Given that a = 6i- 3j, find:
a the unit vector in the same direction of a
b the angle that a makes with the positive x-axis.

The equation 4x²+8xy+ky²-9 = 0 will have a pair of straight lines when k = 0.

An equation obtained from the standard form of a linear differential equation by replacing the right member by zero.

Given that, an equation having a pair of straight line 4x²+8xy+ky²-9 = 0

The auxiliary equation of a line is given by, ax²+2hxy+by²+2gx+2fy+c = 0

or, abc-2fgh-af²-bg²-ch²= 0

Comparing with the given equation,

a = 4, h = 4, b = k, g = 0, f = 0 and c = -9

4k(-9)+0-0-0+9(4)² = 0

36k = 144

k = 4

Hence, The equation 4x²+8xy+ky²-9 = 0 will have a pair of straight lines when k = 0.

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The median is the middle score in the set.

To find the median, start by arranging all of the data points from smallest to largest.

In an odd-numbered set, the median will be the number in the very middle of the list.

In an even-numbered set, you will need to calculate the average of the two middle numbers.

To do this:

Step 1: Take the two middle numbers of the even-numbered set

Step 2: Add the two numbers together

Step 3: Divide the total by 2

As an example, consider this set of numbers: 5, 9, 11, 9, 7. First, you arrange them in numerical order (5, 7, 9, 9, 11). Since you have an odd number of scores, the number in the third position of the data set is the median which, in this case, is 9 (5, 7, 9, 9, 11).

To calculate the median for an even number of scores, imagine that your research revealed this set of data: 2, 5, 1, 4, 2, 7. Your first step is to put them in numerical order (1, 2, 2, 4, 5, 7). The two middle scores are 2 and 4, so you should add them together (2+4=6) and then divide 6 by 2, which equals 3. In this data set, the median score is 3.

The median is calculated by arranging the scores in numerical order, dividing the total number of scores by two, then rounding that number up if using an odd number of scores to get the position of the median or, if using an even number of scores, by averaging the number in that position and the next position.

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The Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.

Multiples are numbers that are multiplied by another number to get a particular number.

In mathematics, multiples are the results of multiplying an integer by a given number.

Multiples of 5 include, for instance, 10, 15, 20, 25, 30, etc.

Numerous 7s include 14, 21, 28, 35, 42, 49, etc.

A multiple in mathematics refers to the outcome of multiplying two numbers together.

Here, the number 7 is multiple by 56.

Because the result of multiplying 0 by any number is 0, 0 is a multiple of all numbers.

So, in order to know what tables come in 64, we need to check that what numbers multiples ae 64:

64/1 = 64

64/2 = 32

64/4 = 16

64/8 = 8

64/16 = 4

64/32 = 2

64/64 = 1

Therefore, the Multiplication table that comes in the number 64 is 1, 2, 4, 8, 16, 32, and 64.

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The vertex of a parabola is the point at which the parabola changes direction, the vertex of y =-x² + 4 is (0, 4).

The equation for a parabola in standard form is y = ax² + bx + c. To find the vertex of y = -x² + 4, we need to use the formula x = -b/2a. In this equation, a is -1, and b is 0, so x = 0. Therefore, the vertex of y = -x² + 4 is (0, 4).

To find the vertex of a parabola, we can use the formula x = -b/2a. In this formula, a is the coefficient of x², and b is the coefficient of x. Therefore, to find the vertex of a parabola, we need to find the coefficients of x² and x and then plug them into the formula. This formula will give us the x-coordinate of the vertex, and we can then use the equation of the parabola to find the y-coordinate of the vertex. In the case of y = -x² + 4, the coefficient of x² is -1 and the coefficient of x is 0. Plugging these values into the formula, we get x = 0. We can then use the equation of the parabola to find the y-coordinate of the vertex, which is 4. Therefore, the vertex of y =-x² + 4 is (0, 4).

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Answer:

⭐ There are 3 ways you can write a linear function (⭐ = most common):

Answer:

Step-by-step explanation:

The perimeter of a rectangle is the sum of its 2 widths and 2 lengths.

Lets call the width ‘W’ and the length ‘L’. The perimeter (P) is equal to 2W + 2L. So 28 = 2W + 2L which simplifies to 14 = W + L.

28/2=14

The area of a rectangle is the width multiplied by the length so the formula is A = W x L. We want to get rid of the length. So, if we rearrange the first equation 14 = W + L to make L the subject we get L = 14 - W. We can now substitute this into the area equation so we get → A = W x (14 - W). That’s your answer!

Square Bases:  A = s².

Rectangle-shaped bases: A = l x w.

Circular bases: A = pi x r².

In geometry, a three-dimensional object's bottom is referred to as its base; if the solid's top is parallel to its bottom, it is also referred to as a base.

The bases of cubes as well as square pyramids are square. The length of one of a square's sides multiplied on its own, or squared, determines the area of a square: It goes like this: A = s².

Pyramids and several rectangular solids have rectangular bases. A rectangle's area is determined by multiplying its length, l, by it's own width, w: A = l x w.

Cones and cylinders have round bases. The radius of a circle, r, squared, plus the number pi, is equal to a area of the circle:

A = pi x r².

Pi is  approximately 3.14.

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Answer:

x=13

Step-by-step explanation:

the bottom line is 11 the top line is 6 the difference is 5 hence we use the the formula 12 5 13 i mean the pythogrious formula

A t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.

The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesized value relative to its standard error.

Through the Student's t-test, it is utilized in hypothesis testing.

In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.

When the variance and standard deviation of the population are unknown, a t-statistic is employed rather than a z-score.

The p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data.

The t-value is a way to measure the difference between population means.

Therefore, a t-statistic rather than a z-score is used when (C) the population's variance and standard deviation are unknown.

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Correct question;
In what circumstances is the t-statistic used instead of a z-score for a hypothesis test?

(A) the t-statistic is used when the population variance (or standard deviation) is known

(B) you use the z-test when the sample size is less than 30

(C) the t-statistic is used when the population variance (or standard deviation) is unknown

To graph linear inequalities with two variables separation of variables and plotting are two basic steps.

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

3x-2y>1 is an illustration of a linear inequality. The inequality equation's LHS is in this case clearly greater than the RHS.

Step 1:Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In the X, Y, XY, XY plane, graph the boundary line from step 2.

Step 4:The final step is to shade a portion or one side of the border line.

If your boundary line contains the inequality symbols >> or \ge≥., shade the upper side of the boundary line.

If the inequality symbols << or \le≤ are present, shade the boundary line's bottom side.

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Answer:

0.002827 m^2

Step-by-step explanation:

A = pi * r^2

d = 2r

r = 3 cm = 0.03 m

A = pi * (0.03) ^ 2

A = 0.002827 m^2

The area of the circle is - 0.028 [tex]m^{2}[/tex]

The diameter (D) of a circle - 6cm

                          D=[tex]\frac{r}{2}[/tex]

The radius of a circle is = [tex]\frac{6}{2}[/tex] cm

                                      = 3 cm  = 0.03 meter

Now,  

       The formula of the area of a circle  = π[tex]r^{2}[/tex]

                    (the value of π = [tex]\frac{22}{7}[/tex] )

        Area of a circle = [tex]\frac{22}{7}[/tex] * [tex](0.03)^{2}[/tex]   [tex]m^{2}[/tex]

                                  =[tex]\frac{22}{7}[/tex] * 0.0009 [tex]m^{2}[/tex]

                                  = 0.028 [tex]m^{2}[/tex]

∴ The area of the circle is - 0.028 [tex]m^{2}[/tex]

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The value of x° and y° are 48.5° and  38.6°.

What is the cosine law?

The square of the length of any one side of a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, multiplied by the cosine of the angle they are a part of.

The length of sides of the triangle are 10, 12, and 16.

Assume that AB = c = 10, BC = a = 16, and AC = b = 12

m∠B = x° and m∠C = y°.

Cosine law:

c² = a² + b² - 2ab cos C  ....(i)

b² = a² + c² - 2ac cos B  ....(ii)

a² = b² + c² - 2bc cos A  ....(iii)

Putting a = 16, b = 12, c = 10, and C = y° in law (i)

10² = 16² + 12² - 2×16×12 cos y

100 = 256 + 144 - 384 cos y

384 cos y = 300

cos y = 300/384

y = 38.6°

Putting a = 16, b = 12, c = 10, and B = x° in law (ii)

12² = 16² + 10² - 2×16×10 cos x

144 = 256 + 100 - 320 cos x

320 cos x = 212

cos x = 212/320

x =48.5°

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The book  'Terrible Weather' was written by WAYNE DROPS

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

Solving the equations,

1) 5x-7 = 4x+3

x = 10 (N)

2) 6+2x = 7x-9

5x = 15

x = 3 (O)

3) 8x+1 = -8-x

-9x = 9

x = -1 (A)

4) -5+12x = 18x+7

6x = -12

x = -2 (S)

5) -4x+3 = 5x-13-x

8x = 16

x = 2 (R)

6) -10-11x+24 = 3x

14x = 14

x = 1 (E)

7) 8+3x = x+11+2x

3x-3x = 11-8

3 = 0

No solution (Y)

8) 5+17x+9 = 2x+21x+14

6x = 0

x = 0 (D)

9) 6x+8-13x+10 = 4-6x-11+4x

-7x+18 = -7-2x

5x = 25

x = 5 (W)

10) -14+5-x-3 = x+6+x+3x

-18 = 6x

x = -3 (P)

Now, the answer is coded as 93716 852104

Decoding with the help of the solutions of the given equations

WAYNE DROPS

Hence, the answer is WAYNE DROPS

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Answer:

( D ) x must be a number divisible by 3

Step-by-step explanation:

Rational numbers cannot be whole numbers.

( A ) x must be an odd number

if x is an odd number, Let's take x as 1 then the answer will be in rational number. So, Option A is wrong.

( B ) x must be an even number

If x is an even number, Let's take x as 2 then the answer will be in Rational number. So, Option B is wrong.

( C ) x must be a number greater than 3

Let's take x as 4, then the answer will be in Rational number. So, Option C is wrong.

( D ) x must be a number divisible by 3

Let's take x as 6 as 6 is divisible by 3, then

[tex] \frac{2}{3}x+ 1[/tex]

[tex] \frac{2}{3}(6)+ 1[/tex]

[tex]2(2) + 1[/tex]

[tex]4 + 1[/tex]

[tex]5[/tex]

The coordinate of the image point A (-1, 4).

In mathematics, a translation is an up, down, left, or right movement of shapes. Because the translated shapes appear to be identically similar in size to the original ones, they are congruent with one another.

The Rule of Translation of points is given by (x, y) → (x ± h, y ± k)

where the horizontal and vertical shiftings are h units and k units, respectively.

Given that

The image point of A after a translation right 4 units and up 4 units is the point B

Let A(x, y) be the point that translated to right 4 units and up 4 units

According to the given formula

(x, y) → (x ± h, y ± k)

Since the point is translated to right and up

=> (x, y) → (x + h, y + k)  

=> (x, y) → (x + 4, y + 4)

From the given data the final point is B(3, 8)

=> (x + 4, y + 4) = (3, 8)  

=> x + 4 = 3  and  y + 4 = 8

=> x + 4 = 3      

=> x = 3 - 4 = -1

=> x = -`1          

=> y + 4 = 8  

=> y = 8 - 4

=> y = 4  

Therefore,

The coordinate of the image point A (-1, 4).

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Answer:

45 million

Step-by-step explanation:

There will be approximately 45 million streams on the seventh day after the song's release.

To solve the problem, use the formula for exponential growth:

[tex]N(t) = N0 * (1 + r)^t[/tex]

where

N(t) is the number of streams at time t,

N0 is the initial number of streams,

r is the daily growth rate expressed as a decimal, and

t is the time elapsed in days.

In this case, N0 = 15 million, r = 0.2 (since the number of streams increases by 20% per day), and t = 7 (since we want to know the number of streams on the seventh day).

Plugin these values into the formula

[tex]N(7) = 15 * (1 + 0.2)^7\\N(7) = 15 * 1.2^7[/tex]

N(7) = 15 * 2.985984

N(7) = 44.78976

N(7) ≈ 45 million

Therefore, there will be approximately 45 million streams on the seventh day after the song's release.

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The mean of following numbers is 4.

To find: mean of given numbers .

Given data : 1, 2, 3, 4, 5, 6, 7

Mean: Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here, sum of observations =1+2+3+4+5+6+7=28

sum of observations=28

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data

Total number of observations =7

The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.

Substituting values in above formula,

=[tex]\frac{28}{7}[/tex]=4

Therefore, the mean is 4.

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Answer:

x² -9x + 20

Step-by-step explanation:

x²-4x -5x + 20

x² - 9x + 20

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)

the X and Y Intercepts of a Line Using Algebra

When the equation is written in the slope-intercept form (y=mx +b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)

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Answer:

99%

Step-by-step explanation:

10% = 0.1

Take 550 times 0.1 = $55

So, 10% of $550 is $55

Because it is a discount, so we subtract it

550 - 55 - $495

Then we know it marks up by 10%

10% of 495 is $49.50

495 + 49.50 = $544.50

Then take 544.50 divided by 550, then times 100% = 99%

The cost of 1 oz in dollars if 10 oz cost $0.95 is $0.095

Based on the given concept; we can solve by using ratio

Cost of 10 oz = $0.95

Cost of 1 oz = x

Equate the ratio of number of oz to cost in dollars

10 : 0.95 = 1 : x

10/0.95 = 1/x

cross product

10 × x = 0.95 × 1

10x = 0.95

divide both sides by 10

x = 0.95/10

x = $0.095

In conclusion, 1 oz cost $0.095

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The median of 1 - 50 is 25.5.

The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.

The first fifty numbers are 1,2,3,4,5................50

The number of terms in the data, n=50.

As the number of terms is even thus the median will be (n/2 th term + n/2 +1 th term) / 2

Median = (50/2 +50/2+1)/2

The 25th term of the sequence is 25.

The 26th term of the sequence is 26.

Median = 25+26/2 = 25.5.

Thus, the median of 1-50 is 25.5.

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The first fifty numbers are 1,2,3,4,5................50

The number of terms in the data, n=50.

Median = (50/2 +50/2+1)/2

The 25th term of the sequence is 25.

The 26th term of the sequence is 26.

Median = 25+26/2 = 25.5.

Thus, the median of 1-50 is 25.5.

The repeated sampling of a population is known as distribution of sample in R.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution. The frequency distribution of a variety of possible outcomes for a population statistic makes up the sampling distribution of a specific population.

The relationship between observations of various heights is described by the distribution, a mathematical function. Simply said, a distribution is a grouping of data, or scores, on a variable. These scores are typically listed from smallest to largest, after which they might be displayed graphically.

The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.

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We can conclude that under the AAS congruency condition, we can prove that △WXY ≅ △YZX.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

You can move, flip, twist, and turn these triangles to produce the same effect.

When relocated, they are parallel to one another.

So, we know that;
Shared side XZ by △WXZ and △YZX.

Right angles exist between WXZ and XZY.

∠XYZ and ∠XYZ have the same values.

Now that we have the parameters, we can infer that XZ is congruent to itself according to the reflexive property of congruence, and as a result, both triangles have a congruent side.

Second, since WXZ and XZY are right angles, it follows that they are equal and hence congruent.

The last piece of information is that XWZ and XYZ are congruent.

In conclusion, the triangles are congruent according to the AAS Congruency since we have two corresponding angles and one corresponding side that are equal but the corresponding side is not with the included angles.

Therefore, we can conclude that under the AAS congruency condition, we can prove that △WXY ≅ △YZX.

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Answer:

x = 14.4

Step-by-step explanation:

[tex]\frac{30}{18} =\frac{24}{x}[/tex]

30x = 18*24

30x = 432

x = 14.4

The value of x in the triangle is,

⇒ x = 14.4

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle is shown in figure.

Now, We can formulate by definition of proportion as;

⇒ 30 / 24 = 18 / x

⇒ x = 18 × 24 / 30

⇒ x = 14.4

Thus, The value of x in the triangle is,

⇒ x = 14.4

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Your answers are correct! Well done!

Yes, the UNIQUE function is an array function. The results of this function just need to be written once, and the full array will be filled with the results (range of cells).

A formula with numerous computations capabilities on one or more elements in an array is known as an array formula. An array can be thought of as a row, column, or mix of rows and columns of values. Array formulae may provide a single result or a number of outputs.

Array formulae may provide a single result or a number of outputs. Any formula that can provide several outcomes will automatically spill them either down, starting with the Microsoft 365 September 2018 upgrade.

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The sum of these numbers is indeed 131 + 133 + 135 = 399. Therefore, the three consecutive odd numbers are 131, 133, and 135.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Here we will use algebra to find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 399

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 399

3X + 3 = 399

3X + 3 - 3 = 399 - 3

3X = 396

3X/3 = 396/3

X = 132

Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.

132 + 133 + 134 = 399

Since, 132 + 133 + 134 equals 399 as displayed above.

Hence ,The sum of these numbers is indeed 131 + 133 + 135 = 399. Therefore, the three consecutive odd numbers are 131, 133, and 135.

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Answer: see below

Step-by-step explanation:

x=-1 is a vertical line at x=-1

5 is the required mean of the given values 4 and 6.

The mean is a specific type of average.

A list of values, such as measurements or numbers, is used to calculate it by dividing the total number of values in the list by the total number of values in the list.

To find the mean, add up each value in the set.

Now, we got the values which are:

4 and 6

Mean formula: Sum of terms / Number of terms

Now, we will use the above-given formula and calculate the mean of 4 and 6 as follows:

Mean: Sum of terms / Number of terms

Mean: 10/ 2

Mean: 5

Therefore, 5 is the required mean of the given values 4 and 6.

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Complete question:

How do you find the mean of 4 and 6?