Use the equations to find
∂z/∂x and ∂z/∂y.
x2 + 8y2 + 7z2 = 1

Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.

Any equation in algebra that can be written in standard form as

ax^2+bx+c=0,

where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.

The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions. The graph will cross twice if the vertex is below the x-axis and the parabola opens up, and it will cross twice again if the vertex is above the x-axis and the parabola opens down.

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Examining the function  -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0

The sign of the x2 coefficient determines whether a parabolic curve opens upward or downward in this scenario.

In this function, the coefficient of x2 is a and is -9.

Rising downwards results from a negative coefficient, while opening upwards from a positive coefficient

The intercept of y

-9x² + 7x = 0

x(-9x + 7) = 0

x = 0

-9x + 7 = 0

-9x = -7

x = 7/9

Therfore, Examining the function  -9x² + 7x ,  0 and 7/9 is the y intercept.

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Answer: area: 1/2 length * width, perimeter: add the three sides

Step-by-step explanation:

Answer: 6 in each batch

Step-by-step explanation: 54/9 = 6

Marsha and Kristen will be at the same elevation of -72 feet after 4 minutes.

How to find their elevation?

To find out after how many minutes Marsha and Kristen will be at the same elevation, we can set their elevation equations equal to each other:

-24 - 12t = -8 - 16t

Then, we can solve for t by adding 8 to both sides and dividing by 4:

t = 4

So, Marsha and Kristen will be at the same elevation after 4 minutes.

To find out what elevation they will be at that time, we can substitute 4 into either one of the elevation equations and solve for the elevation:

-24 - 12(4) = -24 - 48 = -72

So, Marsha and Kristen will be at the same elevation of -72 feet after 4 minutes.

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The proper method of filling a table with a function has been explained below.

Tables are helpful when we have to plot a function or we have to interpolate a function using given data points. A table usually consists of 2 or more 2 variables whose values are arranged either in a row or in a column. For filling a table with the help of a function, firstly we have to define the values of independent variables which we will input into the function to get the dependent variable's values.

When we get the value of independent data we will be inputting one of one those values in the function we will get the values of the function at the given point and hence the function will be filled by the output values.

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The magnified length of the objects is 0.01 meters in decimal form, based on the height of object and magnification power.

The formula to find magnified length is -

Magnification = image height ÷ object height. Here image height is magnified length.

Keep the values in formula -

Image height = 10⁵ × [tex] {10}^{-7} [/tex]

Performing multiplication on Right Hand Side of the equation. Note that power of products will be used to find the magnified length. The exponents will be added.

Image height = [tex] {10}^{5 + (-7)} [/tex]

Performing addition of exponents to find the image height

Image height = [tex] {10}^{-2} [/tex] meters

Writing the image height in decimal form - 0.01 meters

Therefore, the height of image or magnified length is 0.01 meters.

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The volume of the chamber follows a pattern. The formula that represents the volume of the nth chamber is 6.3% of the previous chamber.

What is a pattern?

A pattern is a repeated arrangement of numbers, shapes, colours, or other elements. The Pattern can be associated with any kind of event or object. A pattern is defined as a set of numbers that are related to one another in a specific way. Patterns are sometimes referred to as sequences.

Given that:

Chamber 7: 1.207 cm³

Chamber 6: 1.135 cm³

Chamber 5: 1.068 cm³

Chamber 4: 1.005 cm³

Chamber 3: 0.945 cm³

Chamber 2: 0.889 cm³

Chamber 2: 0.836 cm³

                          1.207     1.135     1.068   1.005     0.945      0.889      0.836

First difference:        .072        0.067    0.063   0.060    0.056      0.053

Second difference:            0.005     0.004    0.003     0.004    0.003

Since the difference is not the same, thus the volume is not in a linear pattern. Then find the ratio consecutive volume:

1.207/1.135 ≈ 1.063

1.135/1.068 ≈ 1.063

1.068/1.005 ≈ 1.063

1.005/0.945 ≈ 1.063

0.945/0.889 ≈ 1.063

0.889/0.836 ≈ 1.063

Each chamber is 6.3% greater than the previous chamber. The pattern is exponential functions.

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Answer:3/4

Step-by-step explanation:

1/4 multiplied 3/1 =3/4

Answer:

Option 3

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

After dilation of with a scale factor of 0.25 the pre image coordinates

V (1,  1), W (2, -2) T ( 4, 2) and U(3, 3) transformed to

V' (0.25, 0.25)

W' (0.5, -0.5)

T' (1, 0.5)

U' (0.75, 0.75)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

In dilation, transformation rule is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar the rule for r = 0.25 we have

preimage                                       image

V (1,  1)   → (0.25 * 1, 0.25 * 1)  →   V' (0.25, 0.25)

W (2, 2)   → (0.25 * 2, 0.25 * -2) →  W' (0.5, -0.5)

T (4, 2)   → (0.25 * 4, 0.25 * 2) →   T' (1, 0.5)

U (3, 3)   → (0.25 * 3, 0.25 * 3) →   U' (0.75, 0.75)

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The coordinates of the points after the translation are:

All the points are translated on the same way, so let's analyze the translation of P to P'.

The coordinates of Pare (5, 8), and P' is at (3, 4)

Then the translation is:

(3, 4) - (5, 8) = (3 - 5, 4 - 8) = (-2, -4)

So we just need to subtract 2 to the x-value and 4 to the y-value.

The coordinates of Q and R are:

Q = (7, 8)

R = (8, 5)

Then the translated points are:

Q' = (7 - 2,8 - 4) = (5, 4)

R' = (8 - 2, 5 - 4) = (6, 1)

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Answer:N= 10 fo sho m -14 maybe

Step-by-step explanation:

this triangle is an isosceles triangle because of the 90 45 45 angles. This means that the two side lengths are equal and 10 is equal to n. to calculate m is maybe square root of 2 times 10 because this image.

So, the answer after simplifying the given square root equation is 8√5 + 3√30.

A square has four equal sides, and four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.

A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

Solving,

√5 (8+3√6)

= √5 * 8 + √5 * 3√6

= 8 * √5 + √5 * 3√6

= 8√5 + 3√5*6

= 8√5 + 3√30

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An example of a pattern rule is "add 3" which means that to find the next term in a sequence, you add 3 to the previous term.

To write a rule for a sequence, you need to identify the pattern. This involves looking at the differences between the numbers and seeing if there is a pattern of increasing or decreasing numbers. Once you have identified the pattern, you can then write a rule that expresses that pattern.

Examples of pattern sequences include the Fibonacci sequence (1,1,2,3,5,8,13,21,34, etc.), the even numbers (2,4,6,8,10, etc.), and the multiples of 3 (3,6,9,12,15, etc.).

To describe the pattern of a sequence, you need to look at the differences between the numbers and the pattern of increases or decreases. For example, in the Fibonacci sequence, the pattern is that each number is the sum of the two numbers before it so 1+1=2, 1+2=3, 2+3=5, etc.

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Answer:

Maria chose C. 2682

Step-by-step explanation:

Answer:

1000$

Step-by-step explanation:

1000$

The angle when the secant intersect is as follows:

A secant is a line that intersects a circle in exactly two points.

If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

Therefore,

m ∠GPE = 1 / 2 ( mGE -  mHF)

mGE = 99°

mHF = 41°

m ∠GPE = 1 / 2 (99 - 41)

m ∠GPE = 1 / 2 (58)

Therefore,

m ∠GPE = 29 degrees

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Answer:

x=3

Step-by-step explanation:

An equation's omitted factors are the values of x for which the result is unknown. This indicates that if the denominator or x(x-3) equals 0, your solution is undefined.

Set up this equation and solve for the potential possibilities of x to find these numbers: x(x-3)=0

Divide both sides by (x-3) to find one of the values:

x(x-3)/(x-3)=0(x-3)

Because (x-3) cancels on the left side of the equation and everything divided by 0 is zero on the right, you should get: x=0.

Now that you've determined one of the excluded values, work out the other:

To begin, split both sides by x:

x(x-3)=0

x-3=0

Finally, multiply both sides by -3 to get: x=3

Answer:

∠S = 105°

∠T = 95°

Step-by-step explanation:

Cyclic quadrilateral:

   Quadrilateral MNST is a cyclic quadrilateral. In cyclic quadrilateral, the opposite angles are supplementary.

     m∠S + m∠M = 180°

 3x + 2x +  5 = 180

        5x  + 5  = 180           {Combine like terms}

                 5x = 180 - 5     {Subtract 5 from both sides}

                 5x = 175

                    x = 175 ÷ 5  {Divide both sides by 5}

                    x = 35°

∠S = 3x

    = 3 * 35

    = 105°

∠T = 3x - 10

     = (3*35) - 10

     = 105 - 10

     = 95°

Answer:1111

Step-by-step explanation:

11111

The pattern shown by the erosion data measurements for the Western Beach is that the width decreases over time, with a steady decrease of about 10 feet per year. The pattern for the Dunes Beach is that the width increases over time, with an increase of about 5 feet per year.

Based on the data, it appears that the beaches will have approximately the same width around year 20. At this point, the Western Beach will have a width of approximately 50 feet and the Dunes Beach will have a width of approximately 90 feet.

To get a better approximation of when the two beaches will have the same width, it would be necessary to gather more data points over a longer period of time and to take into account other factors that may affect the beaches' widths such as the strength of the waves, the composition of the beach, and human interventions that may be taking place.

The balanced equation is:

CCl₄ --> C + 2Cl₂

The law of conservation of mass states that when a chemical reaction takes place, the mass of the reactants and products should be equal.

Here is an equation that describes a chemical reaction:

CCl₄ --> C + 2Cl₂

Thus, add 2 atoms of Cl to balance the equation.

Then,

The balanced equation is:

CCl₄ --> C + 2Cl₂

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In this case, the highest power on any variable is 2. As a result, the degree of polynomial is 2.

The degree of a polynomial in mathematics is the highest of the degrees of the polynomial's monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer. The degree of a polynomial is the greatest or maximum power of a variable in a polynomial equation. A degree represents the polynomial with the greatest exponential power. Finding the degree of a polynomial. 2 x 2 + 2 x - 364 = 0. The maximum degree of the polynomial in the preceding equation.

Here,

Given : 2x^2

Degree of polynomial = Highest power of a variable.

Here, 2 is the highest power on any variable. So, degree of polynomial is 2.

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Answer:

[tex]c+d=\langle-3,9\rangle[/tex]

Step-by-step explanation:

We simply add the respective horizontal and vertical components:

[tex]c+d=\langle 6,2 \rangle+\langle-9,7\rangle=\langle6+(-9),2+7\rangle=\langle6-9,9\rangle=\langle-3,9\rangle[/tex]

Every 10 degrees higher in temperature, the slope would be around -3 so draw a line from (40,20) to (80,8) .

How steep a line is defined by its slope. Gradient overflow is a term used to describe a gradient-based mathematical equation (the change in y divided by the change in x). The slope is calculated by dividing the horizontal change (run) between two points by the vertical change (rise) between the same two points. The slope-intercept form of an equation is used to express the equation of a straight line, which is written as y = mx + b. The line's y-intercept is situated where the slope is m, b is b, and (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 (0, 7).

givenI won't use (40,2) because it is an extreme case.

If I were to draw a line from those points, I would roughly estimate that it would have the same number of dots above and below the line, indicating that it is a line of best fit.

Every 10 degrees higher in temperature, the slope would be around -3 so draw a line from (40,20) to (80,8) .

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After simplification, the formula 4 (2x - 1) + 3 (2x + 5) becomes 14x + 11.

A number's arithmetic value for each digit can be expressed using the expanding form. Expanded numbers are numerical expressions that consist of the place value of each digit added to the total of the digits. To improve place value comprehension, expanded form is an excellent strategy.

It is given that,

4 (2x - 1) + 3 (2x + 5)

We have to expand and simplify the expression,

= 4 (2x - 1) + 3 (2x + 5)

Multiply the term out of the bracket into the bracket as

= 8x - 4 + 6x + 15

Add comparable terms together so that we can execute mathematical operations like addition and subtraction on the result.

= 14x + 11

As a result, the simplified expression for 4 (2x - 1) + 3 (2x + 5) will be 14x + 11.

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The transformations that apply are Horizontal stretch or compression by a factor of 3, Vertical shift up by 24 units, Reflection over the x-axis, The leading coefficient of 1/3 is a vertical compression and The exponent of 2 on x is a parabola.

Vertical Stretch/Compression by a factor of 3: The coefficient in front of the x^2 term is 1/3, which stretches or compresses the graph vertically by a factor of 3.

Horizontal Stretch/Compression by a factor of 24: The exponent on the x term is 24, which stretches or compresses the graph horizontally by a factor of 24.

Reflect over the x-axis: The coefficient in front of the x^2 term is positive, so the graph is reflected over the x-axis.

Shift up or down: The constant term is not present, so the graph does not shift up or down.

Shift left or right: The constant term is not present, so the graph does not shift left or right.

Rotation: The graph does not rotate as it is a parabola in the standard form y=ax^2 + bx + c, it does not have any trigonometric function in it.

Therefore, The transformations that apply are Horizontal stretch or compression by a factor of 3, Vertical shift up by 24 units, Reflection over the x-axis, The leading coefficient of 1/3 is a vertical compression and The exponent of 2 on x is a parabola.

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Answer:

[tex]I'(-0.5,0.25), J'(0.5,0.5), K'(0.5, -0.25)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, we can use the rule that: