write the equations in cylindrical coordinates. (a) 9x2 − 2x 9y2 z2 = 1 (b) z = 2x2 − 2y2

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Explanation:

Matrix C has 3 rows and 2 columns. The size or dimensions can be written in shorthand as 3x2.

Matrix D has dimensions 2x1, aka 2 rows and 1 column.

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Write "3x2" and "2x1" side by side in that exact order.

Notice the inner '2's match up. This is important. We need the inner numbers to match so that matrix multiplication is possible. The outer values '3' and '1' will help form the dimensions of the final answer matrix. The final answer matrix will have dimensions 3x1

Luckily we don't need to compute the value of CD. We just need to use the justification mentioned in the previous paragraphs to conclude that matrix CD is possible.

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Something like BC is not possible because B is 3x2 and C is 3x2. We don't have a match of inner values this time. We can then rule out the answer choice "BC". The answer choices "DC" and "CB" are ruled out for similar reasoning.

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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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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The length of the vegetable garden as a function of its length will be given as: y = 3x + 2

The expression of the garden width in terms of the width of the tomato patch is given as:

y = x + 5

Let the length of the garden be y

Let the length of the tomato patch be x

If Melissa wants the length of  the garden to exceed three times the length of the tomato patch by 2 feet, the length of the vegetable garden as a function of its length will be given as:

y = 3x + 2

Therefore, If she also wants the garden's width  to exceed the width of the tomato patch by 5 feet,  the expression of the garden width in terms of the width of the tomato patch is given as:

y = x + 5

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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:

Answer:

Maria chose C. 2682

Step-by-step explanation:

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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The inverse function is used to find the temperature in Celsius,

the temperature in celsius is  -12.22°C and 32.22°C.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator).

Given expression for temperature calculation

Original function: F =  9/5​C + 32

Inverse function: C = (F − 32)5/9

where C is temp. in Celsius and F is temp. in Fahrenheit,

so when the temperature is given in Fahrenheit we have to use the inverse function formula to calculate the temperature in degree celsius,

because it will be easy to calculate.

temperature = 10°F

C = (F − 32)5/9

C = (10 - 32)5/9

C = -22 x 5/9

C =  -12.22°C

when temperature = 90°F

C = (90 - 32)5/9

C = 32.22°C

Hence the temperature is  -12.22°C and 32.22°C.

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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

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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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 lengths 5, 13 and 12 can form a right angled triangle as they follow Pythagoras theorem.

The lengths can form a right triangle if they follow Pythagoras theorem. The longest side will be hypotenuse which is 13. Remaining will be base and height.

Pythagoras theorem -

Perpendicular² = Base² + Height²

Keep the values in formula

13² = 12² + 5²

Taking square on each side of the equation

169 = 144 + 25

Performing addition on Right Hand Side of the equation

169 = 169

Thus, the righ triangle can be formed based on the mentioned dimensions.

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The graph which could be the graph of the polynomial f( x) with roots-8,-5, 1, and 2 is Graph 4.

What is Polynomial function?

A polynomial function is a function that involves onlynon-negative integer powers or only positive integer expounders of a variable in an equation like the quadratic equation, boxy equation, etc. For illustration, 2x 5 is a polynomial that has exponent equal to 1.

Given that;

Root of polynomial = 4.

This means that the polynomial f( x) has 4 roots.

Now, when f( x) = 0, we're told that the 4 roots are;

x = -8

x = -5

x = 1

x = 2

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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.

Answer:

1000$

Step-by-step explanation:

1000$

Answer: The interval in which the greatest number of scores would occur is between (20 - 2.6) and (20 + 2.6), which is approximately 17.4 and 22.6 respectively. This interval is also known as the "bell curve" or the "normal distribution curve" and it is centered at the mean (20) and covers approximately 68% of all possible scores. Most of the data points would fall within one standard deviation of the mean, hence the greatest number of scores would occur in this interval.

Step-by-step explanation:

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:3/4

Step-by-step explanation:

1/4 multiplied 3/1 =3/4

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:

8, 15, 16

Step-by-step explanation:

8, 15, 16 is not a Pythagorean triple because it doesn't satisfy the Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex]

When we plug this set of numbers into the theorem:

[tex]8^2 + 15^2 \stackrel{?}{=} 16^2[/tex]

[tex]289 \neq 256[/tex]

we get an inequality, not an equality which would make this set of numbers a Pythagorean triple.

Note that all of the other given triples satisfy the Pythagorean Theorem.

The  area of the triangle is equal to: Area = (|A| x |B| x sin(θ))/2

To calculate the area of a triangle with 3 vectors, we will use the vector triple product formula. This formula states that the area of the triangle is equal to the magnitude of the cross product of two of the vectors divided by two.

Let's say we have three vectors A, B, and C. The area of the triangle is then equal to the magnitude of the cross product of vector A and B, divided by two.

The magnitude of the cross product of A and B can be calculated as follows:

Magnitude of (A x B) = |A| x |B| x sin(θ)

Where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

Therefore, the area of the triangle is equal to:

Area = (|A| x |B| x sin(θ))/2

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Answer:

A and B

Step-by-step explanation:

to determine which pairs are solutions , substitute the x and y coordinates into the left side of the equation and if equal to the right side then solution.

A (- 6, - 14 )

7(- 6) - 5(- 14) = - 42 + 70 = 28 ← true , so solution

B (- 1, - 7 )

7(- 1) - 5(- 7) = - 7 + 35 = 28 ← true , so solution

C (4, 10 )

7(4) - 5(10) = 28 - 50 = - 22 ≠ 28 , not a solution

D (7, 9 )

7(7) - 5(9) = 49 - 45 = 4 ≠ 28 , not a solution

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

Step-by-step explanation:

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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