Evaluate the limit.lim(x,y)→(4,−4)3x2−3y2x+y

Lorenzo uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85

The cost of each pizza is $12.95.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

Lorenzo orders 3 pizzas for delivery.

The total bill, including a $4.00 delivery fee, is $42.85.

He uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85

3c = 42.85 - 4

3c = 38.85

c = 12.95

Therefore, the cost of each pizza is $12.95.

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A straight angle is a 180-degree angle formed by two sides that create a straight line.

It represents a complete reversal of direction and plays a fundamental role in geometry and practical applications involving angles and spatial relationships.

A straight angle is an angle that measures 180 degrees.

It is formed by two sides that are opposite to each other and together form a straight line.

The concept of a straight angle can be visualized as a half turn, where you rotate or pivot around a point by 180 degrees, resulting in a complete reversal of direction.

The measurement of 180 degrees for a straight angle is derived from the fact that a complete circle is divided into 360 degrees.

Since a straight angle covers half of the circle, it occupies 180 degrees.

In geometry, a straight angle can be formed by combining two right angles.

A right angle measures 90 degrees, so when two right angles are placed next to each other, they create a straight angle with a total measurement of 180 degrees.

This relationship highlights the complementary nature of right angles within a straight angle.

Understanding the concept of a straight angle is essential in geometry and helps in analyzing and classifying various angles.

By recognizing and identifying straight angles, we can apply geometric principles and solve problems involving angles, lines, and shapes.

In real-life applications, knowledge of straight angles can be useful in areas such as engineering, architecture, and navigation.

It allows for accurate measurement and calculation of angles, ensuring precise positioning and alignment in various structures and systems.

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Answer:

the answer is c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

just took the test

The statement given "regression equations are usually used to predict values of unavailable data. if the data do not closely model a particular type of function, then that type of function is not appropriate to use in statistical regression. the more closely data fit a model, the more predicted values will be." is true because regression equations are indeed employed for predicting values of unavailable data.

Regression equations are commonly utilized to make predictions for unavailable data. When the data does not closely conform to a specific type of function, that function is deemed inappropriate for statistical regression. The accuracy of predicted values is contingent on the degree of resemblance between the data and the chosen model. Hence, a strong fit between the data and the model enhances the reliability of predicted values, ensuring that regression analysis is effectively applied for making accurate predictions.

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Answer:

The is m = 1

y = -8 + x

Step-by-step explanation:

check m a t h w a y to make sure I am right and you have what you are looking for

Answer:

Step-by-step explanation:

6) √48, √12

√48 = √4² x 3 = 4√3

√12 = √2² x 3 = 2√3

= 4√3, 2√3

7) √28, √63

√28 = √2² x 7 = 2√7

√63 = √3² x 7 = 3√7

=2√7, 3√7

8) ⁴√32, ⁴√162

⁴√32 = ⁴√2⁴ x 2 = 2 ⁴√2

⁴ √162 = ⁴√3⁴ x 2 = 3 ⁴√2

=2 ⁴√2, 3 ⁴√2

9) ∛40, ∛135

∛40 = ∛2³ x 5 = 2∛5

∛135 = ∛3³ x 5 = 3∛5

=2∛5, 3∛5

10) √8, √200

√8 = √2² x 2 = 2√2

√200 = √10² x 2 = 10√2

=2√2, 10√2

-{ModPatrol}

Answer:

\(d=\sqrt{58}\approx7.6\)

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

\(d=\sqrt{(-2-1)^2+(8-1)^2\)

Subtract:

\(d=\sqrt{(-3)^2+(7)^2\)

Square:

\(d=\sqrt{9+49}\)

Add:

\(d=\sqrt{58}\)

This cannot be simplified.

So, the distance between the two points is √58 or about 7.6 units.

And we're done!

So... where's my cookie :)?

Answer:

a) = 7x² + 4y²

b) = 3x + 7xy - 7

Step-by-step explanation:

a) = (9 - 2) x² + (-3 + 7) y²

= 7x² + 4y²

b) = (8 - 5) x + (3 + 4) xy - 7

= 3x + 7xy - 7

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer: A (3, -4)

Step-by-step explanation:

A minimum is at the lowest point on the parabola. The minimum and maximum can be seen by looking at the vertex.

If you go right 3 spaces on the x-axis horizontally, then down 4 spaces vertically on the y-axis you get (3, -4).

4 is negative because you are going down below the x-axis.

That's two possibilities of a total of six =

2/6=1/3=33.33%

(1/3)

Answer:

40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

Given that,

The lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

We have to find identify the container's dimensions and maximum volume.

We know that,

2(x+y)=4

x+y=2

Now,

Volume is π(x/2)²y

=π(x²/4)(2-x)

=π(f(x))

Now, volume will be maximum when f(x) will be max,

f(x)=x²/4(2-x)

f'(x)=2x(2-x)-x²

f'(x)=4x-3x²

We get,

f'(x)=0

4x-3x²=0

x(4-3x)=0

x=0, 4-3x=0

x=4/3

y value is 2-4/3=6-4/3=2/3

Therefore, The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

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Answer:

1144

Step-by-step explanation:

100 + 98 + 96 +.... + 78+76 =

(12-0)/2 (176)  

(6.5) (176) = 1144

The sum of the series will be 1068.

We have the following expression -

\(\sum_{i=0}^{12} 100 - 2i\)

We have to rewrite the series as the sum.

A series in mathematics is the sum of a list of numbers that are generated according to some pattern.

We have the following expression -

\(\sum_{i=0}^{12} 100 - 2i\)

The terms of this series can be calculated by calculating the value of the function at different values of i.

The series is as follows -

100 + 98 + 96 +.... + 78+76

This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -

\(S = \frac{n}{2} \times {2a + (n-1)d}\)

S = \(\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22]\)

S = 6 x 178 = 1068

The sum of the series will be 1068.

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John earned $400 interest at a rate of 6% for 3 years. Therefore, the amount of money John originally invested was $2,222.22.

We are able to use the Simple interest formula to resolve this problem:

Simple interest is a simple concept in finance that is used to calculate the interest earned or paid on a essential amount over a positive time period.

Simple interest = (principal x charge x time)

Given that John earned $400 in interest at a price of 6% for three years, we are able to set up the equation as:

400 = (P x 0.06 x 3)

In which P is the principal (the original amount invested).

Simplifying this equation, we get:

400 = 0.18P

Dividing both facets through 0.18, we get:

P = $2,222.22

Thus, John originally invested $2,222.22.

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Answer:

x = -1

Step-by-step explanation:

10x + 8 = 5x + 3

5x = 3 - 8

x = -1

Answer:

z = 54 − 45. 12.

Step-by-step explanation:

There are 2 tablespoons in an ounce. So for 2 ounces, you will need 4 tablespoons, for 4 ounces 8 tablespoons, and so on.

A tablespoon is a unit of volume measurement in United States, and some other countries. It is equal to approximately 15 milliliters (0.51 fluid ounces). One tablespoon can be further divided into three teaspoons, meaning that one tablespoon is equal to three teaspoons.

In the United States, one tablespoon is equal to 0.5 ounce, which is equal to 14.3 grams. This is slightly different in the UK, where one tablespoon is equal to 0.6 ounces (which is equal to 17.7 grams). To convert tablespoons to ounces, you can use the following formula is 1 tablespoon = 0.5 ounces.

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The equation of the sine wave function can be written in the form: y = A sin(Bθ + C) + D where A is the amplitude, B is the frequency (inverse of the period), C is the phase shift (horizontal shift), and D is the vertical shift (mean value).

A graph is a visual representation of data or mathematical relationships between variables. It typically consists of a set of points or vertices connected by lines or curves, which can help to illustrate patterns or trends in the data. Graphs are used in a wide range of fields, including mathematics, science, engineering, economics, and social sciences, to analyze and communicate information. Some common types of graphs include line graphs, bar graphs, scatterplots, and pie charts.

Here,

Based on the given information, it can be inferred that the function that describes the relationship between the height y, in feet, of the tip of a windmill blade and the angle of rotation Θ made by the blade is a sine wave function. Sine wave functions are periodic and oscillate between an upper bound and a lower bound as the angle increases. The function has a maximum value (upper bound) at Θ=90° and Θ=270° and a minimum value (lower bound) at Θ=0° and Θ=180°. The amplitude of the function is the distance between the maximum and minimum values divided by 2, and the period of the function is the distance between two consecutive maxima or minima.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

Question 1 : A or B or C don't know

Question 2: A = that is what the question is answering

Question 3: B = that is what the question is answering

Question 4: B  = that is what the question is answering

Step-by-step explanation:

The initial velocity (vi) of the ball, when shot into the catcher, is approximately 367.5 m/s.

To solve Eq. 7.5 and Eq. 7.6 for v1​ in terms of m, M, g, and h, we will substitute the given values of m, M, and h into the equations.

Eq. 7.5: mv1​ = (m+M)V2​

Eq. 7.6: (m+M)V22​ = (m+M)gh

Given:

m = 50.0 g (mass of the ball)

M = 200.0 g (mass of the catcher)

h = 15.0 cm (rise in the center of mass)

First, let's solve Eq. 7.6 for V2​ by dividing both sides by (m+M):

V22​ = gh

Next, substitute the expression for V2​ into Eq. 7.5:

mv1​ = (m+M)(gh)

Now, solve for v1​ by dividing both sides by m:

v1​ = (m+M)(gh) / m

Substituting the given values:

v1​ = (50.0 g + 200.0 g)(9.8 m/s²)(0.15 m) / (50.0 g)

Calculating the expression:

v1​ = (250.0 g)(9.8 m/s²)(0.15 m) / (50.0 g)

v1​ = 367.5 m/s

Therefore, the initial velocity (vi) of the ball, when shot into the catcher, is approximately 367.5 m/s.

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here is the answer for question ii

Given the ODE using Frobenius Method x²y"+x²y¹-2y = 0The Frobenius method is used to obtain the power series solution of a differential equation of the form:

xy″+p(x)y′+q(x)y=0Which is given in your question as: x²y"+x²y¹-2y = 0The general form of the Frobenius solution can be expressed as a power series of the form:y(x)=x^r ∑_(n=0)^(∞) a_n x^n+rwhere 'r' is any arbitrary constant and the 'a_n' coefficients are determined from the recurrence relation.

The Frobenius method consists of substituting this power series into the differential equation and equating the coefficient of the same powers of x to zero. This method can be used to solve any second-order differential equation having a regular singular point.

Therefore, substituting the given equation we get:$$ x^2 y'' + x^2 y' - 2y = 0 $$Let the solution of the given equation be:y(x) = ∑_(n=0)^(∞) a_n x^(n + r)Substituting this in the differential equation, we get:$$ x^2y'' + x^2y' - 2y = \sum_{n=0}^\infty a_n [(n+r)(n+r-1)x^{n+r} + (n+r)x^{n+r} - 2x^{n+r}] $$Equating the coefficient of each power of x to zero, we get:Coefficients of x^(r):$$ r(r-1)a_0 = 0 \Rightarrow r=0,1 $$Coefficients of x^(r + 1):$$ (r+1)r a_1 + (r+1)a_1 - 2a_0 = 0 $$Taking r = 0, we get:a_1 - 2a_0 = 0a_1 = 2a_0

The solution becomes:y_1(x) = a_0 [1 + 2x]Taking r = 1, we get:$$ 6a_2 + 3a_1 - 2a_0 = 0 $$a_2 = (1/6) [2a_0 - 3a_1]Substituting the value of a_1 from above, we get:a_2 = a_0/3The second solution is given by:y_2(x) = a_0 [x^2/3 - 2x/3]Therefore, the required solution of the given ODE using Frobenius method is:y(x) = c_1 y_1(x) + c_2 y_2(x)y(x) = c_1 [1 + 2x] + c_2 [x^2/3 - 2x/3]

Hence, the second and third-degree Legendre polynomials generated and the solution of the given ODE using the Frobenius method is obtained above.

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Answer:

The surface area of the cone is 126π cm².

Step-by-step explanation:

The surface area of a cone can be found using this formula:

In this problem, we are told that the cone has a radius of 9 cm and a slant height of 5 cm.

Substitute these values into the formula for the surface area of a cone.

The surface area of the right cone is 126 π cm².

The equation of the line which passes through points (-3,-4) and (3,2) is y = (2/3)x - 2.

The data in the given question is-

The passing points are-

(x1, y1) =(-3,-4) and

(x2, y2) =  (3,2)

Slope = m = (y2 - y1)/(x2 - x1)

m = (2 + 4)/(3 + 3)

m = 6/9

m = 2/3

Equation of the line is evaluated using slope intercept form.

y - y1 = m (x - x1)

y + 4 = (2/3)(x + 3)

y = (2/3)x - 2

Thus, the equation of the line which passes through points (-3,-4) and (3,2) is y = (2/3)x - 2.

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