Find the product. (6y − 2)2

Answer:

The result can be shown in multiple forms.

Exact Form:

− 3/2

Decimal Form:

− 1.5

Mixed Number Form:

−1 1/2

Step-by-step explanation:

Answer:

[tex]\displaystyle -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \biggr(\frac{7}{4}-\frac{8}{3}\biggr)-\biggr|\frac{1}{6}-\frac{3}{4}\biggr|\\ \\=\biggr(\frac{7*3}{4*3}-\frac{8*4}{3*4}\biggr)-\biggr|\frac{1*2}{6*2}-\frac{3*3}{4*3}\biggr|\\ \\=\biggr(\frac{21}{12}-\frac{32}{12}\biggr)-\biggr|\frac{2}{12}-\frac{9}{12}\biggr|\\ \\=-\frac{11}{12}-\biggr|-\frac{7}{12}\biggr|\\\\=-\frac{11}{12}-\frac{7}{12}\\\\=-\frac{18}{12}\\ \\=-\frac{3}{2}[/tex]

The equation that has the solutions [tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex] will be a) 2x² + 6x + 9

Here we have to find the equation which has roots

[tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex]

This means that the factors of the roots will be

[tex]x+\frac{3 + \sqrt{3}i }{2}[/tex] and [tex]x+\frac{3 - \sqrt{3}i }{2}[/tex]

Now since all our options are quadratic equations, they have to be a product of these 2 factors and ONLY an additional numerical co-efficient

Hence we get

[tex][x+\frac{3 + \sqrt{3}i }{2}][x+\frac{3 - \sqrt{3}i }{2}][/tex]

rearranging this will give us

[tex][x+\frac{3}{2} + \frac{ \sqrt{3}i }{2}][x+\frac{3}{2} - \frac{ \sqrt{3}i }{2}][/tex]

using the formula

a² - b² = (a + b)(a - b) we get

(x + 3/2)² - (√3i/2)²

= x² + 9/4 + 3x + 9/4                                                                  [since i² = -1]

Hence we get x² + 3x + 9/2

= a) 2x² + 6x + 9

To learn more about Complex Numbers visit

https://brainly.com/question/21097829

#SPJ4

Correct Question

Which equation has the roots

[tex]\frac{3 \pm \sqrt{3}i }{2}[/tex]

a) 2x² + 6x + 9 = 0

b) x² + 3x + 12 = 0

c) x² + 3x + 3 = 0

d) 2x² + 6x + 3 = 0.

The total amount of flour used for the oatmeal cookies is 6 cups and Each batch of oatmeal cookies uses 2 cups of flour.

We can start by using the information given to set up an equation for the total amount of flour used for the chocolate chip cookies.

We know that each batch of chocolate chip cookies uses 2 1/4 cups of flour and there are 3 batches of chocolate chip cookies.

So the total amount of flour used for the chocolate chip cookies is:

2 1/4 cups x 3 batches = 6 3/4 cups

We also know that the total amount of flour used for all 6 batches is 12 3/4 cups and we know how much flour is used for chocolate chip cookies: 12 3/4 cups - 6 3/4 cups = 6 cups

So the total amount of flour used for the oatmeal cookies is 6 cups.

And since there are 3 batches of oatmeal cookies, we can find out how many cups of flour are needed for each batch by dividing the total amount of flour by the number of batches:

6 cups / 3 batches = 2 cups

So each batch of oatmeal cookies uses 2 cups of flour.

Therefore, The total amount of flour used for the oatmeal cookies is 6 cups and Each batch of oatmeal cookies uses 2 cups of flour.

To learn more about equations,

Visit; brainly.com/question/29657992

#SPJ4

A movie is not a real image, it is a series of still images or frames that are played back in rapid succession to create the illusion of motion.

Real images are those that are formed by light that has been refracted or reflected by an object or lens. These images are located on the same side of the lens as the object and can be projected onto a screen or viewed directly.

In movie, the images are typically captured on film or digitally and then played back on a screen at a high frame rate (usually 24 or 30 frames per second) to create the illusion of motion.

This is known as the persistence of vision effect. The images are not actually moving, but the human eye and brain perceive them as moving because of the rapid succession of still images.

In conclusion, a movie is not a real image, it is a series of still images played back in rapid succession to create the illusion of motion.

Real images are formed by light that has been refracted or reflected by an object or lens, whereas in movie the images are captured on film or digitally and then played back on a screen at a high frame rate to create the illusion of motion.

Learn more about real image at

https://brainly.com/question/13197137

#SPJ4

Answer:

12

Step-by-step explanation:

squares have equal sides

To convert 2D image to 3D in image processing, first Pre-Processing,  Feature Extraction, Modeling, Rendering, and then Post-Processing.

The process of converting a 2D image to a 3D is called 3D reconstruction. It is a challenging task as it requires a lot of knowledge and skill. The steps to convert a 2D image to 3D are:

1. Pre-Processing: This step involves noise removal, image enhancement, and image segmentation.

2. Feature Extraction: This step involves extracting important features from the image such as lines, circles, and other shapes.

3. Modeling: This step involves creating a 3D model using the extracted features.

4. Rendering: This step involves adding textures, colors, and shadows to the 3D model to make it look realistic.

5. Post-Processing: This step involves editing the 3D model to make it look better. It includes smoothing, blending, and other post-processing techniques.

The result of these steps is a 3D image that looks realistic and has the same features as the original 2D image.

To know more about 2D and 3D:

brainly.com/question/18893825

#SPJ4

The line passing through x- intercept 1 and y- intercept 1 so equation of line is x+y = 1

Depending on the various parameters, there are several ways to express the equation of a given line in mathematics. Point-slope form, slope-intercept form, two-point form, intercept form, etc. are among the ways that are most frequently observed.

By The Intercept A line's equation has the form x/a + y/b = 1. The x-intercept in this case is "a," and the y-intercept is "b."

The distance from the origin and on the x-axis where this line crosses the x-axis is represented by the value of "a," and the distance from the origin and on the y-axis where this line crosses the y-axis is represented by the value of "b."

We are able to determine the quadrants through which this line travels by using the signs of these intercepts.

To be learn more about intercepts refer to:

https://brainly.com/question/3334417?referrer=searchResults

#SPJ1

The number of balls that Eve has will be 25 balls.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this situation, Eve had some balls she tried to share them evenly first in 2 bags ,then in 3bags,and finally in 4 bags and each time ,she had one ball left over.

The number of balls that Eve has will be:

= (2 × 3 × 4) + 1

= 24 + 1

= 25 balls

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

Answer:

19 - 3(x - 2)²

Step-by-step explanation:

7 + 12x - 3x² ( rearrange terms in x )

7 - 3x² + 12x ( factor out - 3 from each of the x- terms )

= 7 - 3(x² - 4x)

using the method of completing the square on x² - 4x

add/subtract ( half the coefficient of the x- term )² to x² - 4x

= 7 - 3(x² + 2(- 2)x + 4 - 4)

= 7 - 3(x - 2)² - 3(- 4)

= 7 - 3(x - 2)² + 12

= 19 - 3(x - 2)² ← in the form a + b(x + c)²

with a = 19 , b = - 3 , c = - 2

Answer:

A prime triplet is a set of three prime numbers that are consecutive and differ by 2 (e.g. 3, 5, 7). The first prime triplet is (3, 5, 7), and it is well known that there are no other prime triplets. There is only one prime triplet that exist.

It is important to note that the concept of prime triplet is not commonly used in number theory and there are not many studies that focus on counting the number of prime triplets. Also, it is not known if there are an infinite number of prime triplets or not.

Step-by-step explanation:

The solution of the inequality are n  ≤ -7 and n ≥ -12.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality individually.

n + 2 ≤ −5 and  n + 6 ≥ −6

Hence,

n + 2 ≤ − 5

subtract 2 from both sides of the inequality

n + 2 - 2 ≤ − 5 - 2

n  ≤ -7

n + 6 ≥ −6

subtract 6 from both sides of the inequality

n + 6 ≥ −6

n + 6 - 6 ≥ −6 - 6

n ≥ -12

Therefore, n  ≤ -7 and n ≥ -12

learn more compound inequality here:https://brainly.com/question/29951684

#SPJ1

Answer: 1,667

Step-by-step explanation:

The numbers that 904 is divisible by are 1, 2, 4, 8, 113, 226, 452, and 904. You may also be interested to know that all the numbers that 904 is divisible by are also known as the factors of 904.

There are 301 numbers less than 904 divisible by 3, as per arithmetic progression.

What is an arithmetic progression?

"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."

Let, there are 'n' terms less than 904 divisible by 3.

Now, the first term divisible by 3 is(a) = 3.

The second term divisible by 3 is = 6.

Therefore, the common difference between terms divisible by 3 is(d)

The last term that is less than 904 and divisible by 3 is() 903.

Now, if we compare it with arithmetic progression, then

The required number is 301.

Learn more about divisible here:

brainly.com/question/24873057

#SPJ4

[tex]5x - 2x + 7 - x[/tex]

Combine Like Terms:

[tex](5x-2x-x)+(7)[/tex]

[tex]=\fbox{2x + 7}[/tex]

Answer:

2x+7

Step-by-step explanation:

5x -2x +7 -x (Add or subtract common fields[our common field is x])

5x -3x +7 Add the negatives toghether first( your dept)

2x+7 subtract your dept from the value you have

Measure of angle A is m∠A = 18.358

Every matching portion of one triangle is congruent to the other if two triangles are congruent.

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the result of adding the three triangle angles.

given

PQ = 12 units, and PS = 12 units, with PR dividing ZQPS.

OA validates AAS's triangular display. Triangle is consistent with PRQ. Triangle is shown by SAS thanks to PRS OC. Triangle is consistent with PRQ. SRP

Every matching portion of one triangle is congruent to the other if two triangles are congruent.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

The rate of change of the system will be equal to 5.

An indicator of how one quantity changes in proportion to another is called a rate of change. Consequently, if y is the dependent variable and x is the independent variable.

Rate of change = Slope of the line

Given that a baker is making cookies and the number of cookies is represented by the function y = 5x + 9 where x is the time in hours and y is the total number of cookies in the bakery.

For the given equation the slope is,

y = 5x + 9

Rate of change = slope

Rate of change = 5

To know more about the rate of change follow

https://brainly.com/question/8728504

#SPJ1

Step-by-step explanation:

[tex]\frac12(8k+12k^2+6k^3)\\=4k+6k^2+3k^3\\[/tex]

Rearrange into descending order:

[tex]\boxed{3k^3+6k^2+4k}[/tex]

The intersection of x = -1 and x = 1 is where f(x) = g(x) has its solution.

Therefore,

The intersection of the two lines, or the point at which they are equal, is the answer to the equation f(x) = g(x). According to the table provided, only the values 9 and 12 are shared by both f(x) and g(x).

Consequently, the intersection of x = -1 and x = 1 is where f(x) = g(x) has its solution.

To learn more about intersection, refer to:

https://brainly.com/question/29035054

#SPJ1

Answer: Ronaldo scored 6 goals in his first three soccer games

Step-by-step explanation: Ronaldo scored 6 goals in his first three soccer games because If he scored 4 goals in the fourth match then in the first 3 he would score 6 because 6 + 4 = 10 goals in total. Hope my answer was useful.

The image of the point (3, 4) with respect to the line x = y is the point that results from reflecting (3, 4) across the line x = y.

To understand this, we first need to understand what it means for a point to be reflected across a line.

Reflection is a transformation that flips a figure across a mirror line or line of reflection. In this case, the line of reflection is x = y. When a point is reflected across a line, the image point is located on the opposite side of the line from the original point, and it is the same distance from the line as the original point.

To find the image of points (3, 4) with respect to x = y, we need to first draw a line x = y in the coordinate plane. Then, we can visualize points (3, 4) on one side of the line and their image on the other side.

When we reflect points (3, 4) across the line x = y, the coordinates of the point will be flipped. The new coordinates will be (4, 3) instead of (3, 4). So the image of the point (3, 4) with respect to x=y is (4,3)

In summary, the image of the point (3, 4) with respect to the line x = y is (4, 3), which is the point that results from reflecting (3, 4) across the line x = y by flipping the coordinates of the point.

To learn more about the distance, visit:

brainly.com/question/15172156

#SPJ4

Step-by-step explanation:

8-11= -3

which means it negative number

The possible measures of the other two angles would be -

56° and 68° respectively.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane

Given is that one angle of an isosceles triangle measures 56°.

Angles opposite to equal sides are equal. In a isosceles triangle, two sides are equal. So, we can write -

∠1 = ∠2 = 56°    {Angles opposite to equal sides are equal}

∠3 + ∠1 + ∠2 = 180

∠3 = 180 - 2 x 56

∠3 = 180 - 112

∠3 = 68°

Therefore, the possible measures of the other two angles would be -

56° and 68° respectively.

To solve more questions on triangles, visit the link below -

brainly.com/question/12413243

#SPJ1

The percentage of vertebrates that are reptiles is approximately 13.8%

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to express rates, ratios, and proportions. A percentage is represented by the symbol "%" and is calculated by multiplying a number by 100 and dividing the result by the total number of items being considered.

In this problem, we need to determine the percentage of vertebrate that are reptiles.

This can be represented mathematically as;

Percentage of reptiles = [number of reptiles / total number of vertebrates] * 100

Percentage = [8240 / 59811] * 100

Percentage = 13.8%

The percentage of reptiles is 13.8%

Learn more on percentage here;

https://brainly.com/question/843074

#SPJ1

The depth of water in the tank is increasing at the rate of approximately 0.0135 meters per minute when the depth is 8 meters.

A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.

To find the rate at which the depth of water in the tank is increasing, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

Where V is the volume, π is pi, r is the radius, and h is the height (depth) of the cone.

We know that the radius at the top of the tank is 15 meters, the depth of the tank is 8 meters, and the rate of water flow is 2 cubic meters per minute.

So we can use the above formula to find the rate at which the depth is increasing.

Let's call the rate at which the depth is increasing "dh/dt"

V = (1/3) * π * 15^2 * 8

dV/dt = (1/3) * π * 15^2 * dh/dt

Now we know that the rate at which the water is flowing is 2 cubic meters per minute, so we can substitute it for dV/dt

2 = (1/3) * π * 15^2 * dh/dt

Solving for dh/dt

dh/dt = 2/( (1/3) * π * 15^2 )

Therefore, the depth of water in the tank is increasing at the rate of approximately 0.0135 meters per minute when the depth is 8 meters.

To know more cones refer to:

brainly.com/question/16394302

#SPJ4

Answer:

B，8.8cm

Step-by-step explanation:

I don't know if you have learned about the relations between the three sides of a 30,60,90 right-angled triangle. It shows one angle is 29, we will estimate it for 30.

Relations： 30 angled face side DF is 1, 60 face side EF is √3=1.732， 90 face side DE is 2

And we knew EF=7.7

So, 1.732/7.7=2:DE

1.732DE=15.4

       DE=8.89

Sorry, I hope someone can help you in a simpler way.

Point G is two, which divides the directed line segment from D to F into a 5:4 ratio at that place.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

From negative five to positive ten is a number line.

Points D and F are at -2 and +7, respectively.

The distance between point D and F is,

=9

If Point G divides the directed line segment from D to F into a 5: 4 ratio, then,

=2

Hence, The directed line segment from D to F is divided into a 5:4 ratio at point G by the number 2.

learn more about straight-line equations click here:

brainly.com/question/25969846

#SPJ4

The area occupying a three-dimensional shape's exterior is known as its surface area.

The quantity of space enclosing the exterior of a three-dimensional shape is its surface area. The surface area of a three-dimensional shape refers to how much open space it occupies outside of itself.

The entire area of all the faces makes up the surface area of a three-dimensional form. We calculate the area of each face and put them together to determine the shape's surface area.

The total area that all of a 3D object's faces cover is the surface area.

Add up every region. SA=2B+2πrh. Find the base's area, multiply it by 2, and then add those areas to the rectangle's areas, which are equal to the rectangle's diameter times its height.

To learn more about surface area refer to:

https://brainly.com/question/16519513

#SPJ1