nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

The two column proof that completes each statement is as shown below.

We are given that ∠ABD = 85°

We are also told that;

Statement 1: m∠ABC + m∠CBD = M∠ABD

Reason 1: Angle Addition Postulate

Statement 2; m∠ABC + x° = 85°

Reason 2; Substitution Property

Statement 3; m∠ABC + x° - x° = 85° - x°

Reason 3; Subtract x° from both sides.

Statement 4;  m∠ABC = 85° - x°

Reason 4;  Simplify

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Answer:

[tex]7.2\leq pH\leq 7.8[/tex]

(any variable can be used in place of "pH")

Step-by-step explanation:

Since the pH has to be between 7.2 and 7.8, it is more than 7.2 and less than 7.8.

The less than equal to sign was used because the pH can also equal 7.2 and 7.8.

Like mentioned, any variable like x can be used instead of the "pH" I put in the equation, but make sure to define your variable.

Hope I helped!!! :)

Answer:

x= 32

Step-by-step explanation:

3x-2+3x-10= 180 (sum of angles in straight line)

6x-12=180

6x=192

6x/6= 192/ 6

x = 32

Step-by-step explanation:

3x - 2 ° + 3x - 10° = 180°

reason : being angle in linear pair ...

6x - 12 = 180°

6x = 180° + 12

6x = 192°

[tex] x = \frac{192}{6} \\ [/tex]

x = 32°

Now ,

3x - 2 °

= 3 × 32 - 2

= 96 - 2

= 94°

Again ,

= 3x - 10°

= 3 × 32 - 10°

= 86°

☘☘☘...

b - a = 5

Here we have to find the value of b-a,

Where, a = 2 and b =7

By putting the value of a and b we have,

b - a =7 - 2

       = 5

Therefore b-a = 5 that is option b is the correct answer.

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59263 divided by a number raised to the power of 10 × 843 is presented as follows;

[tex] \frac{59263}{843}\times x^{-10} [/tex]

The given number to be divided is 59263

Let x represent the number that is raised to the power of 10, we have;

The number by which 59263 is divided = x¹⁰ × 843

Therefore, we have;

[tex] \frac{59263}{x^{10} \times 843} = \frac{59263}{843}\times x^{-10} [/tex]

The given expression expressed using the rules of indices is therefore;

[tex] \frac{59263}{843}\times x^{-10} [/tex]

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The circumference of the given circle is: 16πcm.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Given: Area of a circle = 64π cm²

To find: Circumference of the circle.

Finding:

We know that the formula of the area of a circle = πr²,

On comparing it with the given value, we get:

πr² = π(64)

πr² = π(8)²

8² = r²

r = 8cm (as the side of a circle can never be negative).

Also, the formula of the circumference of a circle = 2πr

Thus, for the circle having radius 8 cm, circumference = 2π(8) = 16πcm.

Hence, The circumference of the given circle is: 16πcm.

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Answer:

Y = 44

Step-by-step explanation:

44/4 - 2 = 9

11 - 2 = 9

Y = 44

<3

89 degrees

Triangles will always have 180 degrees. This means that given 2 angles, we can find the missing measurement.

Setting Up an Equation

To help us solve for the unknown angle, a, we can set up an algebraic equation. To make this equation remember that all 3 internal angles sum to 180.

This is only one equation that you could set up to represent this situation.

Solving For a

Now that we have an equation we can begin to solve it. First, combine like terms that are on the same side of the equation.

Next, subtract 91 from both sides.

To check our answer we can plug it back into the original equation.

This means that the missing angle must be 89 degrees.

Answer:

x + 10

Step-by-step explanation:

It says 10 MORE than a number.

SO that's + 10

The numbr is x so:

x + 10

Answer

x + 10

Step-by-step explanation:

The question asking "more than" implies that you need to add, and x represents your unknown number.

how much is in the spice mix? context is necessary

See attachment for the graph of the function and the features

The function is given as

h(x) =(x - 1)^2 - 9

The x-intercept

Set h(x) to 0

So, we have

(x - 1)^2 - 9 = 0

Add 9 to both sides

(x - 1)^2 = 9

Take the square root of both sides

x - 1 = ±3

This gives

x = 1 ± 3

Expand

x = (1 - 3, 1 + 3)

Evaluate

x = (-2, 4)

Hence, the x-intercepts are x =2 and x = 4

The y-intercept

Set x to 0

So, we have

h(0) = (0 - 1)^2 - 9

Evaluate

h(0) = -8

Hence, the y-intercept is h(x) =-8

The vertex

We have

h(x) =(x - 1)^2 - 9

Expand

h(x) = x^2 - 2x + 1 - 9

Differentiate

h'(x) = 2x - 2

Set to 0 and solve for x

2x - 2 = 0

This gives

x = 1 --- this represents the axis of symmetry

Substitute x = 1 in h(x) =(x - 1)^2 - 9

h(1) =(1 - 1)^2 - 9

Evaluate

h(1) = -9

Hence, the vertex of the function is (1, -9)

See attachment for the graph of the function and the features

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Answer:

I don't know

Step-by-step explanation:

I don't know

The unit rate in minutes per meter is 12½ min./m if it takes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters.

It takes 15/2 mins to fill an empty aquarium to a depth of 3/5 meters.

In a situationism like this we can make a equation such as

15/2 = 3/5

Lets multiply 5 in both sides

15/2 × 5= 3/5 × 5

75/2 = 3

Now lets divide both sides with 3

(75/2)/3 =3/3

25/2 = 1

Thus, the unit rate in minutes per meter is 12½ min./m if it akes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters.

Which car goes faster, a car that travels 42 miles in three hours or a car that travels 132 miles in seven hours? The solution is determined by the unit rate of each automobile. Rather than comparing the distances traveled in two or seven hours, compare how far each car drives in one hour.

A unit rate is just a ratio of two unit values, with the denominator always being one. This enables easy comparison of data values. To mention a few, common unit rates in the real world include miles per hour (MPH), price per unit, miles per gallon (MPG), revolutions per minute (RPM), and pay per year.

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If a quadrilateral is a rhombus, then opposite sides are congruent.    True

If a quadrilateral is a rhombus, then it is a rectangle.                              False

If a quadrilateral has four right angles, then it is a square.                     True

If a quadrilateral is a square, then it is a rectangle.                                  True

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. Four non-collinear points are connected to produce it. A quadrilateral's internal angles add up to 360 degrees in all cases.

The Latin words "Quadra" for four and "Latus" for "sides" are combined to get the English word quadrilateral. A quadrilateral need not have equally long sides on all four sides. So, depending on the sides and angles, we can have many quadrilateral forms.

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The measure of angle A in the triangle is 18°

The angles in the triangle are given as:

m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°

The sum of angles in a triangle is 180

So, we have

m∠A + m∠B + m∠C = 180

Substitute the known values in the above equation

So, we have:

2x − 24 + x + 8 + 4x + 49 = 180

Evaluate the like terms

7x = 147

Divide both sides by 7

x = 21

Substitute x = 21 in m∠A = (2x − 24)°

m∠A = (2 * 21 − 24)°

Evaluate

m∠A = 18°

Hence, the measure of angle A in the triangle is 18°

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By compatibility principle of inequalities we complete the following sentence:

If p and q are negative integers such that p² > q², then p³ < q³. (Correct choice: B)

According to the statement, the elements p and q are negative integers such that p² > q². By the sign law, the product of two negative numbers is always equal to a positive number, then by compatibility principle:

p² > q²                   Given

p · p > q · q            Definition of power

p < q                       Compatibility principle

p³ < q³                    Compatibility principle / Result

Please notice that the inequality symbol, that is, from "<" to ">" and viceversa, changes when the compatibility principle is applied in the given inequality.

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i.  The equipment elevator is at a depth of 270 feet (-270 feet), while the miners elevator is at a depth of 180 feet (-180 feet) below the surface.

ii. The equipment elevator is deeper than that of the miners elevator.

The speed of an object is the rate at which the object moves.

speed = distance / time.

Thus,

Speed of the equipment elevator = 6 feet per second

Speed of the miners elevator = 15 feet per second.

Time of descent of the equipment elevator = 33 + 12

                                                                   = 45 seconds

So that, the distance of the elevator at this time is;

⇒ distance = speed x time

                  = 6 x 45

                   = 270 feet

 distance = - 270 feet

The distance of the miners elevator after 12 seconds is:

⇒ distance = speed x time

                  = 15 x 12

                  = 180 feet

distance = - 180 feet

Thus after another 12 seconds, the equipment elevator is at a depth of 270 feet (-270 feet), while the miners elevator is at a depth of 180 feet (-180 feet) below the surface.

Therefore, the equipment elevator is deeper than that of the miners elevator.

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average inflation rate of cold drink will be 100%

Inflation is the term used to describe an increase in the price of goods and services that households buy. It is determined by how quickly these prices fluctuate. Prices frequently rise with time, but they can also fall (a situation called deflation).

You will subtract the starting price (A) from the later price (B), and divide it by the starting date (A). Then multiply the result by 100 to get the inflation rate percentage.

FORMULA FOR FINDING AVERAGE INFLATION = ((B-A)/A)*100

            plugging in the values =

∵ given in the question that cost will double in the next 8 years i.e.

                                                                             = Rs. 4.50 * 2

                                                                             = Rs.9.00

∴ when we plug in  the values in the formula we get

                                                 = ((9-4.5)/4.5) * 100

                                                 = 100 % inflation rate

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[tex]16 : (200 \cdot 100) =[/tex]

[tex]16 : 20000 = 0.0008[/tex]

Answer:

8

Step-by-step explanation:

To solve this problem we use PEMDAS; Parenthesis, Exponents, Multiply, divide, add, subtract

Let's set up an equation:

16/200*100

Now let's solve:

16/200=0.08

Now we multiply 0.08 by 100

0.08*100=8

Thus, our answer is 8

Answer:

3rd option

Step-by-step explanation:

find the cost of 1 ounce and see which one is the cheapest

Answer: -81

Hope this helps

Answer:

In points (1,2), 1 is the value of X which represents Time in Hours and 2 is the value of Y which means Cost or $ per hour for the duration of the parking in the lot. I hope this helps.

Step-by-step explanation:

Students no longer have to visit a physical store to buy course books because most course books can now be obtained online.

What should you try first if an online course is having technical issues?

What drawbacks exist with online learning?

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Answer:

3 1/5

Step-by-step explanation:

8×2/5 is 16/5= 3 1/5

because u multiple the top number

Answer:

m³

Step-by-step explanation:

have a good night :)

:)

The number of the dollars given to the charity will be $99,000,000.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that someone has a net worth of 7.92×10¹⁰.Suppose that this individual now decides to give one-eighth of a percent of his new net worth to charity.

The number of dollars given to the charity will be calculated as below:-

Networth: 7.92 × 10¹⁰.

The percentage given to the charity is:-

1/8 %= 0.125 % = 0.00125 × networth

The number of dollars given to the charity is:-

Number of dollars = 0.00125 × 7.92 × 10¹⁰.

Number of dollars = $99,000,000.

Therefore, the number of dollars given to the charity will be $99,000,000.

The complete question is given below:-

If someone has a net worth of 7.92 × 10¹⁰.Suppose that this individual now decides to give one-eighth of a percent of his new net worth to charity. How many dollars are given to charity?

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The expression (8x+64) can be rewritten as a common factor as 8(x+8).

According to the question,

We have the following expression:

(8x+64)

It is to be noted that a common factor is such a number including a variable that it can completely divide a term. For example, in this expression, 8 is such a number that it can divide both 8x as well as 64.

(This can be better understood using more examples. For example, 4 is a common factor in 4x+24 and 5 is a common factor in 5x+30.)

Now, taking 8 as a common factor:

8 (x+8)

Hence, the correct expression is D (the fourth one).

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