Solve for the value of c.
(2c-3)°
97°

The phrase "well-ordered by ∈" refers to a specific kind of ordering or relation on a set using the element-of symbol (∈). In set theory, the symbol "∈" represents membership, indicating that an element belongs to a set.

A well-ordering is a particular type of total order, where every non-empty subset of the set has a least element. In other words, for any subset of the set, there is always a smallest element in that subset according to the ordering relation.

When we say that a set is "well-ordered by ∈," it means that the elements of the set are arranged in a specific order such that the membership relation (∈) satisfies the properties of a well-ordering. This implies that every non-empty subset of the set has a smallest element with respect to the membership relation (∈).

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The equation does not have a unique solution for x. It is true for any value of x.

The given equation is:

(5/7)(x + 2) - (3/7)x = (2/7)(x + 5)

To solve for x, we'll first simplify both sides of the equation using the distributive property and combining like terms:

[(5/7)x + (5/7)(2)] - (3/7)x = [(2/7)x + (2/7)(5)]

Simplifying further:

(5/7)x + 10/7 - (3/7)x = (2/7)x + 10/7

Next, we'll collect the x terms on one side and the constant terms on the other side of the equation:

(5/7)x - (3/7)x - (2/7)x = 10/7 - 10/7

Combining like terms:

[(5/7) - (3/7) - (2/7)]x = 0

Simplifying further:

(0/7)x = 0

Any value of x will satisfy this equation since (0/7)x will always be zero.

Therefore, the equation does not have a unique solution for x. It is true for any value of x.

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Answer:

  31.2 g

Step-by-step explanation:

You want to know the average weight of the remaining eggs if two from a dozen with average weight 32 g are broken, and their weights are 35 and 37 g.

The two broken eggs differ from average by ...

  (35 -32) +(37 -32) = 3 +5 = 8 . . . . . grams

The remaining eggs must differ from that average by the opposite amount, a total of -8 g.

Distributed over 10 eggs, this difference is -0.8 g, so the average weight of the remaining eggs is 32 -0.8 = 31.2 g.

The average weight of the remaining 10 is 31.2 g.

The average weight is the sum of all weights divided by the number of eggs:

  avg = W/N

  W = N·avg = 12·32 g = 384 g

The new sum of weight will be this amount less the weights of the broken eggs:

  W' = 384 g -35 g -37 g = 312 g

The new number of eggs is 2 fewer: N' = 12 -2 = 10.

So, the new average weight is ...

  avg' = W'/N' = 312 g/10 = 31.2 g

__

Additional comment

By working with the differences from average, we don't have to figure the old and new sums. We're only concerned with the way that sum changes, and the average amount of that change. Often, this means we can solve the problem using only mental arithmetic.

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The formula to find the 10th term of the sequence is -512(x-1).

The given sequence is generated by starting with the term x-1 and then multiplying each term by -2 to get the next term.

Therefore, the nth term of the sequence can be expressed as:

[tex](-2)^(n-1) * (x-1)[/tex]

To find the 10th term of the sequence, we substitute n = 10 into the formula

[tex](-2)^(10-1) * (x-1) = (-2)^9 * (x-1)[/tex]

= -512(x-1)

So the formula to find the 10th term of the sequence is -512(x-1).

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The average rate of change of the function over the interval is 4x + 2h

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

f(x) = 2x² + 9

The interval is given as

From x = x to x = x + h

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(x) = 2x² + 9

f(x + h) = 2(x + h)² + 9

Next, we have

Rate = (2(x + h)² + 9 - 2x² - 9)/(x + h - x)

Evaluate

Rate = 4x + 2h

Hence, the rate is 4x + 2h

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Answer:

The answer is 692

Step-by-step explanation:

a₁₇ = 72, a₅₁ = 208

aₙ = a + (n-1)d

a₁₇ =a + 16d = 72→ 1

a₅₁ = a + 50d = 208 →2

2-1

34d = 136

d= 4

a₁₇ = a + 16d = 72

72 = a + 64

a = 8

a₁₇₂ = a + (172-1)4

a₁₇₂ = 692

[tex]P=100\left( \frac{1}{2} \right)^{\frac{t}{30000}} \\\\[-0.35em] ~\dotfill\\\\ \boxed{A}\\\\ t=20000\hspace{5em}P=100\left( \frac{1}{2} \right)^{\frac{20000}{30000}}\implies P=100\left( \frac{1}{2} \right)^{\frac{2}{3}}\implies P\approx 63.0 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ P=40\hspace{5em}40=100\left( \frac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{40}{100}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}[/tex]

[tex]\cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{1}{30000}t}\implies \log\left( \cfrac{2}{5} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}t} \right] \\\\\\ \log\left( \cfrac{2}{5} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}} \right]\implies \cfrac{\log\left( \frac{2}{5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{30000}} \right]}=t\implies 40000\approx t[/tex]

Based on the information provided, the total area of the shape given is 25 square centimeters.

The shape given is made up of two different shapes or two different rectangles. Due to this, to calculate the area, let's calculate the area of each of the rectangles, and then let's add the areas obtained.

First rectangle:

area = side x side

area = 2 cm x 3 cm

area = 6 square centimeters

Second rectangle:

area = side x side

area = 4 cm x 2 cm

area = 8 square centimeters

Total area: 6 square centimeters +  8 square centimeters

Total area = 14 square centimeters

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Answer:

B = 76, C = 38

Step-by-step explanation:

A + B + C = 196

substitute A = 82 and B = 2C into the equation

82 + 2C + C = 196

82 + 3C = 196 ( subtract 82 from both sides )

3C = 114 ( divide both sides by 3 )

C = 38

B = 2C = 2 × 38 = 76

Answer:

(4 - π)r²

= 0.86 r²

Step-by-step explanation:

The radius of the circle = r

The diammeter of the circle = 2r

Area of circle = πr²

The side of the square = diammeter of the circle = 2r

The area of the square = (2r)² = 4r²

Area of shaded region = ar(square) - ar(circle)

= 4r² - πr²

= (4 - π)r²

= (4 - 3.14)r²

= 0.86 r²

The value of x in the given expression is 1/25

Given the expression :

To solve for x, we make x the subject of the expression

5x = 1/5

multiply both sides by 5

25x = 1

divide both sides by 25 to isolate x

x = 1/25

Therefore, the value of x in the expression is 1/25

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Answer:

Answer 1008

Step-by-step explanation:

The statements that are true are:

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

C. f(-1) = 6

To determine the truth of each statement, we need to analyze the given table of values for the function f(x).

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

The x-values listed in the table are -2, -1, 0, 1, 2, 3, 4, 5, and 6. These are the inputs for the function, and therefore, they represent the domain of f(x). Thus, statement A is true.

B. The range for f(x) is all real numbers.

Looking at the y-values listed in the table for f(x), we can see that the range of f(x) is from 5 to 13. It does not include all real numbers, so statement B is false.

C. f(-1) = 6

From the table, we can see that when x = -1, f(x) = 6. Thus, statement C is true.

D. f(5) = -2

There is no entry in the table for f(5), so we cannot determine the value of f(5) from the given information. Therefore, statement D is false.

In conclusion, the true statements are A and C.

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Answer:

Step-by-step explanation:

Bob made a little mistake there. 5 multiplied by 800 is actually equal to 4,000.

The function [tex]y = e^4x[/tex] has a range of (0,∞). Here's why: The range of a function is the set of all possible output values.

To determine the range of a function, you must examine its graph or find the output for every input value.

In this case, [tex]y = e^4x[/tex] is an exponential function with a base of e, which is a constant that is approximately equal to 2.71828.

The exponential function [tex]y = e^x[/tex] is always positive.

Therefore, [tex]y = e^4x[/tex] will also be positive for all values of x.

As a result, the function's range will start at 0 and continue up to positive infinity, but will not include 0.This can be shown by graphing the function or plugging in various values of x to see what output values result. However, by knowing the properties of exponential functions, you can determine the range of[tex]y = e^4x[/tex] without graphing it.

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Answer:

Both are incorrect

Step-by-step explanation:

In the right triangle ΔABC, ∠ABC = 90 and two angles = 45,

∠ACB = ∠BAC = 45

Therefore, the sides opposite to these angles are equal

⇒ x = z

By  Pythagorean theorem,

x² + z² = y²

⇒ x² + x² = y²

⇒ 2x² = y² -----eq(1)

In the right triangle ΔABD,

∠ADB = 90

∠BAD = 45 (since ∠BAC = 45)

⇒ ∠ABD = 180 - 90 - 45

⇒ ∠ABD = 45

Since ∠BAD = ∠ABD = 45, the sides opposite to these angles are equal

⇒ AD = 3

Also since ΔABC is an isoceles triangle, BD bisects AC

⇒ AD = DC = AC/2 = y/2

⇒ y/ 2 = AD

⇒ y = 2AD

⇒ y = 2(3)

⇒ y = 6

From eq(1)

2x² = y²

⇒ 2x² = 6²

⇒ x² = [tex]\frac{6^2}{2}[/tex]

⇒ [tex]x = \sqrt{\frac{6^2}{2} }[/tex]

⇒[tex]x = \frac{6}{\sqrt{2} }[/tex]

and

[tex]z= \frac{6}{\sqrt{2} }[/tex]

[tex]f(x)=7\cos(2x)\hspace{5em}f\left( -\frac{\pi }{4} \right)=7\cos\left( -\frac{\pi }{4} \right) \\\\\\ f\left( -\frac{\pi }{4} \right)=7\left( \frac{\sqrt{2}}{2} \right)\implies f\left( -\frac{\pi }{4} \right)=\cfrac{7\sqrt{2}}{2}[/tex]

The solutions to the matrices are

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

The matrices

The dimensions of the matrices are

A = 2 by 3 i.e 2 rows and 3 columns

B = 3 by 2 i.e 3 rows and 2 columns

For the positions of the matrices, we have

A₂₁ = 4

B₁₂ = 8

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Answer:

Exact Form:

35/6

Decimal Form:

5.83

Mixed Number Form:

5 5/6

Answer:8/3

Step-by-step explanation:

4-4/3

=12-4/3

=8/3

The equivalent expression after combining like terms is 15.4z - 12.

To combine like terms and simplify the given expression, let's distribute the -5 to the terms inside the parentheses and then combine the like terms:

Expression: 7.4z - 5(-1.6z + 2.4)

Distributing -5 to the terms inside the parentheses:

7.4z - 5(-1.6z) - 5(2.4)

Simplifying the distributed terms:

7.4z + 8z - 12

Combining the like terms:

(7.4z + 8z) - 12

(7.4 + 8)z - 12

15.4z - 12

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The correct match of the following item to their definitions are:

A writ authorizing or ordering someone to do something. The term frequently refers to a judge's writ authorizing law enforcement to conduct certain actions, such as making an arrest, searching a place, or seizing property.

A claim is to declare or insist that something is true, usually without giving any support or proof.

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The gap in the histogram tells her that she did not earn any wages that week.

A histogram is a graphical data representation that reveals a dataset's distribution. It consists of a sequence of bars, where the height of each bar denotes the frequency or count of data points falling inside a given range and the width of each bar denotes a range of values.

Alexandra's pay histogram shows a gap from 21 to 30, which indicates that she did not work that week. This is so because no wages in the range of 21 to 30 are recorded in the histogram, which displays the amount she made each week.

It's possible that Alexandra was on vacation or ill and unable to work that week. Whatever the cause, the histogram gap indicates that she did not get any pay that week.

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These methods can be used in the construction of water tanks, oil storage tanks, cans, and tubes. They can also be used in the engineering sector to determine the Volume of certain cylinders like pipes and cylinders.

The cylinder is a geometrical figure which is three-dimensional with two parallel circular bases. There are different ways to calculate the area of a cylinder and the surface area of a cylinder.

The methods and formulas of calculating the area of a cylinder and the surface area of a cylinder are explained below.Area of a CylinderThe area of a cylinder is defined as the region occupied by the cylinder on a two-dimensional plane.

The formula used to calculate the area of a cylinder is A = 2πr² + 2πrh. Here, r denotes the radius of the circular base, and h denotes the height of the cylinder. The area of curved surface area of a cylinder is 2πrh. Surface Area of a Cylinder

The surface area of a cylinder refers to the total area of the figure including the area of the two bases of the cylinder.

The formula for calculating the surface area of a cylinder is A = 2πr(h + r). Here, r denotes the radius of the circular base, and h denotes the height of the cylinder. The surface area of the two circular bases of a cylinder is 2πr².

The two methods of calculating the area of a cylinder and the surface area of a cylinder are very essential in solving real-life problems.

For instance, these methods can be used in the construction of water tanks, oil storage tanks, cans, and tubes. They can also be used in the engineering sector to determine the volume of certain cylinders like pipes and cylinders.

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Answer:

10

Step-by-step explanation:

2x = 2(-10 + 2x)

x = -10 + 2x

-x = -10

x = 10

Answer:

10

Step-by-step explanation:

Multiply the smaller line by 2

which is RS

2x = -20 + 4x

-2x = -20

x = 10

The algebraic expression (3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) can be simplified to give 3x/(x - 3) which makes the option D correct.

Simplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.

Simplifying the algebraic expression we have:

(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4)

by factorization;

3x² - 6x = 3x(x - 2)

x² - 6x + 9 = (x - 3)(x - 3)

x² - x - 6 = (x - 3)(x + 2)

x² - 4 = (x + 2)(x - 2)

(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) = 3x(x - 2)/(x - 3)(x - 3) × (x - 3)(x + 2)/(x + 2)(x - 2)

cancel out common factors we have;

(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) = 3x/(x - 3)

Therefore, the algebraic expression (3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) can be simplified to give 3x/(x - 3)

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Answer:

23 would form the base

7 would form the exponent

Step-by-step explanation:

23 is being multiplied by itself 7 times, so you can write it as [tex]23^7[/tex] where 23 is the base and 7 is the exponent

Answer:

I would say D

Step-by-step explanation:

since it already tells you what y equals it makes it easier to substitute the others take more work so the best first step is substituting for y

Answer:

Option D) Substitute for y in the first equation

Step-by-step explanation:

When solving for a system of equation, we always need 1 equation to have x or y already isolated by itself.  This makes it easy to substitute that variable into the other equation, solve, then substitute the other variable into another equation.

This will give us an ordered pair, known as the solution.

In this system, we have 2 equations.  In the first one, we have no variables isolated.  In the second one, we have y isolated on the left side of the equal sign.  This means we can take what y equals (3x+2) and substitute that in for y in the first equation.

Hope this helps! :)

The best answer choice among the given options is O 15 m², as none of the provided options match the correct Ccalculation.

To find the area of a rhombus, we need the lengths of the diagonals. In this case, the lengths of the diagonals are not provided. However, we can use the given information to determine the area based on the side lengths.

A rhombus is a quadrilateral with all sides of equal length, so the given side lengths of 5.5 m and 2 m can help us find the area.

We know that the diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right triangles. Each side of the rhombus is the hypotenuse of one of these triangles.

Given that the side length is 5.5 m, we can consider one of these right triangles. One leg of the right triangle is half of the side length, which is (5.5 m)/2 = 2.75 m. The other leg of the triangle is the length of the diagonal, which is unknown.

Using the Pythagorean theorem, we can find the length of the diagonal:

(diagonal)^2 = (leg)^2 + (leg)^2

(diagonal)^2 = (2.75 m)^2 + (2 m)^2

(diagonal)^2 = 7.5625 m² + 4 m²

(diagonal)^2 = 11.5625 m²

diagonal ≈ √11.5625 m ≈ 3.4 m (rounded to the nearest tenth)

Since the diagonals of a rhombus are perpendicular bisectors of each other, the length of the other diagonal would also be approximately 3.4 m.

Now, we can calculate the area of the rhombus using the formula: area = (diagonal1 * diagonal2) / 2

area = (3.4 m * 3.4 m) / 2

area = 5.8 m²

The area of the rhombus is approximately 5.8 m².

The best answer choice among the given options is O 15 m², as none of the provided options match the correct area calculation.

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Answer:

2/3

Step-by-step explanation:

You set up the formula then come out with 2/3

Its also positive because the arrows are facing to the right.