The area of the figure is square units.

3 units, 8 units, 3 units, 9 units, 3 units, 21 units

Answer:

draw the diagram and multiply 5x20

Answer:

13.75

Step-by-step explanation:

Slash and dash.  turn the both minuses into positives and add like normal.  6.5 plus 7.25 equals 13.75.

Answer:

You have  and you want to know how many eighths you have

You need to have the denominator to eighths to find out correctly

So 4 times 2 equals 8 but what you do one side (denominator/bottom) has to be done on the other side (numerator/top) to make it the equal value of the original fraction

So ×≈

So that means that you have 6, eighths

Answer: You have 6 eights of flour

Step-by-step explanation:

Reduced the equation to one of the standard forms

(a) z²/36 = 4x²/36 + 9y²/36 + 1

(b) x = 2y² + 3z

(c) (x + y + 2z)²

(d) (x - y + z)²

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

(a) The equation z² = 4x² + 9y² + 36 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

z²/36 = 4x²/36 + 9y²/36 + 1

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3/2, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(b) The equation x = 2y² + 3z² is a standard parabolic cylinder equation. The surface is a cylinder and is classified as a parabolic cylinder.

(c) The equation 4x² + y² + 4z² - 4y - 24z + 36 = 0 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

x² + y² + 4z² - 4y - 24z + 36 = 0

= (x + y + 2z)²

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(d) The equation x² - y² + z² - 4x - 2y - 2z = 0 can be reduced to the standard form of a hyperboloid of two sheets by subtracting 1 from both sides:

x² - y² + z² - 4x - 2y - 2z + 1 = 1

= (x - y + z)²

This is the equation of a hyperboloid of two sheets with center at the point (-2, -1, -1) and semi-axes of length √2, √2, and √6, respectively. The surface is a solid and is classified as a hyperboloid of two sheets.

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After reducing the equation to one of the standard forms, the equations will be (a) z²/36 = 4x²/36 + 9y²/36 + 1, (b) x = 2y² + 3z, (c) (x + y + 2z)², and (d) (x - y + z)²

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

(a) The equation z² = 4x² + 9y² + 36 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

z²/36 = 4x²/36 + 9y²/36 + 1

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3/2, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(b) The equation x = 2y² + 3z² is a standard parabolic cylinder equation. The surface is a cylinder and is classified as a parabolic cylinder.

(c) The equation 4x² + y² + 4z² - 4y - 24z + 36 = 0 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

x² + y² + 4z² - 4y - 24z + 36 = 0

= (x + y + 2z)²

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(d) The equation x² - y² + z² - 4x - 2y - 2z = 0 can be reduced to the standard form of a hyperboloid of two sheets by subtracting 1 from both sides:

x² - y² + z² - 4x - 2y - 2z + 1 = 1

= (x - y + z)²

This is the equation of a hyperboloid of two sheets with center at the point (-2, -1, -1) and semi-axes of length √2, √2, and √6, respectively. The surface is a solid and is classified as a hyperboloid of two sheets.

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1st row

1. 2x + x + x, x = 0

Plug in 0 as x.

0 + 0 + 0 = 0

2. 2x + x + x, x = 1

Plug in 1 as x.

2 + 1 + 1 = 4

3. 2x + x + x, x = 2

Plug in 2 as x.

4 + 2 + 2 = 8

2nd row

1. 4x, x = 0

Plug in 0 as x.

4 * 0 = 0

2. 4x, x = 1

Plug in 1 as x.

4 * 1 = 4

3. 4x, x = 2

4 * 2 = 8

Notice how the answers are the same.

This is because 2x + x + x = 4x, meaning they are the same equation.

Answer:

Attached in file

Step-by-step explanation:

What does this mean by substitution?

The act of substituting in algebra / pre-algebra / etc is plugging in a number for 'x'

In this question, they are wanting you to plug in 0, 1, and 2 to two different equations (2x+x+x and 4x) to see if they are the same equations.

(I'm going to try and make a graph, as visual learning helps)

     | 2x+x+x       4x

x=0|      a             b

x=1 |       c             d

x=2|        e           f

Now I know that this is not perfect, but I inputted letters so that you know what I am solving for.

Solve for a:

Plug in x=0

2(0) + 0 + 0

2*0 = 0

0 + 0 + 0 = 0

So, a = 0 (What I am saying is the first blank is a, the blank next to it is b, etc)

Solve for b:

Plug in x=0

4(0) = 0

So, b = 0

Solve for c:

Plug in x=1

2(1) + 1 + 1

2 + 1 + 1

= 2  + 2

=4

b = 4

Solve for d:

Plug in x=1

4(1) = 4

d=4

Solve for e:

Plug in x=2

2(2) + 2 + 2

4 + 2 + 2

4 + 4

=8

e=8

Solve for f:

Plug in x=2

4(2)

f=8

There we go! I annotated this picture to have these values plugged into their respective spots!!

Hope this helped!!

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Data handling is the process of ensuring that research data is stored, archived, or disposed of in a safe and secure manner during and after the conclusion of a research project.

The following are the given details:

Item  Leadtime   On hand Inventory Lot sizing criteria Schedulereceipts

A             2                0                                   L4L                  10 in week 2

B             1                 0                                   LAL                       0

C             1                 10                                  50                       0

D             2                0                                   50                       0

E             1                 50                                180               50 in week 1

F             1                180                                L4L               50 in week 1

The Complete MRP schedule can be seen in the attached images below:

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The gross requirements for each component are as follows:

b = 2 x a = 44 units in week 7

c = 3 x a = 66 units in week 7

d = 2 x e + 1 x c + 2 x a

= 110 units in week 3, 56 units in week 6, 44 units in week 7

e = 1 x b = 44 units in week 5

f = 2 x b + 2 x c = 88 units in week 5 and 112 units in week 6

Net requirements = Gross requirements - Projected on hand

Projected on hand = Planned order receipts - net requirements

Planned order receipts = net requirements

Planned order releases = net requirements adjusted as per the lead time

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The equation that can be used to determine the number of bean bags in the instuctor's box is b = 17 x 4.

The number of bean bags in the instructor's box is 68.

Multplication is a mathematcial operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

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Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Answer:

x=3/2

x=-2

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

$21.76

Step-by-step explanation:

15% of $25.60= $3.84

$25.60-$3.84= $21.76

Answer:

  (c)  32

Step-by-step explanation:

Given a map between x, g(x), and f(g(x)), you want to find f(g(13)).

You want the function value that results when 13 is the argument of g(x), and g(x) is the argument of f(x).

Locate the input (13) in the left column of the diagram. Follow the arrow to find g(13) = 16. Follow the arrow again to find f(16) = 32.

  f(g(13)) = 32

On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Use the variables a and y to represent the number of student and adult tickets sold, respectively.

Then write the following system of inequalities -

a ≥ 10 (they must sell a minimum of 10 student tickets)

y ≥ 55 (they must sell at least 55 adult tickets)

7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)

The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.

To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.

Alternatively, solve the system of inequalities using algebra.

First, simplify the third inequality by subtracting 7a from both sides -

10y ≥ 690 - 7a

Then, divide both sides by 10 -

y ≥ (690 - 7a)/10

This inequality represents the revenue constraint in terms of the number of student tickets sold.

Now combine the revenue constraint with the other two constraints -

a ≥ 10

y ≥ 55

y ≥ (690 - 7a)/10

Use substitution to solve for a in terms of y -

y ≥ (690 - 7a)/10

10y ≥ 690 - 7a

7a ≥ 690 - 10y

a ≥ (690 - 10y)/7

To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -

(690 - 10y)/7 ≥ 10

y ≥ 55

These inequalities can be simplified -

690 - 10y ≥ 70

y ≥ 55

The first inequality can be solved for y -

-10y ≥ -620

y ≤ 62

Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -

55 ≤ y ≤ 62

Now use the expression for a in terms of y to find the corresponding values of a -

a = (690 - 10y)/7

For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -

a ≥ 10

y ≥ 55

7a + 10y ≥ 690

For example, when y = 55 -

a = (690 - 10(55))/7 = 20

7a + 10y = 7(20) + 10(55) = 690

Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.

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Value of the expression 4n - 5r when n = -2 and r = 3 is -23.

The surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given expression:

4n - 5r

When n = -2 and r = 3

The value of the expression become,

4(-2) - 5(3)

= -8 - 15

= -23

Hence, option D is correct.

Now, it is given that the surface area for a rectangular prism with a square base is given by the expression 2s²+4sh, where s is the side length of the square h is the height of the prism.

The surface area in square feet rectangular prism when s=4 feet and h=6feet is

2\((4)^{2}\) + 4(4)(6)

= 2(16) + 96

= 32 + 96

= 128 square feet

therefore, the surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.

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Answer:

Step-by-step explanation:

1). Let the equation of a line is,

   y = mx + b

   Here, m = slope of the line

   b = y-intercept

   From the graph attached,

   Slope = \(\frac{\text{Rise}}{\text{Run}}\) = \(\frac{1}{4}\)

   y-intercept = -2

   Equation → y = \(\frac{1}{4}x-2\)

2). Slope of the line = \(\frac{\text{Rise}}{\text{Run}}=\frac{3}{4}\)

   y-intercept 'b' = -3

   Equation → y = \(\frac{3}{4}x-4\)

3). Slope of the line = \(\frac{\text{Rise}}{\text{Run}}=\frac{-5}{0.75}\)

                                 = \(-\frac{20}{3}\)

    y-intercept = 5

    Equation → y = \(-\frac{20}{3}+5\)

4). Slope of the line = \(\frac{\text{Rise}}{\text{Run}}=\frac{-2}{4}=-\frac{1}{2}\)

    y-intercept = 4

    Equation → y = \(-\frac{1}{2}x+4\)

5). Since, line is passing through origin (0, 0)

    y-intercept = 0

    Slope = \(\frac{\text{Rise}}{\text{Run}}=\frac{1}{1}\)

    Equation → y = x

6). Slope of the line = \(\frac{\text{Rise}}{\text{Run}}=\frac{1}{4}\)

    y-intercept = -4

    Equation → y = \(\frac{1}{4}x-4\)

Answer:

301.44

Step-by-step explanation:

V=π r² h

V=π (4)² (12)

V= 603.19

divide by 2 to find half full: ≈ 301

301.44

The graph of y = x^2 should be translated by 1 unit to the right and 3 units up.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

Therefore, we have the following:

f(x) = x^2

g(x) = f(x - 1) + N

g(x) = (x - 1)^2 + 3

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Answer:

35 Pupils

Step-by-step explanation:

You would add up each number: 13 + 12 + 3 + 7 = 35. I Hope This Helps :)

Answer:

45

Step-by-step explanation:

13 + 12 + 3 + 7

Answer:

\(slope = \dfrac{-680}{9}\)

Step-by-step explanation:

We are given coordinates of two points:

Let the points be A and  B respectively:

\(A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})\)

To find the slope of line AB.

Formula for slope of a line passing through two points with coordinates \((x_1, y_1)\) and \((x_2,y_2)\) is given as:

\(m = \dfrac{y_2- y_1}{x_2- x_1}\)

Here, we have:

\(x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\\)

Putting the values in formula:

\(m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}\)

So, the slope of line AB passing through the given coordinates is:

\(m = \dfrac{-680}{9}\)

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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Answer:

c or Brahe

Step-by-step explanation:

Answer: Option #4 or D. Copernicus’s

Step-by-step explanation: Correct answer is C on Edge.

This is a very tricky answer when you think about it!!

Because Kepler modified Copernicus's Model using data from Tycho Brahe.

Johannes Kepler accurately described the motions of the planets.

Answer:

you can eat candy for 25 days

Step-by-step explanation:

Answer:

Step-by-step explanation:

h(t)=-5t²+10t+80=-5(t²-2t+1-1)+80

=-5(t²+2t+1)+5+80

=-5(t-1)²+85

maximum height reached=85 ft

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

given that

they have 10 bags full of coins

in each bag are infinite coins.

but one bag is full of forgeries, and you can't remember which bag.

you know that genuine coins weigh= 1 gram

forgeries weight = 1.1 gram

now, we need to find which bag has  forgeries  in minimum readings

then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins

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Total weight=55gm ,then there is no forgeries coin bag

1 bag with forgeries = take 1 coin from first bag

from 2 bag = take 2 coin

and similarly with all 10 bags.....

from 10th bag = take 10 coin

if there is no forgeries ,then  total weight    = (1+2+3+4+5+6+7+8+9+10)

                                                                        =55gm

If bag weight 55.3 than we know that there are 3 forgeries.

So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.

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2(z²+4) -17x

1) Factorizing this polynomial 2z²-17x +8

2z²-17x +8 Let's find the LCM of 2, 8

2(z²+4) -17x

There's no step further to go since 17x and 2 can't be decomposed into prime factors.

2) So, the answer is

2(z²+4) -17x