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A linear relationship is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.

What does the term "linear relationship " mean?

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association).

                         Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.

Why are relationships linear and nonlinear?

Plotting a linear relationship on a graph results in a straight line, whereas plotting a nonlinear relationship results in a curve.

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The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.

Given,

Function,

y = x² - 8x + 12

The supplied equation's vertex must be located.

The equation is a parabolic equation when we look at it.

We are aware that a parabolic equation's generic form is

y = x² - 8x + 12

where the parabola's vertex's x and y coordinates are denoted by h and k.

We can determine the following by comparing the aforementioned equation with the parabola's general form:

x = 4, y = 4 and h = -8

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

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The value of angle x that extends from the given polygon is 61°.

How to find the value of x?

The angle of straight line will be 180°

119° + x = 180°

x = 180° - 119°

x = 61°

Hence, the value of x that extends from the given polygon is 61°.

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1. True (The center of dilation lies on the segment)

2. False (The center of dilation does not line on the segment)

3. False (The center of dilation lies on the segment)

4. True (Since the segments are not collinear as a result of the dilation, they are parallel)

5. True (Scale factor is 2)

6. False (Scale factor is 2)

7. True (by definition)

8. True (by definition)

Answer: y=(13/3)*x-6

Step-by-step explanation: -3y=18-13x    -y=6-13/3 x

y= (13/3)x-6

The angle of x in the triangle is 30 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

In other words, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

Therefore, the value of x can be found using the exterior angle theorem as follows:

x + 45 = 2x + 15

x - 2x = 15 - 45

- x  = - 30

divide both sides by - 1

Therefore,

x = 30

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The correct answer is 64

Demoivre's theorem states that for all complex numbers z and all positive integers n:

z^n = (r^n) × (cos(n∅) + isin(n×∅))

where r is the magnitude of z and theta is the argument of z.

To use Demoivre's theorem to simplify (1−i)^12, we can first write (1−i) in polar form as r × cis(∅). where r is the magnitude and cis(∅) is the size complex number. is 1, the argument ∅. In this case the size of (1−i) is √(1^2 + (-1)^2) = √(2) and the argument of (1−i) can be found using the arctangent function.

∅ = arctan(-1÷1) = -45 degrees.

So (1−i) can be written as sqrt(2) × cis(-45 degrees). Applying this to Demoivre's theorem, we get:

(1−i)^12 = (√(2)^12) × (cos(-540°) + i×sin(-540°))

We can simplify this to:

(1−i)^12 = 2^6 × cis(-180°)

This can be further simplified as follows.

(1−i)^12 = 64 × (-1)

the final answer is -64.

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Answer: The number it is a power too

To determine how many times greater something is in scientific notation, you need to compare the exponents of the numbers and calculate the ratio between them.

In scientific notation, a number is expressed as the product of a coefficient (a decimal number between 1 and 10) and a power of 10. The exponent represents the number of places the decimal point has been moved.

To find how many times greater one number is than another, you compare the exponents of the powers of 10. If the exponent of the first number is n and the exponent of the second number is ᵃ, you can calculate the ratio by dividing 10ⁿ by 10ᵃ.

The result of this division will give you the factor by which the first number is greater than the second number. For example, if the result is 100, it means the first number is 100 times greater than the second number.

In summary, to determine how many times greater something is in scientific notation, compare the exponents of the powers of 10 and calculate the ratio between them.

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Step-by-step explanation:

when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is

cos(our angle) × radius

15×sqrt(3) × cos(our angle) = 15

cos(our angle) = 1/ sqrt(3) = 0.577350269...

our angle = 54.73561032...°

The value of kinetic energy will be 37.5 Jules.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.

Now,

Since, A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.

Hence, The value of kinetic energy with a mass of 3kg and a velocity of 5m/s create will be;

⇒ Kinetic energy = 1/2 mv²

⇒ Kinetic energy = 1/2 × 3 × 5²

                           = 1/2 × 3 × 25

                           = 37.5 Jules

Thus, The value of kinetic energy will be 37.5 Jules.

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Answer:

1+i

Step-by-step explanation:

Divide by 1

(1/1+i)

(1+i)

Identify the components of the numbers and add the real and imaginary parts separately

=(1)+(1)i

=(1)+(1)i

=(1+i)

Answer: not sure on this problem too

Step-by-step explanation:

sorry, can't really help!

The area of the circle is 66.50cm²

A circle is an object in which all distances are equal from the center.

In a circle, the length of the two tangents are equal.

From the figure, BP=CP

Also, the angles between a tangent and a radius is = 90⁰

⇒<OCP=90⁰

<PCB=<PBC=(180-60)/2 = 120/2 = 60⁰

Using cosine rule,

p²=b²+c²-2bccosP

p²=8²+8²-2*8*8*cos60

p²=64+64-128*0.5

p²=128-64

p²=64

Take the square root of both sides to get

p=√64=8

Note that CB=8  .....................(given)

Cx=8/2=4cm

Using trigonometric ratio

CosC = Adjacent/Hypotenuse

Cos30 = 4/CO

CO = 4/cos30

CO = 4/0.8660

CO = 4.6cm

CO = radius (r)

Area of circle = пr²

Area = 22/7 * 4.6 * 4.6

Area = 66.50 cm²

In conclusion, the area of the circle is  66.50cm²

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The monthly share of annual expenses is $1820/month.

The monthly Share is calculated by dividing the annualized net amount of non-monthly billed services by 12.

Nonrecurring billing:

A one-time transaction is a non-recurring payment.

There is usually only one invoice or bill involved, and it only happens once.

Frequently, the amount is greater than the sum for recurring payments.

Subscriptions that are on monthly billing are billed on the same day each month for as long as the subscription is current.

So, we have:

Annual: $4200

Living: $670

Fixed: $800

Now, calculate as follows:

4200/12 = 350

Then,

350 + 370 + 800 = $1820/month

Therefore, the monthly share of annual expenses is $1820/month.

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28sinθ is the maximum area of the triangle

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The two sides of triangle are of length 7 and 8.

Triangle has an included angle has a measure of θ degrees.

We need to find the maximum area

A=1/2×7×8×sinθ

A equal to one by two time of seven times of eight times sin theta.

A=7×4×sinθ

A=28sinθ

Hence, 28sinθ is the maximum area of the triangle

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The equation in standard form for the circle will be;

⇒ (x + 2)² + (y - 9)² = 1

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle that has a diameter with endpoints (-2,10) and (-2,8).

Now,

Since, The circle that has a diameter with endpoints (-2,10) and (-2,8).

Hence, The radius of circle is the half of the distance between two points of the diameter.

So, Radius = 1/2 (√ (8 - 10)² + (- 2 - (-2))²

                 = 1/2 √4

                = 1/2 × 2

                 = 1

Thus, Radius (r) of circle = 1

And, The center of circle is midpoint of the endpoints of the diameter.

Hence, Centre = (- 2 + (-2))/2, (10 + 8)/2

                       = - 4/2 , 18/2

                       = (- 2, 9)

Hence, The equation of circle with center (-2, 9) and radius 1 is;

⇒ (x - (-2))² + (y - 9) = 1²

⇒ (x + 2)² + (y - 9)² = 1

Thus, The equation in standard form for the circle will be;

⇒ (x + 2)² + (y - 9)² = 1

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The exponential growth of three sections is given below.

Exponential growth means whose growth more rapid in proportion.

An exponential function is of the form , where b is a positive number not equal to 1.

The value of b determines whether tha function is an exponential growth or an exponential decay.

An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.

Given the function= y 4(5/6)^x

B= 5/6 < 1

Therefore, the function  is an exponential decay.

Given the function

Therefore, the function  is an exponential growth.

Therefore, the function  is an exponential growth is y= 129(1.63)^x is an exponential growth.

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Answer:

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

If it is in the center than DC is 21 and CM is 21

42÷ 2

Answer:

(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab)

Which of the following shows the sum of the polynomials rewritten with like terms grouped together?

[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)

[3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab)

[3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2)

[3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)

The answer is A.

Step-by-step explanation:

Answer: 15x15

Step-by-step explanation:

I'm assuming this is an optimization problem in a Calculus class, if not just disregard all of this and be happy with the answer.

We can write two equations for the value of x and y lengths of this rectangle.

2y+2x=60

xy=A

Solve our perimeter equation for y, y=30-x.

This gives us x(30-x)=A, and 30x-x²=A.

Find the derivative of the area function: A'=30-2x

To maximize we set A' to 0: 0=30-2x, x=15

Plug back into our perimeter formula: 2y+2(15)=60, y=15

So both sides will be 15 inches.

Answer:

y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 2 ) , then

y - 2 = - [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is

y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)

Answer: 119/6

Step-by-step explanation:

-3 1/2 can be written as -7/2

-5 2/3 can be written as -17/3

-7/2 times -17/3 = 119/ 6

Answer:

y = x + 2

Step-by-step explanation:

Use the slope-intercept form:

y=mx+b

M represents the slope of the line

B represents the y-intercept

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The simplest polynomial with the given roots will be equal to x⁴ + 5x² - 36.

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and raising non-negative integers to power, together with uncertainty and coefficients. x² + 4x + 7 is an illustration of a single indeterminate x polynomial.

The total of terms with the pattern [tex]kx^n[/tex] forms a polynomial. Where n is indeed a positive number and k is any number. For instance, the polynomial 3x + 2x - 5 exists.

As per the given information in the question,

The given roots are 3i, -2, 2

As we know that if 3i is a root then -3i is also a root.

Then, the factored form of this polynomial will be:

p(x) = (x - 3i)(x + 3i)(x + 2)(x - 2)

= (x - (3i)²) (x² -2x + 2x - 4)

It will become: (x² + 9)(x² - 4)

It can be further expanded,

x⁴ - 4x² + 9x² - 36

x⁴ + 5x² - 36

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The given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image).

We can picture what would happen if you turned the form across the line to graph a reflection.

So, we have a triangle with coordinates:

(8, 2), (3, 4), (2, 7)

Now, we will reflect it according to the rule:

(x, y)→(−x, y)

Then, the coordinates will be:

(-8, 2), (-3, 4), (-2, 7)
(Refer to the graph attached below)

Therefore, the given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

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Answer:

Step-by-step explanation:

The measure of the required angle of the given rhombus ABCD is m∠ADC = 64°.

The given rhombus has four angles as

∠ADC, ∠DCB, ∠CBA, and ∠BAD

It has two diagonals that bisect each other at point E.

And we have ∠ABD = 32° and ∠ACD = 58°

Here, the angles ∠ABD and ∠BDC are alternate angles. Since we know that, the alternate angles are equal in measure, we can write

∠ABD = ∠BDC

⇒ 32° = ∠BDC

Since we know that the diagonals of a rhombus bisect the angles, we get

∠ADC = 2∠BDC

⇒ ∠ADC = 2 × 32° = 64°

Therefore,  the required angle of the rhombus is ∠ADC = 64°.

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The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.

It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.

Let X be the random variable that defines the number of people with the mutation in the sample.

Since every person can or can't have the mutation, this is a Binomial distribution.

Here,

n = 800

p = 0.1

According to the formula for a Binomial Distribution,

the mean = np

Therefore, the mean for the above distribution will be

800 X 0.1

= 80.

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