

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Answer:

Sample model as the picture attached, which shows 2/3 of 18 are circled.

Step-by-step explanation:

Here is the correct question: Your class has 18 students. Exactly 2/3

of them say that, out of all their subjects, they like science the most. Which model shows 2/3  of 18 circled?

Given: Total number of student is 18.

           2/3 of the total students like science the most.

Now, calculating the number students like the science the most.

∴ Number of students who like the science most= [tex]\frac{2}{3} \times 18= 12 \ students[/tex]

12 students like the science most out of total students.

Sample model are shown in the picture attached, where out of 18 students only 12 are inside the circle to show they like science the most.

Answer:

310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.

Step-by-step explanation:

Given:

Let number of tickets sold in advance be 'x'.

Cost of advance ticket = $3

Cost of door tickets = $5

Also given:

Thirty more tickets were sold at door in advance

Hence number of door tickets sold = [tex]x+30[/tex]

Total Money Collected = $2630

Now we can say that Total Money Collected is equal to sum of number of tickets sold in advance multiplied by Cost of advance ticket and number of door tickets sold multiplied by Cost of door tickets.

Framing in equation form we get;

[tex]3x+(x+30)5=2630[/tex]

Solving the equation to find the value of x we get;

[tex]3x+5x+150=2630[/tex]

Combining the like terms we get;

[tex]3x+5x=2630-150\\\\8x= 2480[/tex]

Now Dividing 8 on both side using division property we get;

[tex]\frac{8x}{8} =\frac{2480}{8}\\ \\x=310[/tex]

Substituting the value of x to find number of door tickets been sold.

number of door tickets sold = [tex]x+30=310+30 =340[/tex]

Hence, 310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.

Answer:

A)

Step-by-step explanation:

Answer:

There are 7 chairs in each row length.

Step-by-step explanation:

Let number of chairs in 1 row be 'x'.

Let total number of chairs be 'y'.

Given:

Hue can form 6 rows of a given length with 3 chairs left over.

It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 6 plus number of chairs which is left which is 3.

Framing in equation form we get.

[tex]y=6x+3 \ \ \ \ \ equation \ 1[/tex]

Also Given:

Hue can form 8 rows of that same length if she gets 11 more chairs.

It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 8 minus number of chairs which is required more which is 11.

Framing in equation form we get.

[tex]y=8x-11 \ \ \ \ \ equation \ 2[/tex]

From equation 1 and equation 2 we can say that L.H.S is same.

So according to law of transitivity we get;

[tex]6x+3=8x-11[/tex]

Combining like terms we get;

[tex]8x-6x=11+3[/tex]

Using Subtraction and Addition property we get;

[tex]2x=14[/tex]

Now Using Division Property we will divide both side by 2.

[tex]\frac{2x}{2}=\frac{14}{2}\\\\x=7[/tex]

Hence there are 7 chairs in each row length.

By setting up the equations as described, we find that each row has 7 chairs.

The subject of the question is a mathematical problem involving the concept of solving linear equations. Let's denote the number of chairs in a row as x. According to the problem, Hue can form 6 rows with 3 chairs leftover. So the total number of chairs she has is 6x + 3. Also, if she gets 11 more chairs, she can form 8 rows of the same length. So, in that case, the total number of chairs would be 8x. So we can write the equation 6x + 3 + 11 = 8x.

This equation simplifies to 14 = 2x. Therefore, x = 7. That is, each row has 7 chairs.

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Answer:

The cost price of 12 boxes of pudding is $3.96

Step-by-step explanation:

Given as :

The quantity of pudding boxes = 3

The cost price for 3 boxes = $0.99

Again ,

The quantity of pudding boxes = 12

Let The cost price for 12 boxes = $x

Now, According to question

Using Unitary method

∵ The cost price of 3 boxes of pudding = $0.99

or,The cost price of 1 boxes of pudding = [tex]\dfrac{0.99}{3}[/tex] = $0.33

∴The cost price of 12 boxes of pudding =$0.33 × 12

I.e x =$3.96

So,The cost price of 12 boxes of pudding = x =$3.96

Hence,The cost price of 12 boxes of pudding is $3.96 Answer

Answer:

The decimal point should be placed between the digits 8 and 7 because the quotient should be greater than 56 ÷ 7 and less than 63 ÷ 7.

Step-by-step explanation:

The division of the number 59.50 by 6.8 is equal to 8.75.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations.

Given that the number 59.50 is divided by the number 6.8. The division will be done as below,

Division = 59.50/6.8

Division = 8.75

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The values of x are -22 and 10

The dimensions are 4 cm , 11 cm , 21 cm

Step-by-step explanation:

The given is:

We want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions

The volume of a cuboid is the product of its three dimensions

∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)

∴ Its volume = 4(x + 1)(x + 11)

- Multiply the two brackets and then multiply the product by 4

∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)

∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms

∴ (x + 1)(x + 11) = x² + 12x + 11

∴ Its volume = 4(x² + 12x + 11)

∴ Its volume = 4x² + 48x + 44

∵ The volume of the cuboid = 924 cm³

- Equate the expression of the volume by 924

∴ 4x² + 48x + 44 = 924

- Subtract 924 from both sides

∴ 4x² + 48x - 880 = 0

- Simplify it by dividing all terms by 4

∴ x² + 12x - 220 = 0

Now let us factorize it into two factors

∵ x² = x × x

∵ 220 = 22 × 10

∵ 22(x) - 10(x) = 12x ⇒ the middle term

∴ x² + 12x - 220 = (x + 22)(x - 10)

∴ (x + 22)(x - 10) = 0

- Equate each factor by 0 to find x

∵ x + 22 = 0 ⇒ subtract 22 from both sides

∴ x = -22

∵ x - 10 = 0 ⇒ add 10 to both sides

∴ x = 10

∴ The values of x are -22 and 10

We can not use x = -22 because there is no negative dimensions, then we will use x = 10

∵ The dimensions are 4 , (x + 1) , (x + 11)

∵ x = 10

∴ The dimensions are 4 , (10 + 1) , (10 + 11)

∴ The dimensions are 4 cm , 11 cm , 21 cm

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Answer: Showed that: [tex]x^2+12x-220=0[/tex].

Both values of x are -22 and 10.

The dimensions are: 4 cm,  11 cm,  21 cm.

The given dimensions are 4cm,(x + 1)cm and (x + 11)cm.

So the volume is = [tex]4(x+1)(x+11)[/tex].

Given that volume= 924 [tex]cm^3[/tex].

Equating the volumes we get:

[tex]4(x+1)(x+11)=924\\4(x^2+12x+11)=924\\x^2+12x+11=\frac{924}{4}\\ x^2+12x+11=231\\x^2+12x+11-231=0\\x^2+12x-220=0\\[/tex]

Then we factor and solve the equation:

[tex]x^2+12x-220=0\\x^2+22x-10x-220=0\\x(x+22)-10(x+22)=0\\(x+22)(x-10)=0\\x=-22,10\\[/tex]

Since x can not be negative, so x = 10.

So the dimensions are: 4 cm, (x + 1) = (10 + 1) = 11 cm, (x + 11) = (10 + 11) = 21 cm.

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Answer:

More wins required = 59 wins

Step-by-step explanation:

Given:-

Total numbers of games played = 160.

Total games won = 50.

Total win percentage required = 68 %

Now,

Total percentage of games won = [tex]\frac{50}{160} \times 100[/tex]

Total percentage of games won = 0.312 [tex]\times[/tex]100

Total percentage of games won =31.25% ------------(equation 1)

Balance percentage of wins required = total win percentage required   - total percentage of games won

Balance percentage of wins required = 68 - 31.25 -----(from equation 1)

Balance percentage of wins required = 36.75%

More wins required = [tex]\frac{Balance\ percentage\ of\ win\ required}{100} \times 160[/tex]

More wins required =[tex]\frac{36.75}{100}\times 160[/tex]

More wins required = 0.368 [tex]\times[/tex] 160

More wins required =58.88

More wins required = 59 wins --------------(rounded value)

St. Louis Cardinals need to win 59 more games to achieve at least a 68% winning percentage for the season.

To determine how many more games the St. Louis Cardinals must win in order to achieve at least a 68% winning percentage for the season, let's go through the calculations step by step.

Total Games: The Cardinals play a total of 160 games in a season.

Current Wins: The Cardinals have currently won 50 games.

Winning Percentage Goal: We want the Cardinals to win at least 68% of their games.

The formula to calculate the winning percentage is:

[tex]\text{Winning Percentage} = \frac{\text{Wins}}{\text{Total Games}} \times 100\%[/tex]

Therefore, the number of wins needed to achieve at least a 68% winning percentage can be calculated as follows:

[tex]\text{Wins Needed} = 0.68 \times 160 = 108.8 \text{ (approximately 109 games)}[/tex]

Calculating Additional Wins Needed: To find out how many more games the Cardinals need to win, we'll subtract the current wins from the wins needed:

[tex]\text{Additional Wins Needed} = \text{Wins Needed} - \text{Current Wins}[/tex]

[tex]\text{Additional Wins Needed} = 109 - 50 = 59[/tex]

Answer:

E) [tex]f(x)=|x-8|+2[/tex]

Step-by-step explanation:

We will check each of the given choices by finding [tex]f(2)[/tex] of the given functions.

In order to find [tex]f(2)[/tex], we plugin [tex]x=2[/tex] in the function.

A) [tex]f(x)=2x+1[/tex]

[tex]f(2)=2(2)+1[/tex]

[tex]f(2)=4+1[/tex]

[tex]f(2)=5[/tex]

B) [tex]f(x)=3x-2[/tex]

[tex]f(2)=3(2)-2[/tex]

[tex]f(2)=6-2[/tex]

[tex]f(2)=4[/tex]

C) [tex]f(x)=x(5x-2)[/tex]

[tex]f(2)=2(5(2)-2)[/tex]

[tex]f(2)=2(10-2)[/tex]

[tex]f(2)=2(8)[/tex]

[tex]f(2)=16[/tex]

D) [tex]f(x)=3x-2x+4[/tex]

[tex]f(2)=3(2)-2(2)+4[/tex]

[tex]f(2)=6-4+4[/tex]

[tex]f(2)=6[/tex]

E) [tex]f(x)=|x-8|+2[/tex]

[tex]f(2)=|2-8|+2[/tex]

[tex]f(2)=|-6|+2[/tex]

[tex]f(2)=6+2[/tex]   [Since absolute value of any number is positive]

[tex]f(2)=8[/tex]

So, the function in E has value =8 for [tex]f(2)[/tex]

Answer:

square so all sides are equal

bc^2+mc^2=bm^2

16x^2+4x^2=20x^2=2root5x

nd^2+dm^2=nm^2

x^2+4x^2=5x2=root5x

then:-

1/2*b*h=1/2*2root5x*root5x

=1/2*10x^2=5x^2

==================================

Work Shown:

ND = x

AN = 3x

MD = 2x

MC = 2x

BC = 4x

AB = 4x

-------

P = Area of square ABCD

P = (AB)^2

P = (4x)^2

P = 16x^2

-------

Q = Area of triangle ABN

Q = (1/2)*base*height

Q = (1/2)*AN*AB

Q = (1/2)*3x*4x

Q = 6x^2

-------

R = Area of triangle MBC

R = (1/2)*base*height

R = (1/2)*BC*MC

R = (1/2)*4x*2x

R = 4x^2

-------

S = Area of triangle MND

S = (1/2)*base*height

S = (1/2)*ND*MD

S = (1/2)*x*2x

S = x^2

-------

T = Area of triangle BMN

T = P - Q - R - S

T = 16x^2 - 6x^2 - 4x^2 - x^2

T = 5x^2

-------

An alternative method is to use the pythagorean theorem to find the lengths of BM and MN. Then you can directly compute the area of triangle BMN. You should find that BM = sqrt(20)*x and MN = sqrt(5)*x.

Answer: 12/13

Step-by-step explanation:

In a deck of cards there are 4 of each number. Therefore there are 4 sevens in the deck. 4/52 are 7, but you want the probability of getting a card that IS NOT 7. That means there are 48 cards that aren’t a 7. 48/52 is the probability. But you can simplify this by finding a number that divides evenly into both, which in this case is 4. This simplifies to 12/13.

As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.

Step-by-step explanation:

We have to find the rate of change of the function

The rate of change of function is given by:

[tex]Rate\ of\ change = \frac{h(b)-h(a)}{b-a}[/tex]

Given function is:

[tex]h(x) = -2x+5[/tex]

Here

a =1

b = 2

So,

[tex]h(2) = -2(2) +5\\= -4+5\\= 1\\h(1) = -2(1) +5\\= -2+5\\= 3[/tex]

Putting the values in the formula

[tex]Rate\ of\ change = \frac{1-3}{2-1} = -2[/tex]

As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.

Keywords: Functions, rate of change

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Answer:

(5) ∠ FEH ≅ ∠ GHE : CPCTC

(6) ∠ FEH and ∠ GHE are supplementary : Consecutive angles of a parallelogram are supplementary.

(7) m∠ FEH = 90° : Congruent supplementary angles are right angles.

(8) EFGH is a rectangle : Definition of a rectangle.

Step-by-step explanation:

Given:

Quadrilateral EFGH is a parallelogram.

[tex]\overline{EG}\cong \overline{HF}[/tex]

Statements                                                           Reasons

1. EFGH is a parallelogram.                                  Given

  [tex]\overline{EG}\cong \overline{HF}[/tex]

2. [tex]\overline{EF}\cong \overline{GH}[/tex]    If a quadrilateral is a parallelogram, then the opposite sides are congruent

3. [tex]\overline{EH}\cong \overline{EH}[/tex]    Reflexive property of Congruence.

4. Δ EFH ≅ Δ HGE                                SSS Triangle Congruence Postulate.

Now, when two triangles are congruent by SSS, their corresponding angles are also congruent by CPCTC.

(5) ∠ FEH ≅ ∠ GHE                                    CPCTC

Also, for a parallelogram, the same side angles sum is 180 degrees. ∠ FEH and ∠ GHE are supplementary as their sum is 180°.

(6) ∠ FEH and ∠ GHE are supplementary  Consecutive angles of a parallelogram are supplementary.

Now, from statement (5), ∠ FEH ≅ ∠ GHE, so the supplementary pair are congruent. Therefore, each angle is equal to 90°.

Let ∠ FEH = ∠ GHE = [tex]x[/tex]. Then,

[tex]x+x=180\\2x=180\\x=\frac{180}{2}=90\°[/tex]

Therefore, ∠ FEH = ∠ GHE = 90°

(7) m∠ FEH = 90°  Congruent supplementary angles are right angles.

Now, for a parallelogram with congruent diagonals, if any two consecutive angles are 90 degree each, then the remaining angles are also 90 degrees.

Now, if a parallelogram has all its angles equal to 90°, then the parallelogram is a rectangle from the definition of a rectangle.

(8) EFGH is a rectangle                        Definition of a rectangle.

The other angles in the isosceles triangle with an angle of 100° will be 40°

Step-by-step explanation:

Lets define an isosceles triangle first.

"An isosceles triangle is a triangle with two equal sides and two equal angles.

Given that an angle of the triangle is 100°

We know that the sum of internal angles of a triangle is 180°

The sum of remaining two angles is:

=180°-100°

=80°

As the triangle is an isosceles triangle, the two angles will be equal.

So the angles will be:

[tex]=\frac{80}{2}\\=40[/tex]

The other angles in the isosceles triangle with an angle of 100° will be 40°

Keywords: Triangle, isosceles triangle

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