A. Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC
B. Determine the y coordinate of each coin described in Part A: yA, yB, and yC.
C. Determine the x and y coordinates xcg and ycg of the center of gravity of the three coins described in Part A.

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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Answer:

\((x+2, y+7)\)

Step-by-step explanation:

\((x,y) \longrightarrow (x-3, y+5) \longrightarrow (x+2, y+7)\)

Answer:

18000

Step-by-step explanation:

20x2=40

40x15=600

600x30=18000

If thirty security personnel need to be hired the security labor cost for a four-week month will be $18000.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

The term PEMDAS describes the sequence in which arithmetic operations must be carried out in an equation.

It is given the number of hired security personnel is 30. If they work for only two weeks in the four-week month with a duration of 20 hours per week the total time they will give in a month is,

= 20 × 2

= 40 hours

Rate of work = $15/hour

The total cost that the individual earns,

= 40 hours × $15/hour

= $ 600

If the number of security personnel is the total cost spent,

= $ 600 x30

=$ 18000

Thus, if thirty security personnel need to be hired the security labor cost for a four-week month will be $18000.

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Answer:

5 folders and 5 pens = yes

6 pens and 6 erasers = yes

1 pen and 4 notebooks = no

3 folders and 7 erasers = no

4 folders and 2 notebooks = yes

Step-by-step explanation:

Max total = $10

(5 folders x 1.29) + (5 pens x 0.70)

6.45 + 3.50 = 9.95

(6 pens x 0.70) + (6 erasers x 0.89)

4.20 + 5.34 = 9.54

(1 pen × 0.70) + (4 notebooks × 2.35)

0.70 + 9.40 = 10.10

(3 folders × 1.29) + (7 erasers × 0.89)

3.98 + 6.23 = 10.21

(4 folders × 1.29) + (2 notebooks × 2.35)

5.16 + 4.70 = 9.86

Answer:

54 minutes

Step-by-step explanation:

1) There are 60 minutes in an hour. So, you can do 60-36 to find the first value. (24)

2) Add 24 minutes to 30 and get 54 minutes.

The maximum possible number of elements in set B is 62.

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.

The universal set is A consisting of the primary one hundred positive integers.

Now, Set B is a subset of A.

Set B might be made up of the first 62 positive numbers, for example.

Only then is 123 the largest number that can be formed by adding all the components of set B.

Set B contains 62 items altogether.

Additionally, we can carefully swap out one or more pieces from set B and add them to its complement.

In the majority of these cases, set B may have 62 elements.

Therefore, we get the number of elements in set B will be 62.

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Answer:

Step-by-step explanation:

This is a question about naming parts of a polynomial. The attached image has more on the subject.

The word "degree" refers to the number of times a variable is a factor in a term. When there is only one variable, the degree of the term is the exponent of the variable. A missing exponent is understood to be 1. A missing variable is understood to have a degree of 0.

When there are two or more variables, the degree of the term is the sum of their exponents.

In some cases, we're only interested in the degree associated with a particular variable. For example, 7x²y³ is a 5th-degree term that is 2nd degree in x and 3rd degree in y.

A "quadratic" term is one that has degree 2, or one in which the variable of interest has degree 2.

In the given function definition, the term -3x² is the quadratic term.

A "linear" term is one that has degree 1.

In the given function definition, there is no linear term.

If you must identify one, it would be 0x, a degree-1 term with a coefficient of 0.

A "constant" term is one that has no variables, or no variables of interest. It has degree zero.

For example, in the expression x² +2ax +a², when we are concerned with the variable x, the a² term is called the "constant" term because it does not contain the variable x. The same expression could be considered as a quadratic in 'a', in which case the x² term would be the "constant term."

In the given function definition, the term 1 is the constant term.

Answer:

100

Step-by-step explanation:

1 yard = 3 feet

6 yards = 18 feet

(18*2)+(32*2)

36+64

100

Answer:  The perimeter is a 100 feet.

Step-by-step explanation:

If it is 32 feet long and 6 yards wide then I am thinking that the shape will be a rectangle.

To find the shape of a rectangle, you can use the formula,  P = 2l+2w  were P is the perimeter, l is the length, and w is the width.  

But first since feet and yards are different measurements, and the question is asking for the perimeter in feet, then you will first have to convert 6 yards to feet.  

6 yards = 18 feet  

This means that the sides  will be 32 feet long and 18 feet wide.

Now using the formula, input 32 for L and 18 for W and solve for P the perimeter.

 P  = 2(32) + 2(18)

P = 64+ 36

P = 100  

**Kind note:

Since there are two variables in one equation, it is impossible to determine a specific value for x and y. (Unless the trial-and-error method is used).

How to determine the value of x using the equation (16x - 8y = 72)?

To determine the value of "x", we need to isolate the x-variable on one side. The value (or expression) obtained on the opposite side of the x-variable will be the value of x.

How to determine the value of y using the equation (16x - 8y = 72)?

To determine the value of "y", we need to isolate the y-variable on one side. The value (or expression) obtained on the opposite side of the y-variable will be the value of y.

Determining the x-variable:

⇒ 16x - 8y = 72

⇒ 16x = 72 + 8y                            [Adding 8y to both sides of the equation]

⇒ 16x/16 = (72 + 8y)/16                [Dividing 16 to both sides of the equation]

⇒ x = 9/2 + y/2                               [Simplifying both sides of the equation]

⇒ x = (9 + y)/2                                     [Combining the denominators]

Determining the y-variable:

⇒ 16x - 8y = 72

⇒ 16x - 8y - 16x = 72 - 16x         [Subtracting 16x both sides of the equation]

⇒ -8y = 72 - 16x                              [Simplifying both sides of the equation]

⇒ -8y/-8 = (72 - 16x)/-8                [Dividing -8 to both sides of the equation]

⇒ -8y/-8 = 72/-8 - 16x/-8

⇒ -8y/-8 = -72/8 + 16x/8

⇒ y = -9 + 2x                                  [Simplifying both sides of the equation]

First simplify it to suitable form of slope intercept then you can get values

The pairs are

And so on

Thus, the magnitude of value of |a+b| is Sqrt (9), which simplifies to just 3.

To find the magnitude of the sum of two vectors, we need to add the two vectors together and then take the square root of the sum of their squares.

So, let's first add the two vectors together:

a+b = (3i+4j-4k) + (-2i-6j+2k)
    = i - 2j - 2k

Now, we can find the magnitude of this vector by squaring each of its components, summing them, and then taking the square root:

|a+b| = sqrt((1^2) + (-2^2) + (-2^2))
     = sqrt(1 + 4 + 4)
     = sqrt(9)
     = 3

Therefore, the value of |a+b| is Sqrt (9), which simplifies to just 3.

In summary, the magnitude of the sum of two vectors can be found by adding the vectors together, squaring each of their components, summing them, and then taking the square root.

For the given vectors a=3i+4j-4k and b=-2i-6j+2k, their sum is i - 2j - 2k, and the magnitude of this vector is 3.

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Answer:

OP = 4

Step-by-step explanation:

N is the midpoint of MO.

Since NO = 3, then MN = 3, and MO = 3 + 3 = 6

MO + OP = MP

6 + OP = 10

OP = 4

A line segment is also a line but the line with finite length and having fixed endpoints. The length of the line segment OP is 4 units.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given the following details as:

Now, from the figure, We have,

Since O is between M and P and N is the midpoint between MO

MP = MN + NO + OP _____(1)

Now,

N is the midpoint of MO so,

MN = N0

N0 = 3 and MP = 10 ____(2)

MN = NO = 3 _______(3)

From (1)

MP = MN + NO + OP

Substituting (2) and (3) in (1)

10 = 3 + 3 + OP

10 = 6 + OP

Subtracting 6 on both sides

10 - 6 = 6 + OP - 6

4 = OP

OP = 4

Thus, OP = 4.

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Answer:

Step-by-step explanation:

Slope of AC= (a-0)/(a-0) = 1

Slope of BD = (0-a)/(a-0) = (-a)/a =-1

Slope of AC x Slope of BD =1 x -1 = -1

Therefore AC perpendicular to BD

Main answer: The diameter of the silver wire is approximately 1.31×10^−5 m.

Step-by-step solution:

Step 1: Determine the charge passing through the cross section.

Charge (Q) = Number of electrons * Charge of one electron

Q = 1.4×10^16 * 1.6×10^−19 C (charge of one electron)

Q ≈ 2.24×10^−3 C

Step 2: Calculate the current in the wire.

Current (I) = Charge (Q) / Time (t)

t = 300 μs = 300×10^−6 s

I = 2.24×10^−3 C / 300×10^−6 s

I ≈ 7.467 A

Step 3: Use the drift speed formula to find the wire's area.

Drift speed (v_d) = I / (n * A * e)

where n is the number density of silver (free electrons per unit volume), A is the cross-sectional area, and e is the charge of one electron.

For silver, n ≈ 5.86×10^28 m^−3.

v_d = 7.6×10^−4 m/s

Rearrange the formula to solve for A:

A = I / (n * v_d * e)

A ≈ 7.467 A / (5.86×10^28 m^−3 * 7.6×10^−4 m/s * 1.6×10^−19 C)

A ≈ 1.35×10^−10 m^2

Step 4: Calculate the diameter of the wire.

The cross-sectional area of the wire (A) is related to its diameter (D) through the formula for the area of a circle:

A = π(D/2)^2

Rearrange the formula to solve for D:

D = 2 * sqrt(A/π)

D ≈ 2 * sqrt(1.35×10^−10 m^2 / π)

D ≈ 1.31×10^−5 m

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Answer:

B

Step-by-step explanation:

Imagine a mirror on the X axis, looking at the original triangle in the mirror would make the new triangle appear.

Answer:

Reflection across the x-axis

Step-by-step explanation:

The two shapes are just simply being reflected across the x-axis.

Hope this helps!:)

Answer:

no

Step-by-step explanation:

If you want to make 1/2 the recipe, then \(1\frac{11}{16}\) tablespoon of sugar you need.

In the given question, a recipe calls for \(3\frac{3}{8}\) tablespoons of sugar.

If you want to make 1/2 the recipe, then we have to find how much sugar you need.

As given that;

1 recipe = \(3\frac{3}{8}\) tablespoons of sugar

Before solving the question, we convert the mixed fraction into simple fraction.

To convert in simple fraction we multiply 3 by 8 then we add 3 on the result of multiplication of 3 and 8.

1 recipe = 27/8 tablespoons of sugar

We have to find sugar need for making 1/2 recipe.

1/2 recipe = \(\frac{27}{8}\times\frac{1}{2}\) tablespoons of sugar

1/2 recipe = 27/16 tablespoons of sugar

1/2 recipe = \(1\frac{11}{16}\) tablespoons of sugar

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Answer:what

Step-by-step explanation:what does this mean

The correct answer is option (a) n < 27. By dividing both sides of the inequality by -3, we get n > -27.

To solve the inequality -3n < 81, we divide both sides by -3. Remember that when dividing by a negative number, the direction of the inequality sign changes. Dividing both sides by -3 gives us n > -27. So, the correct answer is option (d) n > -27.

The reasoning behind this is that dividing by -3 reverses the inequality sign, which means that the less than ("<") sign becomes a greater than (">") sign.

Option (a) n < 27 is incorrect because dividing by -3 changes the direction of the inequality. Option (b) is stated to be wrong. Option (c) n = 27 is incorrect because the original inequality is strict ("<") and not an equality ("=").

Therefore, By dividing both sides of -3n < 81 by -3, we get n > -27. Therefore, the correct answer is option (a) n < 27.

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The value of x in (8^x/5) (8^x/4)=8^4 is 80/9

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

The equation;(8^x/5) (8^x/4)=8^4

LHS=(8^x/5) (8^x/4)

=(8^x/5) (8^x/4)

=8^(x/5+x/4)

=8^((4x+5x)/20)

=8^(9x/20)

Now, by comparing LHS to RHS

We will get;

9x/20=4

9x=80

x=80/9

Therefore the answer of the equation will be 80/9

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Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

There are \(355,687,428,095,976\) ways to arrange the 12 identical apples and 5 different oranges in a row.

To solve this problem, we can use the concept of permutations with restrictions.

First, let's consider how many ways there are to arrange the 12 identical apples and 5 different oranges with no restrictions. This is simply the number of permutations of 17 items, which is:

P(17, 17) = 17!

Now, we need to subtract the number of arrangements where two oranges appear side by side. To count these arrangements, we can treat the two oranges as a single object (let's call it O), and then we can arrange the 11 apples, O, and the other 3 oranges in a row. There are 4 objects to arrange, and the 3 oranges can be arranged in 3! = 6 ways, while the other object (O) can be arranged in 2 ways (either before or after the 3 oranges). So the total number of arrangements where two oranges appear side by side is:

\(4*6*2 = 48\)

However, we have overcounted the arrangements where there are two pairs of oranges next to each other (e.g. O1O2). To correct for this, we can treat each pair of adjacent oranges as a single object, and then arrange the 10 apples and 3 pairs of oranges in a row. There are 4 objects to arrange, and the 3 pairs of oranges can be arranged in 3! = 6 ways. So the total number of arrangements with two pairs of adjacent oranges is:

\(4 * 6 = 24\)

Therefore, the total number of arrangements of the 12 identical apples and 5 different oranges such that no two oranges appear side by side is:

\(17! - 48 + 24\)

which simplifies to:

\(355687428096000 - 48 + 24 = 355687428095976\)

So there are \(355,687,428,095,976\) ways to arrange the 12 identical apples and 5 different oranges in a row such that no two oranges will appear side by side.

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The largest area you can enclose with 20 meters of fencing against a long, straight wall is 50 square meters. Itcan be found using optimization methods.

Step 1: Define the variables
Let x be the length of the fencing parallel to the wall and y be the length of the fencing perpendicular to the wall.
Step 2: Set up the constraint equation
Since you have 20 meters of fencing, the sum of x and 2y (both sides perpendicular to the wall) should equal 20. The constraint equation is:x + 2y = 20
Step 3: Express one variable in terms of the other
Solve the constraint equation for one variable. In this case, solve for x: x = 20 - 2y

Step 4: Write the area function
The area of the rectangle can be expressed as A = xy. Substitute x from the previous step into this equation: A(y) = (20 - 2y)y.

Step 5: Find the critical points
Differentiate the area function with respect to y and set it to zero to find the critical points: dA/dy = 20 - 4y = 0, Solve for y:4y = 20, y = 5
Step 6: Find the corresponding value for x
Plug the value of y back into the equation for x: x = 20 - 2(5), x = 10

Step 7: Check for maximum area
The critical point we found (x=10, y=5) is indeed a maximum since the second derivative of the area function is negative.Step 8: State the largest area
The largest area you can enclose with 20 meters of fencing against a long, straight wall is A = xy = 10 * 5 = 50 square meters.

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The set of variables that is most likely to have a cause-and-effect relationship is option C: the weight of a box and the postage rate we have to pay to ship the box to California.

Based on the given sets of variables, the set most likely to have a cause-and-effect relationship is:
B. The height of a person and the weight of a person

This is because there is a general correlation between a person's height and their weight, as taller individuals tend to have higher weights. While this is not an absolute rule, there is a stronger cause-and-effect relationship in this set compared to the other options.

This is because the weight of the box is a likely cause of the postage rate, as the heavier the box, the more postage we will have to pay to ship it. In options A and B, there may be a correlation between the variables, but it is less likely that there is a direct cause-and-effect relationship. In option D, the make of a car is not a likely cause of its mileage, as there are many other factors that can affect a car's mileage.

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Answer:

x + .35X - .11(x - .35x)

Step-by-step explanation:

Let x = the original price of the stock.

x + .35x  This is first year

-.11( x + .35x) is the second year

x + .35X - .11(x - .35x)

Answer:

  -3

Step-by-step explanation:

You want the value of p(2), given the piecewise definition of function p.

The function definition divides its domain into three (3) parts. The first step in evaluating the function for a particular value of x is to find the applicable domain.

Here, you want the value of p(x) for x = 2.

The third domain expression (2 ≤ x < 5) includes the value x = 2, so the third function definition applies:

  p(x) = x -5

  p(2) = 2 -5 = -3

The value of p(2) is -3.

__

Additional comment

A graph of the function is attached. The point of interest is circled in green. (2, p(2)) = (2, -3).

#95141404393

Answer:

It depends if you pick a D or a T for P(not a vowel)

The value of derivative f'(x)  is ƒ'(x) = (7/2)x^2 + 3x + C. f(3)= 49.

To find the derivative of ƒ(x), denoted as ƒ'(x), we need to integrate the given second derivative function, ƒ"(x) = 7x + 3.

Let's integrate ƒ"(x) with respect to x to find ƒ'(x): ∫ (7x + 3) dx

Applying the power rule of integration, we get: (7/2)x^2 + 3x + C

Here, C is the constant of integration. So, ƒ'(x) = (7/2)x^2 + 3x + C.

Now, we are given that ƒ'(-3) = -2. We can use this information to solve for the constant C. Let's substitute x = -3 and ƒ'(-3) = -2 into the equation ƒ'(x) = (7/2)x^2 + 3x + C:

-2 = (7/2)(-3)^2 + 3(-3) + C

-2 = (7/2)(9) - 9 + C

-2 = 63/2 - 18/2 + C

-2 = 45/2 + C

C = -2 - 45/2

C = -4/2 - 45/2

C = -49/2

Therefore, the equation for ƒ'(x) is: ƒ'(x) = (7/2)x^2 + 3x - 49/2.

To find ƒ(3), we need to integrate ƒ'(x). Let's integrate ƒ'(x) with respect to x to find ƒ(x): ∫ [(7/2)x^2 + 3x - 49/2] dx

Applying the power rule of integration, we get:

(7/6)x^3 + (3/2)x^2 - (49/2)x + C ,  Again, C is the constant of integration.

Now, we are given that ƒ(-3) = 3. We can use this information to solve for the constant C. Substituting x = -3 and ƒ(-3) = 3 into the equation ƒ(x) = (7/6)x^3 + (3/2)x^2 - (49/2)x + C:

3 = (7/6)(-3)^3 + (3/2)(-3)^2 - (49/2)(-3) + C

3 = (7/6)(-27) + (3/2)(9) + (49/2)(3) + C

3 = -63/6 + 27/2 + 147/2 + C

3 = -63/6 + 81/6 + 294/6 + C

3 = 312/6 + C

3 = 52 + C

C = 3 - 52

C = -49

Therefore, the equation for ƒ(x) is: ƒ(x) = (7/6)x^3 + (3/2)x^2 - (49/2)x - 49.

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Answer:

8/9

Step-by-step explanation:

Order of operations: Parentheses first.

(30+6)=36,

Then subtract 32

36-32 = 4

Left to right, so don't divide by 18. Instead, divide by 9.

4/9 = 4/9

4/9 times 2/1 = 8/9

Answer:

6

Step-by-step explanation:

i took the test