(a) Find the coordinates of the stationary point of the curve with equation (x + y - 2)2 = ey - 1 (b) A curve is defined by the parametric equations x = 3 + 2 y = 12 - 1 (0) Find the gradient of the curve at the point where 1 = -2 (ii) Find a Cartesian equation of the curve. 4x (c) Use the substitution u = 4x - 3 to find s. giving your answer in 4X-3 terms of x.

Answer:

The quadrilateral KLMN is a parallelogram.

Step-by-step explanation:

To find the slopes and lengths of the sides of the quadrilateral formed by the points K(7,-9), L(5,0), M(-1,7), and N(1, -2), we can use the formulas for slope and distance between two points.

Slope of KL:

The slope of KL can be calculated as (y2 - y1) / (x2 - x1) using the coordinates of points K and L. Substituting the values, we have (0 - (-9)) / (5 - 7) = 9 / (-2) = -4.5.

Slope of LM:

Using the coordinates of points L and M, we have (7 - 0) / (-1 - 5) = 7 / (-6) = -7/6.

Slope of MN:

The slope of MN is ( -2 - 7) / (1 - (-1)) = -9 / 2 = -4.5.

Slope of NK:

Using the coordinates of points N and K, we have (-9 - (-2)) / (7 - 1) = -7 / 6.

Length of KL:

The length of KL can be found using the distance formula, which is √[(x2 - x1)^2 + (y2 - y1)^2]. Substituting the values, we get √[(5 - 7)^2 + (0 - (-9))^2] = √[4 + 81] = √85.

Length of LM:

Using the distance formula with the coordinates of points L and M, we get √[(-1 - 5)^2 + (7 - 0)^2] = √[36 + 49] = √85.

Length of MN:

The length of MN is √[(1 - (-1))^2 + (-2 - 7)^2] = √[4 + 81] = √85.

Length of NK:

Using the distance formula, we find √[(7 - 1)^2 + (-9 - (-2))^2] = √[36 + 49] = √85.

Based on the slopes and lengths, the quadrilateral KLMN is a parallelogram. A parallelogram has opposite sides that are parallel and equal in length.

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The values of n and m in the expression are 45 and 9 respectively.

The value of n is both 5 times as the value of m and 36 more than the value than value of m. Therefore, the values of n and m can be found as follows:

Using equations,

n = 5m

n = 36 + m

By substitution,

5m = 36 + m

5m - m = 36

4m = 36

divide both sides by 4

m = 36 / 4

m = 9

Let's find the value of n.

n = 5(9)

n = 45

Therefore,

n = 45 and m = 9

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Answer:

Alan can buy the bike for $109.85

Step-by-step explanation:

Start with 100% and subtract the 35% discount.  This results in 65%.  The bike sells for 65% of $169, which is calculated as follows:

0.65($169) = $109.85

Alan can buy the bike for $109.85 under the terms of this sale.

By calculating , the values of angles D and E are 80 , 80 respectively.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees .

Given ,

from the figure ,

In triangle ECD

The sum of three angles = 180

so ,

E+C+D = 180

50+50+D = 180

D = 180-100

D = 80

And in the Quadrilateral AECB,

A+E+C+B = 360

110+70+100 + E = 360

E = 360 - 280

E = 80

Hence, the values of angles D and E are 80 , 80 respectively.

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There are two cases of collisions : Key “23” and “27NLY” collide at slot “1”.

Key “27NLY” and “a” collide at slot “(9+L+Y) mod 11”.

Given a sequence of 5 element keys < 23, I 38, 27 >, for searching task: H(k) = 3, 26, 16, 38, 27 mod 11. The steps and calculations are shown in the table below:

Here are the steps to insert the keys into a hash table of 11 slots using the hash function H(k) = 3, 26, 16, 38, 27NLY mod 11:

Key                                  Hash Value                                             Slot

23                                    23 mod 11 = 1                                             1

38                                    38 mod 11 = 5                                     5

27NLY                    (3 + 26 + 16 + 38 + (27 * N)

                               + L + Y) mod 11 = (86 + N

                                     + L + Y) mod 11                       (86 + N + L + Y) mod 11

N = 13

-> (86 +

N + L +

Y) mod

11= (86

+ 13+ L

+ Y) mod

11 = (99+L

+Y) mod

11 = (9+

L+Y) mod

11 -> Slot:

(9+L+Y)

mod 11  

a                                              a mod 11 = a                                        a

The cases of collision are:

Key “23” and “27NLY” collide at slot “1”.

Key “27NLY” and “a” collide at slot “(9+L+Y) mod 11”.

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Answer:

0.161

Step-by-step explanation:

0 . 7 × 0 . 23

= 0.161

When simplifying algebraic fractions with denominators of cubes, such as sum and difference of cubes, we can utilize factorization techniques.

Algebraic fractions with denominators of cubes can be simplified by applying the factorization formulas for the sum and difference of cubes. These formulas allow us to express the cubic terms as products of binomials and facilitate cancellation of common factors.

For example, the sum of cubes formula (a^3 + b^3) can be factored as (a + b)(a^2 - ab + b^2), while the difference of cubes formula (a^3 - b^3) can be factored as (a - b)(a^2 + ab + b^2).

By identifying these patterns and applying the appropriate factorization formula, we can simplify the algebraic fractions by canceling out common factors and reducing them to their simplest form.

Simplifying algebraic fractions in this way helps to eliminate complex terms and make the expressions more manageable. It is important to recognize the opportunities for applying sum and difference of cubes factorization to simplify algebraic fractions with denominators of cubes effectively.

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In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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Level 1 has 1 cards, level 2 has 3 cards , level 3 has 6 cards ,level 4 has 10 cards and level 5 has 15 cards Here is the completed table based on the given pattern..

The pattern continues in the same way, where each level adds one more card than the previous level.
Level    Number of Cards
1        1
2        3
3        6
4        10
5        15

1. To find the number of cards in each level, we observe that the pattern follows a triangular number sequence.
2. In level 1, there is only 1 card.
3. In level 2, there are 3 cards (1 card from level 1 plus 2 additional cards).
4. In level 3, there are 6 cards (3 cards from level 2 plus 3 additional cards).
5. In level 4, there are 10 cards (6 cards from level 3 plus 4 additional cards).
6. In level 5, there are 15 cards (10 cards from level 4 plus 5 additional cards).

The pattern continues in the same way, where each level adds one more card than the previous level.

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The complete question is-

Suppose you are building towers of cards with levels as displayed below. Each level consists of cards laid out in a rectangular pattern. The table shows the number of cards in each level as the tower grows.

Level Number of Cards

1 1

2 4

3 9

4 16

5 25

6 36

7 49

8 64

9 81

10 100

11 121

12 144

13 169

14 196

15 225

Copy and complete the table, assuming the pattern continues.

The number of cards in each level of the tower follows a pattern where each level adds one more card than the previous level. The formula to calculate the number of cards at a specific level is n * (n + 1) / 2, where n is the level number. By applying this formula, we can accurately determine the number of cards at any given level.

To complete the table of towers of cards, we need to identify the pattern and continue it. Let's analyze the levels of the towers:

Level 1 has 1 card.

Level 2 has 3 cards (1 + 2).

Level 3 has 6 cards (1 + 2 + 3).

Level 4 has 10 cards (1 + 2 + 3 + 4).

We can observe that each level adds one more card than the previous level. So, to find the number of cards at each level, we can use the formula:

Number of cards = 1 + 2 + 3 + ... + n, where n is the level number.

Now, let's complete the table:

Level 5 has 15 cards (1 + 2 + 3 + 4 + 5).

Level 6 has 21 cards (1 + 2 + 3 + 4 + 5 + 6).

Level 7 has 28 cards (1 + 2 + 3 + 4 + 5 + 6 + 7).

Following this pattern, we can continue the table:

Level 8 has 36 cards (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8).

Level 9 has 45 cards (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9).

In general, the number of cards at level n can be calculated using the formula:

Number of cards = n * (n + 1) / 2.

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

2nd choice

Step-by-step explanation:

to find the inital peanuts, we multiply 32 ounces by 3/10 or 0.3. then we add x which are peanuts as well. that makes 0.3 x 32 + x. this is our total peanuts. to find the percantage, we find the whole mixture which is now 32 + x, divide peanuts by the whole mixture and multiply by 100.

Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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Answer:

5,386,830

Step-by-step explanation:

Answer:

4x+4=5x-8

4x-5x+4=-8

4x-5x=-8-4

-x=-8-4

-x=-12

x=12

Step-by-step explanation:

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

D. y=5x+2

Step-by-step explanation:

The y int. is 2, and the slope is 5/1. If you plug that into a calculator, you can see the slope being steep.

In the case when ø21 and ø22 are unknown and can be assumed equal, we can calculate a pooled estimate of the population variance. This statement is True.

In the case where ø21 and ø22 are unknown and can be assumed equal, it is possible to calculate a pooled estimate of the population variance. This pooled estimate combines the sample variances from two groups or populations to obtain a more accurate estimate of the common variance. It assumes that the underlying variances in both groups are equal.

The pooled estimate of the population variance is calculated by taking a weighted average of the individual sample variances, with the weights determined by the sample sizes of the two groups. This pooled estimate is useful in various statistical analyses, such as t-tests or analysis of variance (ANOVA), where the assumption of equal variances is necessary.

However, it is important to note that the assumption of equal variances should be validated or tested before using the pooled estimate. If there is evidence to suggest unequal variances, alternative methods or adjustments may be necessary.

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Answer:

7- 110

11-70

about rest I don't know sorry

Answer:Irrational,2/9,22/100 11/50, Irrational, No Fraction Given, Perfect Square, Non-Perfect Square

Step-by-step explanation:Best fit options for each question.

Answer:

10

Step-by-step explanation:

x-7=?

x=17

17-7=10

7+10=17

17=17 Correct :)

When using the partition algorithm, the goal is to divide a set of elements into two subsets based on a chosen pivot element. This pivot element is typically chosen as the median of the set or a close approximation to it.

To find the median of the set, we first divide it into groups of 5 (or any other fixed number). We then find the median of each group, which will give us a set of medians. We can then recursively find the median of this set of medians, which will give us an approximate median for the entire set.

Once we have the pivot element, we can compare it to each element in the set and divide them into two subsets based on whether they are greater or less than the pivot element. However, we do not need to compare the pivot element to every element in the set.

We only need to compare the pivot element to the elements that we do not already know how they compare. These are the elements that are in different subsets than the pivot element.

For example, if the pivot element is greater than a certain element, we know that this element is in the subset that contains elements less than the pivot. Therefore, we do not need to compare the pivot element to this element.

In general, we only need to compare the pivot element to approximately half of the elements in the set. This is because each comparison will divide the set into two subsets, one of which we already know the relationship to the pivot element.

In conclusion, when using the partition algorithm, we only need to compare the median of medians to approximately half of the elements in the set, those that we do not already know how they compare.

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Answer:

Step-by-step explanation:

Answer: \(y=\frac{1}{2}x+\frac{1}{2}\)

Step-by-step explanation:

The line passes through (-1, 0) and (3,2), so the gradient is \(\frac{2-0}{3-(-1)}=\frac{1}{2}\).

This means the equation of the line is of the form \(y=\frac{1}{2}x+c\) for some constant c.

Substituting in the coordinates of the point (-1,0),

\(0=\frac{1}{2}(-1)+c\\\\0=-\frac{1}{2}+c\\ \\ c=\frac{1}{2}\)

Thus, the equation of the line is \(y=\frac{1}{2}x+\frac{1}{2}\)

Answer:

Answer: 7.4 x10^4 because you have to move the decimal to where the first number less then 10.

Step-by-step explanation:

I apologize, but I am unable to view diagrams or images. However, I can still guide you on how to approach this problem using the given terms. To find the measure of ∠x, you'll need to follow these steps:

1. Identify any given angle measures or relationships in the diagram, such as supplementary or complementary angles, parallel lines, or triangle angle sums.

2. Apply relevant angle properties and theorems, such as alternate interior angles, vertical angles, or the Triangle Sum Theorem (the sum of the angles in a triangle is always 180°).

3. Set up and solve equations using the given information and the angle properties or theorems you've identified. Be sure to include clear and logical steps, showing how you're using the angle relationships to determine ∠x.

4. Conclude with the measure of ∠x, ensuring you've provided enough justification through your work.

Once you follow these steps using the information given in the diagram, you should be able to find the measure of ∠x

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.

Answer:

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Step-by-step explanation:

Given

\(y=c_1e^x +c_2e^{-x\)

\(y(1) = 0\)

\(y'(1) =e\)

Required

The solution

Differentiate \(y=c_1e^x +c_2e^{-x\)

\(y' = c_1e^x - c_2e^{-x}\)

Next, we solve for c1 and c2

\(y(1) = 0\) implies that; x = 1 and y = 0

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(0 = c_1 * e^1 + c_2 * e^{-1}\)

\(0 = c_1 e + \frac{1}{e}c_2\) --- (1)

\(y'(1) =e\) implies that: x = 1 and y' = e

So, we have:

\(y' = c_1e^x - c_2e^{-x}\)

\(e = c_1 * e^1 - c_2 * e^{-1}\)

\(e = c_1 e - \frac{1}{e}c_2\) --- (2)

Add (1) and (2)

\(0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2\)

\(e = 2c_1e\)

Divide both sided by e

\(1 = 2c_1\)

Divide both sides by 2

\(c_1 = \frac{1}{2}\)

Substitute \(c_1 = \frac{1}{2}\) in \(0 = c_1 e + \frac{1}{e}c_2\)

\(0 = \frac{1}{2} e+ \frac{1}{e}c_2\)

Rewrite as:

\(\frac{1}{e}c_2 = -\frac{1}{2} e\)

Multiply both sides by e

\(c_2 = -\frac{1}{2} e^2\)

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Answer:

Point I is on line segment HJ; which means HI and IJ are equal.

HJ = 15

IJ = 10

Finding the length of HI, given the above statements:

Length of HI = 10 (reason: HI and IJ are congruent)