What are the factors of the expression x² 6x 16?

Answer: The sample space of rolling an eight-sided die would be (1, 2, 3, 4, 5, 6, 7, 8)

Step-by-step explanation: Sample space is defined as a set of all possible outcomes. In an eight-sided die, there are eight faces and hence, we have the probability of getting any number within 1 to 8.

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Answer:

D

Step-by-step explanation:

The explicit form that would be used to find the nth term in the sequence is aₙ = 2 + 3n

What is arithmetic sequence?

The difference between each consecutive term in an arithmetic sequence is constant.

An explicit formula for an arithmetic sequence is a = d(n - 1) + c, where d is the common difference between consecutive terms.

According to the given question:

The first term in an arithmetic sequence is 5 that is a = 5

Now, the third term in the sequences is -1

a₃ = a + 2d

By substituting the value of a and a₃ we can find d for the arithmetic sequence.

-1 = 5 + 2d

2d = -6

d = -3

So, the explicit form that would be used to find the nth term in the sequence is

aₙ = 5 - (n - 1)(-3)

Simplifying further to get

aₙ = 2 + 3n

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Answer:

a) 47

b) 61

Step-by-step explanation: We can setup two equations from the information given above:

2c + 4b = 14 where c is the cost if one carousel ticket and b is the cost of four bumper car tickets.

6c + 9b = 33 where where c is the cost if one carousel ticket and b is the cost of four bumper car tickets like in the 1st equation.

If you divide the second equation by 3, you get 2c + 3b = 11, leaving 2c in both equations.

If you subtract both equations by the elimination method:

    2c + 4b = 14

-

    2c + 3b = 11

---------------------------

b = 3, which solves for the cost of one bumper car ticket

If you plug this value back into the first (or second) equation,

ex. 2c + 4(3) = 14 -> 2c = 2 -> c=1

You get c = 1, which solves for the cost of one carousel ticket.

Then you plug these values (c=1 and b=3) in a) and b):

a) 8*1 + 13*3 = 47

b) 10*1 + 17*3 = 61

The formula for finding the altitude of an equilateral triangle is ((sqrt (3))/2)a.

As we know, the sides of an equilateral triangle are equal. Let the side of the triangle be 'a'.

Dropping a perpendicular from the vertex of the triangle, the triangle gets divided into two right triangle where the base of the triangle is divided into two as well.

Therefore, by using the Pythagoras' theorem,

we can get the altitude (say 'h') of the triangle by:

h^2 = a ^ 2 - (a/2) ^ 2 = 3a ^ 2/4

h = sqrt (3a^2/4) = ((sqrt (3))/2)a.

The question is incomplete, the complete question is:

What is the formula for finding the altitude of an equilateral triangle?

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The base in term of the height of the triangle is written as ;b = 2A/h.

A closed triangle has three sides. It is among the fundamental geometric shapes because it has three vertices and three sides.

Thus, the formula for the are area of the triangle is -

A = 1/2 bh

In  which,

b = base of the triangle.

h = height of the triangle.

In term of the height.

b = 2A/h

Thus, the base in term of the height of the triangle is written as;b = 2A/h.

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The total number of sunny days for the three years is 103 days.

This year there were 17 sunny days.

There were 17 sunny days this year, 18 fewer than last year. This is to mean that, last year, sunny days were 18 days more than this year, Which can be found by;

18+17 = 35 sunny days

Sunny days two years ago were three times the sunny days this year which is;

3×17 = 51 sunny days

Therefore, the total number of sunny days for the three years is calculated by adding the total number of sunny days for the three years:

17 + 35 + 51 = 103 sunny days

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Using the mean formula, we will add the two values and divide the result by 2 to determine the mean of the two values.

The average of a group of variables is referred to as the mean in mathematics and statistics.

There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

So, to find the mean of 2 values:

Mean formula: Sum of the terms / Number of terms

Now, using the formula, to obtain the mean of 2 values, we will get the sum of the 2 given values and divide it by 2.

Therefore, using the mean formula, we will add the two values and divide the result by 2 to determine the mean of the two values.

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Correct question:

How do you find mean of 2 values?

The area of the largest rectangle that can be inscribed in the ellipse is 2ab

The term ellipse in math is a circle that has been stretched in one direction to give it an oval shape

Here we have given the following equation x²/a² + y²/b² = 1

Now, we have to find the area of the largest rectangle that can be inscribed in the ellipse

Here we all know that the Area of rectangle = 4xy

That can be written as A = 4xy

Now, we have to differentiate the given expression then we get,

=> dA/dx = 4xdy/dx  + 4y ----------------------(1)

Here we have given an equation  x²/a² + y²/b² = 1

Now, we have to differentiate this one also, then we get,

=> 2x/a²  + 2y(dy/dx)/b² = 0

If we equate both of the equation then we get the value as.

=> dy/dx = - xb²/a²y

Now, substitute the values on equation (1), then we get,

=> dA/dx = 4x( - xb²/a²y)  + 4y

Equate the expression with 0, then we get the value of

=> a²y² = b²x²

=> x²/a² = y²/b²

When we simplify this one then we get the value of x as (a/√2) and  y as b/√2

Therefore, the Area is calculated as,

=> 4xy  =  4(a/√2)(b/√2)  = 2ab

So, the value 2ab is the area of the greatest rectangle that can be inscribed in an ellipse x²/a² + y²/b² = 1

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Answer:

Answer is 4, but in the answer choices provided it is 4b.

Step-by-step explanation:

Use PEMDAS! (Order of PEMDAS: Parenthesis, exponent, Multiplication, division, addition, subraction)

1. Multiply 6b x 2= 12b.

2. Divide 12b by 3b = 4. or 4b

Answer:

---------------------------

Correct choice is D.

The final answers are a) 12 b)3/28 c) 2

In Maths, reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n. It means that we have to convert the number to the upside-down form. For example, the reciprocal of 9 is 1 divided by 9, i.e. 1/9

Given here a) 4÷1/3 = 4×3

                                =12

                   b) 3/8÷7/2 = 2×3/8×7

                                     = 3/28

                   c) 3¹/₂ ÷7/4 = 7/2÷7/4

                                      = 2

Hence the answers are 12, 3/28 , 2

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Therefore, In the figure, a∥b  angle m∠7 = 34° .

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.

Here,

Given that a and b are parallel lines,

∠3 and ∠7  are corresponding angles and congruent

m∠3 = 34°

thus ,m∠7 =m∠3 = 34°

so, m∠7 = 34°

Therefore, In the figure, a∥b  m∠7 = 34° .

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Answer: olynomial Long Division

Dividing :  x3 + x2 - 20x + 24

                             ("Dividend")

By         :    x - 3    ("Divisor")

dividend     x3  +  x2  -  20x  +  24

- divisor  * x2     x3  -  3x2        

remainder         4x2  -  20x  +  24

- divisor  * 4x1         4x2  -  12x    

remainder          -  8x  +  24

- divisor  * -8x0          -  8x  +  24

remainder                0

Quotient :  x2+4x-8  Remainder:  0

Factoring  x2+4x-8

The first term is,  x2  its coefficient is  1 .

The middle term is,  +4x  its coefficient is  4 .

The last term, "the constant", is  -8

Step-1 : Multiply the coefficient of the first term by the constant   1 • -8 = -8

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   4 .

     -8    +    1    =    -7

     -4    +    2    =    -2

     -2    +    4    =    2

     -1    +    8    =    7

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Find roots (zeroes) of :       F(x) = x3 + x2 - 23x + 24

    See theory in step 1.3

In this case, the Leading Coefficient is  1  and the Trailing Constant is  24.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,8 ,12 ,24

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        47.00    

     -2       1        -2.00        66.00    

     -3       1        -3.00        75.00    

     -4       1        -4.00        68.00    

     -6       1        -6.00        -18.00    

     -8       1        -8.00        -240.00    

     -12       1       -12.00       -1284.00    

     -24       1       -24.00       -12672.00    

     1       1        1.00        3.00    

     2       1        2.00        -10.00    

     3       1        3.00        -9.00    

     4       1        4.00        12.00    

     6       1        6.00        138.00    

     8       1        8.00        416.00    

     12       1        12.00        1620.00    

     24       1        24.00       13872.00    

Polynomial Roots Calculator found no rational roots

Answer: x3 + x2 - 23x + 24

 ——————————————————

         x        

Step-by-step explanation:

Answer:

-100

Step-by-step explanation:

To solve -2^6 - 6^2, we can evaluate each term separately.

2^6 = 64

6^2 = 36

-2^6 - 6^2 = -64 - 36 = -100

The slope of the line y =3x(1 ,3) is 3.

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same). In math, we frequently want to quantify the steepness. Slopes B and C are clearly higher than slope A. While slope A is just four units high, they are both seven units high. Therefore, it would seem that height and steepness are related.

Given

Equation

y = 3x (1,3)

Using slope intercept form,

y = mx + b

m = slope

m = 3

The slope of the line y =3x(1 ,3) is 3.

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The two types of functions are linear and non linear functions.

A linear function is a function that can be written in the form f(x) = mx + b, where m and b are constants. This type of function has a constant rate of change, meaning the output will always increase or decrease the same amount for a given change in the input. For example, if the input increases by 3, the output will increase by 6. An example of a linear function is f(x) = 3x + 5. This function will always increase by 3 for each increase in the input, and will always have a y-intercept of 5.

A non-linear function is a function that cannot be written in the form f(x) = mx + b. This type of function has a variable rate of change, meaning the output will increase and decrease at different rates for different changes in the input. An example of a non-linear function is f(x) = x2 - 4x + 5. This function will increase and decrease at different rates for different changes in the input, and will always have a y-intercept of 5.

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As per the quadrilateral ABCD, the value of x will be equal to 36°.

A polygon is described in geometry as a compact, two-dimensional shape having three or more straight lines. Poly, which means "many," and gon, which means "angle," make up the Greek word "Polygon." Polygons of several kinds can be seen all around us.

As per the given diagram in the question,

The given angles are:

∠ A = 72°

∠ C = 3x

For a cyclic quadrilateral,

∠ A + ∠ C = 180°

72 + 3x = 180

3x = 180 - 72

3x = 108

x = 108/3

x = 36°

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Answer:

A = 5 ;  B = 6

B = 7 ; C = 8

C = 9 ; D = 10

convert C:D where C is equals to C in B:C

C = 144 ; D = 160    

convert B:C where B is equals to B in B:C

C = 144 B = 126

convert A:B where B is equals to B in B:C

B = 126 A = 30

A = 30, B = 126, C = 144, D = 160

ratio

Step-by-step explanation:

The correct option is A.Hence the given number follow the pattern of consective powers,so unit digit of given number will be 1.

The unit digit is a number placed in the one's position.It is placed right most digit of the given number.The value of every digit in the number system by specifying the position of the particular digit in the number such as ones,tens,hundreds,thousands and so on.

It is easy to identify the unit place of smaller number but when it comes to the raised to the power it becomes difficult to identify by simple observation.Then we use cyclicity chart.It is based on every digit in the number has its own repetitive pattern when raised to any specific power.

For example 2^5=32 ; Here 2 is the unit digit of given number.

Now we use cyclicity concept to  find and get

Unit digit of 27^1=7(7^1=7)

Unit digit of 27^2=9(7^2=49)

Unit digit of 27^3=3(7^3=343)

Unit digit of 27^4=1(7^4=2401)

Hence for every four consective ,the unit digit will follow pattern of 7,9,3,1.

SO Unit digit of given number is 1.

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Answer:

Slope: 2

Y-Intercept: 47

Equation (in slope-intercept form): p = 2b + 47.

Step-by-step explanation:

To determine the equation, slope, and y-intercept for a function that outputs the total points the Dragons scored based on the number of 2-point baskets made, you will need to use the information given about the number of 3-pointers, foul shots, and 2-point baskets made.

First, let's define p as the total number of points the Dragons scored and b as the number of 2-point baskets made.

We know that the Dragons scored a total of 12 three-pointers * 3 points per 3-pointer + 11 foul shots * 1 point per foul shot = 47 points from 3-pointers and foul shots.

Therefore, the total number of points the Dragons scored can be expressed as:

p = 47 points + 2 points per 2-point basket * b 2-point baskets

This equation is in slope-intercept form, with the slope being 2 points per 2-point basket and the y-intercept being 39 points.

The equation in slope-intercept form is:

p = 2b + 47

Therefore, the slope of the function is 2, the y-intercept is 39, and the equation is p = 2b + 47.

Answer:

neither coz m1=-1/5 and m2=1/5

m1 is not equal to m2 [not parallel]

m1× m2 is not equal to -1.[not perpendicular]

Similar to the plane reflection, the line reflection is the inversion through a straight line. In reality, it goes through the same transformation as a 180-degree rotation.

A reflection is referred to as a flip in geometry.

A reflection is the shape's mirror image.

A line, called the line of reflection, will allow an image to reflect through it.

Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The line reflection is the inversion through a straight line, much as the plane reflection.

Actually, it undergoes the same change as a 180-degree rotation.

For this reflection, the rule would be written as RX-axis (x,y)→(x,y).

Rule of Notation: This notation rule tells you that image A has been reflected across the y-axis and the x-coordinates have been multiplied by -1.

It has the form by-axis A→B = axis (x,y)→(x,y).

Therefore, similar to the plane reflection, the line reflection is the inversion through a straight line. In reality, it goes through the same transformation as a 180-degree rotation.

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Step-by-step explanation:

To find the ratio between Rohit's savings and expenditure, we need to divide his savings by his expenditure:

Savings / Expenditure = (1500 - 1250) / 1250 = 250 / 1250 = 1/5

The ratio between Rohit's savings and expenditure is 1/5.

To find the ratio between Rohit's expenditure and income, we need to divide his expenditure by his income:

Expenditure / Income = 1250 / 1500 = 5/6

The ratio between Rohit's expenditure and income is 5/6.

To find the ratio between Rohit's income and savings, we need to divide his income by his savings:

Income / Savings = 1500 / (1500 - 1250) = 1500 / 250 = 6/1

The ratio between Rohit's income and savings is 6/1.

The probability of forming a bow-tie quadrilateral from four randomly chosen chords is approximately 6.25%.

This is because there are exactly 28 possible quadrilaterals that can be formed from the seven given points, and only one of those 28 quadrilaterals is a bow-tie quadrilateral. This means that the probability of forming a bow-tie quadrilateral is 1/28, which is equal to 0.0357, or 3.57%.

To explain further, when we draw all of the chords from the seven given points, we have 21 distinct chords. Out of these, 10 chords form triangles, leaving us with 11 chords that form quadrilaterals.

Since four of these chords are randomly chosen, the number of possible combinations of quadrilaterals that can be formed is equal to 11C4, or 495. Out of these 495 combinations, only one is a bow-tie quadrilateral. This means that the probability of forming a bow-tie quadrilateral is 1/495, or 0.002041, or 0.2041%.

Since 0.2041% is too small to be expressed as a whole number, it is rounded up to 6.25.

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The graph of inequality x < −2 is as shown below.

In this question we need to graph x is less than or equal to negative 2.

i.e., we need to graph an inequality x < −2

First we draw a straight vertical line x = -2.

The graph of x = -2 is a straight line parallel to y-axis and intersects x-axis at (-2, 0)

We represent the graph of x = −2 by the dashed line.

The dashed line indicates that the line is the boundary of the inequality but not part of it. Shade in the left side of the line to indicate the inequality x<−2.

Therefore, the graph of x is less than or equal to negative 2 is as shown below.

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A function is continuous if its graph is a single, unbroken line without any gaps. A function is discontinuous if its graph has breaks in it, or if it is undefined at certain points.

A function is continuous if its graph is a single, unbroken line without any gaps. This means that the function must have a defined value for every value of the independent variable. If the graph of the function is smooth, without any abrupt changes or jumps, then it is continuous. A function is discontinuous if its graph has breaks in it, or if it is undefined at certain points. This means that the function is not defined at certain values of the independent variable and hence, the graph is not a single, unbroken line. Discontinuities can arise from various sources, such as a function having an infinite value, a function having a zero value or a function having an undefined value. The graph of a discontinuous function typically has gaps or jumps, and it is not a single, unbroken line.

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Step-by-step explanation:

circumcentre:

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle.

othocentre:

The orthocenter is the intersection point of three altitudes drawn from the vertices of a triangle to the opposite sides. A centroid is the intersection point of the lines drawn from the midpoints of each side of the triangle to the opposite vertex.