work out the size of angle x

The rectangular prism in figure 2 has the same volume of 108 m².

Given that the square prism's measurements are as follows:

area = 36 m²

h = 3 m

As a result, the volume of this prism is equal to side² h = area h = 36 3 = 108 m2.

Now, we'll figure out how much each prism in the image is worth.

1) Because it is a right-angled tent or prism, the volume calculation will be

V = 1/2 (base length base width) Height

= 1/2×(3×2×6) = 36/2 = 18 m²

2. Volume of a rectangular prism is equal to length, width, and height, which is 2 18 3 = 108 m2.

3. A tent's or prism's volume is equal to half of its base's length, width, and height

= 1/2×4×9×3 = 1/2×108 = 54 m²

Consequently, the rectangular prism in figure 2 has the same volume of 108 m2.

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The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

Option (D) is correct.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.

Pythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.

The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.

Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2  

We apply the Pythagorean Theorem to determine the kite's height, h

the problem can solve if the kite is 60feet

[tex]h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80[/tex]

h =80 ft (we take the positive solution since the height can not be negative number)

The kite is 80 ft above the ground.

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Step-by-step explanation:

(7 - 6)/(4 - p)= 1/9

4 - p = 9

-p= 5

p = -5

Since starting balance is $922.36 and she deposits $256.71 and then debits $1317.24. Ending Balance will be 922.36+256.71-1317.24=$138.17 in debt.

You make a deposit when you add money to your bank account. To build savings and earn interest, you should put money in a bank. For money you can withdraw at any time, a demand deposit is made. A time deposit is an investment for the long term. When you take out a loan, you might also pay a deposit as collateral.

In double-entry bookkeeping, debits and credits are entries made in account ledgers to record value changes brought on by business transactions. A credit entry represents a value transfer from the account, whereas a debit entry represents a transfer of value to the account.

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When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.

A number is itself divisible by nine if the total of its digits is also nine digits.

Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine.

By utilizing the aforementioned attribute, we can

3 + A +A +1 = 9, OR 18, OR 27

4 + 2A = 9, OR 18, OR 27

using 18

2A = 18 - 4

2A = 14

A = 7

therefore we can say that the number is  3771

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The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. Finally, we divide the y terms, y divided by y is 1. Therefore, the factor of 3x² 12xy is 3x².

The factor of  expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. This means that the x part of the factor is 3x. Next, we divide the y terms, y divided by y is 1. This means that the y part of the factor is y. When we combine the two parts, 3x and y, we get the factor of 3x². Therefore, the factor of 3x² 12xy is 3x². This means that 3x² is a factor of 12xy, which can be seen by multiplying 3x² by 4y, which results in 12xy. This shows that 3x² is a factor of 12xy.

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The equation that represents the relationship of x number of badges to y dollars is y = 9x.

What is an equation?

A mathematical statement called an equation displays the equality of two mathematical expressions. Variables, coefficients, exponents, arithmetic operators, equal signs, and constants are some of the components that make up an equation.

 An equation is said to be linear if the maximum power of the variable is consistently 1.

Let the number of badges be x and the cost of x number of badges be y.

From the question, we know that for 48 badges, the cost is $432.

So the cost of one badge = 432/48 = $9

Now the cost of x number of badges = $(9x)

We mentioned in the beginning that the cost of x number of badges is y

Therefore the equation that represent the relationship of x badge to y dollars is,

        y = 9x

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Answer: x 33/5

Step-by-step explanation:

Answer: 9/11

Step-by-step explanation:

Step 1: Cross-multiply.

3/11 = x/3

(3)*(3) = x*(11)

9 = 11x

Step 2: Flip the equation.

11x = 9

Step 3: Divide both sides by 11.

11x/11 = 9/11

x = 9/11

The solution for the given system of equations is (-1, 2).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of linear equations are y=-3x-1 ------(I) and 4x+3y=2 ------(II).

Substitute y=-3x-1 in equation (II), we get

4x+3(-3x-1)=2

4x-9x-3=2

-5x=5

x=-1

Substitute x=-1 in equation (I), we get

y=-3(-1)-1

y=2

Therefore, the solution for the given system of equations is (-1, 2).

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The coordinates of vertex D in the parallelogram ABCD are (7,-3).

In a parallelogram, opposite sides are parallel and congruent. Therefore, the vector that goes from vertex A to vertex B is the same as the vector that goes from vertex C to vertex D, and the vector that goes from vertex B to vertex C is the same as the vector that goes from vertex D to vertex A.

The vector from vertex A to vertex B is [tex]< 5-(-3), 7-1 > = < 8,6 >[/tex]

So, the vector from vertex C to vertex D is also [tex]< 8,6 >[/tex]

The vector from vertex B to vertex C is [tex]< 6-5, 2-7 > = < 1,-5 >[/tex]

So, the vector from vertex D to vertex A is also [tex]< 1,-5 >[/tex]

To find the coordinates of vertex D, we can add the vector from vertex C to vertex D to the coordinates of vertex C.

The coordinates of vertex C are (6, 2)

So, the coordinates of vertex D are [tex](6+1, 2-5) = (7, -3)[/tex]

Therefore, the coordinates of vertex D in the parallelogram ABCD are (7,-3).

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On solving the provided question, we can say that so, we apply permutation P(12,4) = 12!/ 8! = 11880

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.

so, we apply permutation

P(12,4) = 12!/ 8! = 11880

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You can differentiate best time, worst time and average time of an algorithm like this:

Best time = fastest completion time with optimal inputs.

Worst time = slowest completion time, with pessimistic inputs.

Average time = arithmetic mean

The average-case complexity of an algorithm is the amount of a computational resource (typically time) used by the algorithm, averaged over all potential inputs, according to computational complexity theory. The worst-case complexity, which takes into account the algorithm's maximum complexity given all potential inputs, is frequently contrasted with it.

There are three main reasons to investigate average-case complexity. First off, while some problems may be insurmountable in the worst case, the inputs that cause this behaviour may only occasionally occur in practise, so the average-case complexity may be a better indicator of an algorithm's performance.

Second, tools and techniques to create challenging problems are provided by average-case complexity analysis. These tools and techniques can be used in fields like derandomization and cryptography.

Third, average-case complexity enables the most effective algorithm in practise to be distinguished from algorithms with equivalent best case complexity.

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The correct numbers to complete the statements given are 40, 400, and 4000.

This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:

Based on the above, it can be concluded:

Based on this, the complete statements are:

Note: This question is incomplete; here is the complete question:

Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.

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The answers to each part is mentioned below.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is a straight line problem as shown in the question.

(a) -

Now, 12 oz of honey will cost $5.4. So, we can write that -

1 ounce of honey will cost - (5.4/12)

Cost of 1 oz honey will be - $(0.45)

(b) -

Now, 12 oz of honey will cost $5.4. So, we can write that -

For $1, you can buy - (12/5.4) oz of honey.

Amount of honey bought in 1 dollar - 2.22 ounces

(c) -

We can write the equation as -

c = 0.45h

(d) -

The graph for this function is attached with the answer.

Therefore, the answers to each part is mentioned above.

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Answer:

(x to the second power)+x+4

Step-by-step explanation:

Ur welcome

Answer:

Step-by-step explanation:

Given a tree is 3 ft tall when planted and grows at 3/4 ft per year, you want to identify the point-slope equation that does NOT fit this description, and you want two (2) more point-slope equations that DO fit this description.

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

The point representing the initial height of the tree is (x, y) = (years, feet) = (0, 3). If the rate of growth is 3/4 ft per year, then the equation can be written ...

  y -3 = 3/4(x -0) . . . . . . . . . matches choice (a)

All of the given equations have m = 3/4, so to find the incorrect equation, we need to find the point that is not on the line described by the above equation. We can do this by identifying the point (h, k) in each equation.

The attachment shows the point values used in each of the other equations (b) through (e). We find they all fall on the line except the point (15, 15) used in equation (e).

The incorrect equation is equation (e) y -15 = 3/4(x -15).

We can write additional equations by finding additional points that are on the line. For the purpose, it is convenient to choose x-values that are multiples of 4. Already, equations use x = 0, 4, 12, 15. We can choose x=8 and x=16 for the equations we write. The graph shows the corresponding y-values are 9 and 15, respectively. Then two additional equations could be ...

  y -9 = 3/4(x -8)

  y -15 = 3/4(x -16)

__

Additional comment

There are several ways to find the equation that doesn't belong. Another way, apart from plotting the points on a graph, is to rewrite each equation into the same form. Slope-intercept form is fairly convenient for this.

(a) y -3 = 3/4(x -0)   ⇒   y = 3/4x +3

(d) y -12 = 3/4(x -12)   ⇒   y = 3/4x -9 +12 = 3/4x +3

(e) y -15 = 3/4(x -15)   ⇒   y = 3/4x -11.25 +15 = 3/4x +3.75 (incorrect)

You can see that 3/4x (and y) will be an integer only if x is a multiple of 4. We like integers, so it is convenient to choose x as a multiple of 4.

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A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.

We know that the formula for the lateral surface area of cone:

Area = π × radius × slant height

and the formula for the lateral surface area of cylinder:

Area = 2π × (radius) × (height)

Here we have been given a cone A with radius r and slant height 2h.

Using the above formula, the lateral surface area of cone A would be:

A1 =  π × r × 2h

A1 =  2π × r × h                    ..................(1)

Also, we have been given a cylinder B with radius r and height h.

Using the above formula, the lateral surface area of cylinder A would be:  

A2 =  2π × r × h                   ..............(2)

From (1) and (2) we can observe that,

A1 = A2

Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.

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Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards

Multiplication is an arithmetic operation in which a number (known as a multiplicand) is multiplied by another number (known as a multiplier) to produce a product.

In this problem, we will need to use of some mathematical operators to solve the problem

1.

He currently has 216 cards, but he needs 15 sets of cards.

1 set of card = 72 cards

Let's calculate the number of sets he currently has.

1 set of card = 72 cards

x set = 216 cards

cross multiply both sides and solve for x.

x * 72 = 216 * 1

x = 216 / 72

x = 3 sets

He currently has 3 sets of cards.

Since he wants 15 sets of cards, we will need 12 more set of cards.

The number of cards can be calculated by multiplying 12 by 72

Number of cards = 12 * 72 = 864

He needs 864 more cards.

2.

1 set of card = $27

1 set = 72 cards

But she's bringing $9 to join, we can calculate the ratio of cards she will get.

1 / 27 = x / 9

x = 9 / 27

x = 1/3

She will get 1/3 of the cards bought which will be

72 * 1/3 = 24 cards

She will get 24 cards

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The decimal form of the -1 1/12 is obtained by finding the sum of -1 and -1/12 (-1/12 = -0.08[tex]\overline{3}[/tex] a recurring decimal), which is the option A

A. -1.08[tex]\overline{3}[/tex]

A recurring decimal is a decimal that has a digit or a group of digits that is continuously repeated in the decimal.

The specified expression, -1 1/12, can be presented as follows;

[tex]-1\dfrac{1}{12}[/tex]

The value of the specified expression in decimal form is therefore;

[tex]-1\dfrac{1}{12}= -1+\left( - \dfrac{1}{12}\right)[/tex]

[tex]- \dfrac{1}{12} = -0.08\overline{3}[/tex]

The fraction -1/12, therefore consist of a recurring decimal, with the 3 in the thousandth place after the 8 being the part that repeats.

Therefore, the value of the expression, [tex]-1+\left( - \dfrac{1}{12}\right)[/tex] is -1 + (-0.08[tex]\overline{3}[/tex])

-1 + (-0.08[tex]\overline{3}[/tex]) = -1.08[tex]\overline{3}[/tex]

The specified expression is therefore;

[tex]-1\dfrac{1}{12}[/tex] = -1 + (-0.08[tex]\overline{3}[/tex]) = -1.08[tex]\overline{3}[/tex]

The correct option is option A

The option C. -1.[tex]\overline{083}[/tex] is incorrect, the correct option is option A

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Answer:

Surface Area = 2(22 x 15) + 2(12 x 15) + 2(22 x 12)

Surface Area = 660 + 360 + 528

Surface Area = 1,548 inches²

Step-by-step explanation:

To find the remainder 10 when dividing 2x³ 3x² 8x by 2x 1, the polynomial must be augmented with -12.

A polynomial is an expression that consists of variables, exponents, and coefficients. It is a mathematical function composed of two or more terms, each of which is a number or a variable multiplied by an exponent. It can be used to represent a variety of relationships in mathematics, including equations, linear functions, quadratic functions, and more.

Therefore, the polynomial that will leave a remainder 10 when divided by 2x 1 is 2x³ 3x² 8x -12.

This is because if we divide the polynomial by 2x 1, the remainder will be the last term of the resulting polynomial, which is -12.

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The difference between the two given temperature values is 24 °F

We have got an equation that can relate these three units of measurement of temperature, as given below:

c/5 = (F - 32)/9= (K - 273)/5

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.

The given parameter the lowest temperature = -3 °F

the highest temperature = 21 °F

To determine the difference between the two given temperature values.

The range or difference between the two given temperature values is calculated as follows;

Range = highest - lowest

Range = 21 °F -(-3 °F)

Range = 24 °F

Thus, the difference between the two given temperature values will be 24 °F

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On solving the provided question, we can say that -  here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex]  =  [tex]4+3 = 7[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here-

from graph, x= 2

y = 1

[tex]x^2+ 3y^2 \\[/tex]

[tex]4+3 = 7[/tex]

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Answer:

The population by 2020 is 191,900

Step-by-step explanation:

Given that;

population 2010 (population in 2010): 191000

the population grew from 2010 to 2015: by 3.9%

so, population by 2015 = [tex]191000(1 + \frac{3.9}{100})[/tex]

                                      = [tex]191000(1 + 0.039)[/tex]

                                      = [tex]191000(1.039)[/tex]

                                      = [tex]198449[/tex]

the population drop from 2015 to 2020: 3.3%

so, population by 2015 = [tex]198449(1 - \frac{3.3}{100})[/tex]

                                      = [tex]198449(1 - 0.033)[/tex]

                                      = [tex]198449(0.967)[/tex]

                                      = [tex]191,900.183[/tex]

The cost of oil to fill the drum with height of 4 feet and a radius of 1.2 feet will be $397.90.

An understanding of the different dimensions is necessary to truly understand cubic feet, how big a cubic foot is, and how to measure cubic feet. There are three known dimensions which include a foot measurement. The dimensions expand to include additional measurements with each new dimension.

The cubic foot is an imperial and US customary unit of volume, used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length. Its volume is 28.3168 L. At 60 °F, a cubic foot of water weighs 62.37 pounds. A cubic foot (abbreviated as cu ft. or cubic ft.) is an imperial unit of measurement for the volume of a space or three-dimensional object.

Given: A drum of oil has a height of 4 feet and a radius of 1.2 feet. Oil cost has been given as $22 per cubic feet.

We have to calculate the cost to fill the drum with oil.

Since formula to get the volume of the drum is V = πr²h

V = 3.14×(1.2)²×4 = 18.09 feet³

Now the cost of oil to fill the drum will be

Cost = Volume × cost = 18.09×22 = $397.90

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An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

Interval notation is a simplified way of describing a particular interval. Let’s see how it’s done.

Step 1: We write the first and last number of the interval, which are the endpoints of the interval. For example, if the interval is from 6 to 20, we write 6, 20.

Step 2: We use a round or square bracket on each side of the two numbers. We use:

A square bracket [ ], if we want to include the endpoints

A round bracket ( ), if we don’t want to include the endpoints

So in this example, we use:

So, we can see that some intervals include the endpoints, some partially include them, and some do not include them. Based on this, there are three types of intervals

These are:

This type of interval does not include the endpoints. For example, (5, 10) does not include endpoints 5 and 10.

This type of interval includes the endpoints. For example, [4, 9] includes the endpoints 4 and 9.

This type of interval includes only one of the endpoints.

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Answer:35° being the smallest interior angle of the triangle, the exterior angle attached to it is the largest. It measures 180° - 35° = 145°.p.

Step-by-step explanation:

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

U/5 = 17/11

U = 17/11 X 5

U = 7.72

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The maximum height reached by the ball is 20 units at 1.2 unit time.

The extrema of a function are the maxima and minima. The highest and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, throughout its full range.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

The equation is given as

h = [tex]-10t\x^{2} + 24t + 5.6[/tex]

Differentiating both side with respect to t we get

[tex]\frac{dh}{dt} = -20t + 24[/tex]

To reach maximum value [tex]\frac{dh}{dt} = 0[/tex]

⇒20t = 24

⇒ t = 1.2

So the maximum height reached = [tex]-10 *(1.2)\x^{2} + 24*1.2 + 5.6 = 20[/tex]

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