Find the volume of the composite figure. Round to the nearest tenth if necessary.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in familiar algebraic notation, a2 + b2, are equal to the squares on the legs.

Greek philosopher Pythagoras made significant contributions to mathematics, astronomy, and music theory. Although the Babylonians were aware of the theorem 1000 years prior to Pythagoras, he may have been the first to demonstrate it.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides, according to a theory put forth by Pythagoras.

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Answer:

Below

Step-by-step explanation:

f(1)    -  2 = a(1) + b

        - 2 = a + b             (1)

f(5)     10 = a (5) + b

          10 = 5a + b            (2)

Multiply first underlined equation by -5  to get

      10 = -5a  - 5b       add this to the second equation (this will eliminate 'a')

      20 = - 4 b       so   b = -5

then the first equation becomes   - 2 = a +  (-5)

             which shows a = 3

so your function is just    f(x) = 3x  -5

Answer:

36 square units

Step-by-step explanation:

The figure is made up of a rectangle above with length 6 and width 4.

The bottom part is a triangle with a base of 6 and a height of 4.

total area = area of rectangle + area of triangle

total area = LW + bh/2

total area = 6 × 4 + 6 × 4/2

total area = 24 + 12

total area = 36

Answer:

36 square units

Step-by-step explanation:

We can split the given figure into two familiar figure by drawing a line segment as shown in the attached figure

This splits the composite figure into a rectangle at the top and an inverted triangle at the bottom

The rectangle has a length(horizontal portion) of 6 units and a width(vertical portion) of 4 units

Area of rectangle = length x width = 6 x 4 = 24 square units

The triangle has a base of 6 units and a height of 4 units

Area of rectangle = 1/2 x base x height = 1/2 x 6 x 4 = 1/2 x 24 = 12 square units

Area of figure = 24 + 12 = 36 square units

Answer: I don't speak spanish

Step-by-step explanation:

Answer:

ok whats the question

Step-by-step explanation:

The results of subtractions between perfect square trinomials are listed below:

In this problem we have three cases of subtractions between two perfect square trinomials that must be simplified. According to algebra, perfect square trinomials can be expanded by means of the following definition:

(a + b)² = a² + 2 · a · b + b²

Where a, b are real constants.

The procedure is summarized below:

Case 1

(x + 3)² - (x - 4)²

(x² + 6 · x + 9) - (x² - 8 · x + 16)

x² + 6 · x + 9 - x² + 8 · x - 16

14 · x - 7

Case 2

(7 · b² - 7)² - (2 · b² - 11)²

(49 · b⁴ - 98 · b² + 49) -  (4 · b⁴ - 44 · b² + 121)

49 · b⁴ - 98 · b² + 49 - 4 · b⁴ + 44 · b² - 121

45 · b⁴ - 54 · b² - 72

Case 3

(5 · a · b² + 3)² - (6 · a · b² - 7)²

(25 · a² · b⁴ + 30 · a · b² + 9) - (36 · a² · b⁴ - 84 · a · b² + 49)

25 · a² · b⁴ + 30 · a · b² + 9 - 36 · a² · b⁴ + 84 · a · b² - 49

- 9 · a² · b⁴ + 114 · a · b² - 40

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On solving the provided question, we can say that by addition, the distance between Belmont and Yardley is by adding all distances in between them =  9.75+8324 = 17.99 mils

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

by addition,

the distance between Belmont and Yardley is

by adding all distances in between them =  9.75+8324 = 17.99 mils

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The second ship's route also goes through another site, which is (0, 44)

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope.

In the coordinate plane, it describes the slope of the line.

Finding the slope between two separate points and calculating the slope of a line are related tasks.

In general, we require the values of any two separate coordinates on a line in order to determine its slope.

According to our question-

Parallel lines have equal slopes.

Therefore,

m₁ = m₂

The equation for one ship's trajectory is

y = - 13x + 4

utilizing the slope-intercept model

y = mx + b

m = -13

slope = -13

The second vessel sails by the points (3, 5). The second argument could be

located below. Remember that they share a slope.

Therefore,

y = -13x + b

using (3, 5) b, the following is obtained:

5 = -13(3) + b

5 = -39 + b

5 + 39 = b

b = 44

The second ship's equation will be as follows:

y = -13x + 44

y = -13(0) + 44

y = 44

The key could be (0, 44)

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A sentence for the equation 4m=52 is,

B) Four times m is equal to fifty-two.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

4m=52

i.e. we have,

4×m = 52

Hence, A sentence for the equation 4m=52 is,

B) Four times m is equal to fifty-two.

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Answer:

3.here,tan45°=10/n

or,1=10/n

:.n=10

Now from Pythagoras theorem,

m²=(10)²+n²

or,m=√100+100

:.m=10√2

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A 3 action sequence is a set of three actions that are related and follow one another in a logical order.

It is a technique used to break down complex tasks into smaller, more manageable steps. For example, if you want to cook a meal, a 3 action sequence could be: (1) gather ingredients, (2) prepare ingredients, and (3) cook meal. Each of these three steps is related and follows the one before it.

The 3 action sequence is a great tool for breaking down complicated tasks into more manageable parts. It can help you stay on track and keep focus when working on a task. It can also be used to create a timeline for completing a task, or to create a checklist of items that need to be completed.

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If a number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero.

As the name suggests, divisibility tests or division rules in Maths help one to check whether a number is divisible by another number without the actual method of division.

Finding the product of two or more corresponding integers is done mathematically through the action of multiplication. It is frequently represented by the letters "x" or "*." In order to discover the result of multiplication, a multiplicand, also known as the multiplicand, is multiplied by a multiplier, also known as the multiplier. The result of the two integers, for instance, is 56 if the multiplicand and multiplier are both 8. A multiplication process always yields a greater number as the outcome than either of the initial factors. Multiply is also used to describe the process of adding a number to itself a certain number of times, as in "7 multiplied by 3 equals 21."

How to solve?

For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

This connection is true for every multiplication and division problem as long as the numbers are utilised consistently in both operations.

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Answer: 52(4x+8) in simplified form is 208x + 416.

Step-by-step explanation:

To simplify 52(4x+8) we need to first use the distributive property, which states that:

a(b+c) = ab + ac

So, we can rewrite 52(4x+8) as:

52 * 4x + 52 * 8

Now we can just multiply the numbers:

52 * 4x = 208x

52 * 8 = 416

so the expression simplifies to:

208x + 416

So, 52(4x+8) in simplified form is 208x + 416.

The intersection of plane TUYX and plane VUYZ is found as UY.

For the stated question-

According to the supplied figure, TUYX is one side of both the rectangular prism while UVYZ is its opposite side.

One edge, which is represented by the line segment UY, has both sides intersecting perpendicularly.

It is depicted in the figure.

Thus, UY is the line that intersects as a result.

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The correct question is attached.

If the spring musical cost $600 for costumes and $450 for the stage materials.  the number of tickets  is 56 tickets.

Total ticket = $600 + $450

Total ticket = $1050

Now let find the number of tickets that they have to sell to profit.

Number of tickets = $1,050 - $375 / $12

Number of tickets = $675/$12

Number of tickets = 56 tickets

Therefore the number of tickets  is 56 tickets.

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The complete question is:

The spring musical cost $600 for costumes and $450 for the stage materials.

Students raised $375 from advertisements in the program. Tickets cost $12 each.

How many tickets do they have to sell to profit?

Therefore , the solution of the given problem of quadratic equation comes out to be (x−1)(x+6).

The quadratic equation x ax2+bx+c=0 is an equations regression model in a single variable. a 0. According to the First Theorem of Algebra, this polynomial has at exactly one solutions because it is of second order. There could be simple or complex solutions. A four-variable equation is referred to as a quadratic equation. This implies that it must have at least one squared word. A typical formula for resolving math problems is "ax2 + bx + c = 0," where the numerical factors or constant a, b, and c stand in for the undefined variable "X."

Here,

Given : x²+5x+6

=> x²+bx+c.

Find two integers with the product c and the sum b.

Whose product in this instance is 6 and Whose summation is 5.

Put these integers to use in factoring the expression.

(x−1)(x+6)

Therefore , the solution of the given problem of quadratic equation comes out to be (x−1)(x+6).

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The angle which would be tangent  a 90 degree in the given diagram would be ∠JYQ, ∠JYW  , ∠FYG and ∠FHG

A circle's tangent is a single-pointed line that intersects the circle. The point of tangency is the location where the circle and the tangent cross. The circle's radius, where the tangent touches it, is perpendicular to it.

Therefore, JY is perpendicular to QW which means

∠JYQ=∠JYW=90 degrees

Since, J is the center of circle and GF is diameter, there is a theorem which says that angle substended by diameter at any point of circle is 90 degree.

Therefore, ∠FYG =∠FHG=90 degrees.

Hence, ∠JYQ, ∠JYW  , ∠FYG and ∠FHG are all the equal to 90 degree.

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The evaluation of the algebra tiles are as follows;

A) The area of the algebra tiles is; 2·x² + 3·x

The perimeter of the tiles is; 6·x + 6

B) If the algebra tiles were rearranged, the area remains 2·x² + 3·x

Algebra tiles are figures that can be manipulated to help explore and understand concepts such as expanding algebraic expressions, factoring expressions, and equations.

Please find attached the possible shape in the question created with MS Word.

A) The area of the of the shape is the sum of the areas of the individual shapes, which are found as follows;

The perimeter is the sum of the width and lengths of the rectangles as follows;

The width of the rectangle with area x = 1 unit

The width of the boxes with area x² = x

The length of the sides of each rectangle = x unit

The perimeter, P, of the figure is therefore;

B) The area of the each of the algebra tiles remain the same when the tiles are rearranged, such that the area, of the new shape, which is the sum of the areas of the individual tiles remain the same.

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Answer:

Step-by-step explanation:

The question that can be answered by finding 4 1/2 ÷ 1/4 is this:

C. You are buying 1/4 pound containers of fruits at the store. How many containers do you need to buy to have 4 1/2 pounds of fruit?

The expression that is best represented by the question is statement C. Here, we are told to find how many containers we need to buy 4 1/2 pounds of fruit.

Let's assign the figure x to the number of containers we are to find. So,

1/4x = 4 1/2

Divide both sides by 1/4 to find x

x = 4 1/2 ÷ 1/4

Option C is the right answer.

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The average rate of change from day 2 to day 10 is given as follows:

-0.75 houses sold per day.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The points of interest are given as follows:

(2,8) and (10,2).

The change in the output is of:

2 - 8 = -6.

The change in the input is of:

10 - 2 = 8.

Hence the average rate of change is obtained as follows:

r = -6/8

r = -3/4

r = -0.75 houses sold per day.

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Therefore , the solution of the given problem of trigonometry comes out to be the reciprocal of both the cosine is the secant.

Trigonometry, a branch of mathematics, studies relationships between angles and sides of triangles. Trigonometric exists throughout all of geometry and can be reduced to a grouping of triangles from any horizontal form. Calculus, difficult or real trigonometry, algebra, and infinite series are only a few examples of the mathematics that are related to one another in a startlingly complex way.

Here,

The reciprocal of both the cosine is the secant. This is the fraction of a right triangle's hypotenuse towards the side closest to a particular angle.

The secant of slope in a right angled triangle is calculated by dividing the height of the y axis by the width of the neighboring side.

Thus, its fundamental formula is: sec X  =[tex]\frac{Hypotenuse}{Adjacent Side}[/tex]

Additionally, it is the cosine value's reciprocal.

Therefore , the solution of the given problem of trigonometry comes out to be the reciprocal of both the cosine is the secant.

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A quotient is a number created when two numbers are divided. The formula for this is Quotient = Dividend ÷ Divisor.

The division is the process of dividing one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the number that we get as a result.

Then, the quotient formula is given by Quotient = Dividend ÷ Divisor. For example, 50÷5=10. Here, 50 is the dividend, 5 is the divisor, 10 is the quotient, and 0 is the remainder.

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Answer: To solve the equation 4x^2 + 5 = 6 by factoring, we need to start by isolating x^2 on one side of the equation.

We have:

4x^2 + 5 = 6

subtracting 5 from both sides:

4x^2 = 1

Dividing both sides by 4:

x^2 = 1/4

Taking the square root of both sides:

x = ± √(1/4)

x = ± 1/2

So the solutions are x = 1/2 or x = -1/2.

It's important to note that we can't factor any x^2 term as it's a squared term and it's not possible to factor it out with any integer or variable.

Equation represents the comet's orbit [tex]\frac{x^{2} }{100} -\frac{(y-6)^2}{64} =1[/tex], So correct option is C.

A coordinate plane, also known as a Cartesian plane, is a two-dimensional surface that is used to graph points, lines, and shapes. It is named after the mathematician René Descartes, who is credited with inventing the system in the 17th century.

The coordinate plane is divided into four quadrants by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin and is assigned the coordinates (0,0). The x-axis runs horizontally and is used to measure values along the horizontal (or "x") direction, while the y-axis runs vertically and is used to measure values along the vertical (or "y") direction.

Each point on the coordinate plane can be represented by an ordered pair of numbers, called coordinates, that indicate its position in relation to the x- and y-axes. The coordinates of a point are written as (x, y), where x is the point's distance from the y-axis and y is the point's distance from the x-axis.

The equation that represents the comet's orbit is:

[tex]\frac{x^{2} }{100} -\frac{(y-6)^2}{64} =1[/tex]

This is the standard equation for a hyperbola in the center form, where the center is at (0,6), the distance between the center and the vertex is 8 and the distance between the center and the focus is 2.

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The solution for given equations are: z = 4, b = -12, w = 5, c = -11

An equation is a mathematical statement that expresses the equality of two expressions.

Variables are symbols or letters used to represent unknown values in equations.

To solve for a variable, one must first isolate the variable by performing the same operations on both sides of the equation until the variable is alone on one side of the equation.

For example, if the equation is 2x + 4 = 10, the first step would be subtracting 4 from both sides of the equation to get 2x = 6. The next step would be to divide both sides of the equation by 2 to get x = 3. This is how one would solve for the variable in this equation.

According to question:-

A. 3(7z-6)=-(-18z+6)

21z - 18 = 18z - 6

3z = 12

z = 4

B. -8b+2(-5b-2)=212

-8b - 10b - 4 = 212

-18b - 4 = 212

b = -12

C. 4/5w+5 = 1/5w+8

4/5w-1/5w = 8-5

3/5w = 3

w = 5

D. (-c-8)-(7c-6)= 18c+284

-c-8-7c+6 = 18c + 284

18c + 8c = -2-284

26c = -286

c = -11

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Answer: In a triangle, the sum of the angles is 180 degrees. Therefore, if we know two of the angles, we can use this property to find the measure of the third angle.

In this case, we are given angle B = 27 degrees and we want to find the measure of angle C. We can use the following equation to find angle C:

Angle B + Angle C + Angle A = 180

27 + Angle C + 90 = 180

Angle C = 180 - 27 - 90

Angle C = 63 degrees

Additionally, we can use the Law of Cosines to find the measure of angle C.

c² = a² + b² - 2ab * cos(C)

c² = 28² + 18² - 2 * 28 * 18 * cos(C)

c² = 784 + 324 - 1008 * cos(C)

c = √(1108 - 1008*cos(C))

We know that cos(C) = (a² + b² - c²) / 2ab

cos(C) = (784 + 324 - c²) / (22818)

We can substitute the value of c² that we obtained from the first equation and find cos(C) and thus angle C.

So the measure of angle C is 63 degrees.

Step-by-step explanation:

If you want to buy fewer than 25 shirts, then prefer Shirts By Sam shop. If you want to buy more than 25 shirts, then prefer Might T Shirt shop.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Given that:

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The cost of 10 shirts is $127.5

The cost of 15 shirts is $168.75.

Assume the equation that represents total cost is y = ax+b

Putting x= 10 and y=127.5 in y = ax+b:

127.5 = 10a+b.....(i)

Putting x= 15 and y=168.75 in y = ax+b:

168.75 = 15a+b.....(ii)

Use elimination method to solve equation (i) and (ii).

Subtract equation (i) from (ii)

15a+b = 168.75

10a+b = 127.5

____________

5a = 41.25

a = 8.25

Putting a=8.25 in equation (i)

127.5 = 10×8.25+b

b = 40

The equation is y = 8.25x+40.

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The cost of 8 shirts is $137

The cost of 12 shirts is $163

Assume the equation that represents total cost is y = ax+b

Putting x= 8 and y=137 in y = ax+b:

137 = 8a+b.....(iii)

Putting x= 12 and y=163 in y = ax+b:

163 = 12a+b.....(iv)

Use elimination method to solve equations (iii) and (iv).

Subtract equation (iv) from (iii)

 8a+b = 137

12a+b = 163

____________

4a = 26

a = 6.5

Putting a=6.5 in equation (iii)

137= 8×6.5+b

b = 85

The equation is y =6.5x+85.

The solution of the system of equations:

y = 8.25x+40 .....(vi)

y =6.5x+85   ......(vii)

Use substitution method to solve equations (vi) and (vii).

Subtract equations:

8.25x+40 - 6.5x-85=0

1.75x - 45 =0

x = 45/1.75

x = 25.71

Putting x = 26 in equations (vi) and (vii)

y = 8.25×26+40 = 254.5

y = 6.5×26+85 = 254

Putting x = 24 in equations (vi) and (vii)

y = 8.25×24+40 = 238

y = 6.5×24+85 = 241

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