-1,080?379?-3?15=-683 find missing operators

The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.

In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.

The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:

z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])

where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).

In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:

z - 7 = (-3)(x - 5) + (7)(y - 4)

Simplifying this equation, we get:

z = -3x + 7y + 8

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Answer:

x −4 −3 −2

P(X=x) 0.55 0.39 0.06

Step-by-step explanation:

Answer:The answer is 2.5 pints.

1. The difference between the temperature is 14°C.

2. The value of the expression will be -3x - 6y + 27.

The difference between the temperature will be:

= -10 + 24

= 14°C.

For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:

x + 2y - 5

Next, multiply this expression by 3:

3(x + 2y - 5) = 3x + 6y - 15

Finally, substitute this back into the original expression:

12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27

So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.

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Answer:

1. -7

2. -1

3. 5

Step-by-step explanation:

Substitute the value given into the equation

The equation that best represents the curve of best fit for this set of data is y = ae^{bx}, where a and b are constants to be determined by the data points.

An equation is a mathematical expression that uses symbols, such as numbers and variables, to represent a relationship between two or more values or quantities. Equations are used to describe physical laws, solve problems and to make predictions. Equations are fundamental to all areas of mathematics and science, and their use is essential for understanding and exploring the natural world.


This equation is an example of an exponential function, which is used to model data that increase or decrease at an increasing rate. The constants a and b can be determined using a least-squares regression to find the line of best fit. The equation can then be used to extrapolate future values from the data points.

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The length of the arc that the tip of the pendulum travels is approximately 7 feet.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We can use the formula for the length of an arc of a circle to find the length of the arc that the tip of the pendulum travels:

Arc length = (angle/360) x 2πr

where: angle = the central angle (in degrees or radians) that the arc subtends and r = the radius of the circle

First, we need to convert the angle from degrees and minutes to decimal degrees.

There are 60 minutes in a degree, so:

40°6' = 40 + 6/60 = 40.1 degrees

Now we can plug in the values:

Arc length = (40.1/360) x 2π(10 feet)

Arc length = 6.99 feet

Hence, the length of the arc that the tip of the pendulum travels is approximately 7 feet.

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The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).

By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.

Given function is xy²= 4. The given expression will be different as below,

dy / dx ( xy² ) - 4 = 0

2xy( dy / dx) + y² = 0

dy / dx = -y / 2x

Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).

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The total amount of the single payment will be $6,924.95.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The rate of interest is given as,

r = 0.0775 / 2

r = 0.03875

The amount for 2 years is given as,

A = $1,300 × (1 + 0.03875)⁴

A = $1513.52

The amount for 5 years is given as,

A = $3,700 × (1 + 0.03875)¹⁰

A = $5,411.43

The total amount of repayment is given as,

Total amount = $1513.52 + $5411.43

Total amount = $6,924.95

The total amount of the single payment will be $6,924.95.

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On solving the provided question we can say that The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.

z(180) = (180-185)/4  = -1.25

P(x < 180) = P(z < -1.25)

3)28 C 5

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The relationship between precalculus and calculus has been explained and both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity etc.

Precalculus is the study of mathematics or the course that includes algebra, trigonometry etc. to make a student for study the calculus . The precalculus covers the topics likes complex numbers, composite numbers, trigonometric functions, vectors, matrices, probability etc.

Calculus is the study of mathematics that deals with the rate of changes. Applications of the calculus are finding the slope of the curve, finding the area of region, calculation of x intercept and y intercept etc.

Both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity, acceleration, area, volume etc.

Therefore, the relationship between precalculus and calculus has been explained

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[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.

Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

Annie made 4 glasses of juice

To find = fraction of juice that was left

Total glasses of juice = 4

Her 5 friends drank 1/2 glass each

= 5 × [tex]\frac{1}{2}[/tex]

= [tex]\frac{5}{2}[/tex]

Fraction of juice that left,

5 - [tex]\frac{5}{2}[/tex]

Subtracting by taking LCM,

= [tex]\frac{10 - 5}{2}[/tex]

= [tex]\frac{5}{2}[/tex]

[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.

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Answer:

2

:

5STEP

2

:

Trying to factor as a Difference of Squares:

2.1 Factoring: 5-3x2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

5 - 3x2 = 0

STEP

3

:

Solving a Single Variable Equation:

3.1 Solve : -3x2+5 = 0

Subtract 5 from both sides of the equation :

-3x2 = -5

Multiply both sides of the equation by (-1) : 3x2 = 5

Divide both sides of the equation by 3:

x2 = 5/3 = 1.667

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 5/3

The equation has two real solutions

These solutions are x = ±√ 1.667 = ± 1.29099

Two solutions were found :

x = ±√ 1.667 = ± 1.29099

Answer:

The width of the living room is 10 feet.

Step-by-step explanation:

Let the width of the living room is w.

And the length of the room is 2w - 8 ft.

Given,

The area of the room is 192  feet^2, by using the formula of area of a rectangle we get,

A = l × w

192 = (2w - 8) × w

Now,

192 = 2w^2 - 8w                              ( By expanding)

200 = 2w^2                                     (By adding 8w to both sides)

100 = w^2                                        (Dividing both sides by 2)      

If we take square root on both sides,

w = 10

So,

The width of the living room is 10 feet.

Answer:

  $20M

Step-by-step explanation:

You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.

The minimum rent is ($5/ft²)×(120000 ft²) = $600,000.

The amount of sales that makes $600,000 equal to 3% of sales is ...

  $600000 = 0.03s

  s = $600000/0.03 = $20,000,000

The "natural breakpoint" is $20M in sales.

__

Additional comment

When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.

On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4

The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.

By BODMAS

2.4of4.5-5.6/1.4+3.8*2

10.8-5.6/1.4+3.8*2

10.8-4+3.8*2

10.8-4+7.6

14.4

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Answer:

The correct answer is D. Step 4 is incorrect and should be 10x = 24.

The answers are mentioned below.

In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.

i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).

ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).

iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).

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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards

In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.

i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.

Therefore, the displacement can be calculated as the

√(500² + 300²)

= 583.1 yards (rounded to the nearest hundredth).

ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.

Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be

360 - 31.39

= 328.61 degrees (rounded to the nearest hundredth).

iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.

However, the true bearing is measured from the north and therefore, the true bearing would be

90 + 59.04

= 149.04 degrees (rounded to the nearest hundredth).

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Using fitted curve, a similar new blockbuster would expect

A fitted curve is a curve that is created to model a set of data points, such that the curve passes as closely as possible to the points. The process of finding a fitted curve is called curve fitting or regression analysis.

Tracing the fitted curve, we have that

week 1 = 150 million

Week 2 = 75 million

Week 3 =  40 million

Week 4 =  25 million

Adding up the amounts

= 150 + 75 + 40 + 25

= 290 million

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The number of students who either play hockey or football is given by the equation n ( A ∪ B ) = 45 students

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the total number of students in the class be n ( U ) = 50 students

Let the number of students who play hockey be n ( A ) = 20 students

Let the number of students who play football be n ( B ) = 35 students

Let the number of students who play hockey and football n ( A ∩ B ) = 10

So , from the set theory n(A∪B) = n(A) + n(B) - n(A⋂B)

Substituting the values in the equation , we get

The number of students who play hockey or football = 20 + 35 - 10

On simplifying the equation , we get

The number of students who play hockey or football = n( A ∪ B ) = 45 students

And , the number of students who do not play hockey or football is given by the equation = n ( U ) - n ( A ∪ B )

On simplifying the equation , we get

The number of students who do not play hockey or football = 50 - 45 = 5 students

Hence , the number of students who play hockey or football is 45 students

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Answer:

Step-by-step explanation:

Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:

lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞

As x approaches negative infinity, the square root of x approaches 0, so the function approaches:

lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7

Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.

Step-by-step explanation:

It can  be estimated that there are 395 penguins in the area.

Proportion is a mathematical comparison between two numbers.  According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".

We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.

The proportion should therefore be [tex]x:53=82:11[/tex]  where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:

[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]

Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.

395 penguins are in the area according to our estimation.

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The longest side of a triangle is always opposite the,

A. angle with the greatest measure.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

We know, The length of the largest side in a triangle is opposite to the largest angle.

The statement, The longest side of a triangle is always opposite the

angle with the greatest measure.

Because A longer angle will be more spread out and hence the opposite side will be longer too.

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The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.

In trianngles ΔKTW and ΔRWT, then we have

KW = TR        {Given}

∠W = ∠T       {Isosceles angles}

WT = WT       {Common side}

Then the trianngles ΔKTW and ΔRWT are congruent to each other.

The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.

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The graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x-5.

Substitute x=0, 1, 2, 3, 4, ..... in the equation y=2x-5, we get

When x=0,

y=-5

When x=1,

y=-3

When x=2,

y=-1

When x=3

y=1

So, the ordered pair is (0, -5), (1, -3), (2, -1), (3, 1) and so on.

Therefore, the graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.

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This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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The volume of the cone shown can be described to be A. 513 π cubic units

The volume of a cone can be found by the formula :

= π x radius ² x height / 3

The radius of this cone is 9 units and the height is 19 units.

The volume of this cone then is :

= π x radius ² x height / 3

= π x 9 ² x 19/ 3

= π x 81 x 19/ 3

= π x 513

= 513 π cubic units

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