Factor the expression completely.
x^4-17x^2+72

probability of landing on heads - 49 %

Answer:

49%

Step-by-step explanation:

The transformation of the function is given by reflection along y axis and a translation of 5 units up

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the transformation be represented as A

Now , the equation will be

Let the triangle be represented as ΔODG

Now , the coordinates of ΔODG is

O = O ( -1 , -2 )

D = D ( -5 , -3 )

G = G ( -2 , -4 )

Now , the transformed triangle is ΔACT

The coordinates of ΔACT is

A = A ( 1 , 3 )

C = C ( 5 , 2 )

T = T ( 2 , 1 )

Now , on reflecting the triangle ΔODG along y axis , we get

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse

So , the coordinates of triangle O'D'G' , we get

O' = O' ( 1 , -2 )

D' = D' ( 5 , -3 )

G = G' ( 2 , -4 )

Now , translating the triangle ΔO'D'G' up by 5 units , we get

The y coordinate of the triangle gets incremented by 5

So ,

A = O' ( 1 , -2 + 5 )

C = C ( 5 , -3 + 5 )

T = T ( 2 , -4 + 5 )

And , the coordinates of the triangle ΔACT is

A = A ( 1 , 3 )

C = C ( 5 , 2 )

T = T ( 2 , 1 )

Hence , the transformation is reflection along y axis and followed by translation of 5 units up

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Answer:

[tex]\boxed{D) ~(-6,-12)}[/tex]

Step-by-step explanation:

[tex]\boxed{Rule}:-[/tex]

[tex](x,y)[/tex] → [tex](3x,3y)[/tex]

[tex]p(-2,-4)[/tex] → [tex](3x-2,-4*3)[/tex]

[tex]\boxed{Answer: (-6,-12)}[/tex]

[tex]-------------[/tex]

hope it helps...

have a great day!!

Answer:

(-6, -12)

Step-by-step explanation:

In dilations, the scale factor is how many times larger the figure will be.

In other words, multiply the x and y-coordinates by the scale factor. In this case, the scale factor is 3.

(-2, -4) are the original coordinates.

-2 × 3 = -6

-4 × 3 = -12

Therefore, the new coordinates are (-6 -12).

The solution to the pair of simultaneous equations 2x + y = 5 and 3x - 2y = 4 is (2, 1).

A system of linear equations is a set of two or more equations which includes common variables. The solution to a system of equations, is the value of the unknown variables used in the equations that satisfies both equations.

Given two linear equations in x and y,

2x + y = 5     (equation 1)

3x - 2y = 4     (equation 2)

Use substitution method to find its solution. Express the first equation as y in terms of x and substitute the value of y to the second equation.

2x + y = 5     (equation 1)

y = 5 - 2x

3x - 2y = 4     (equation 2)

3x - 2(5 - 2x) = 4

3x - 10 + 4x = 4

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.

3x - 10 + 4x = 4

7x = 14

x = 2

Substitute the value of x in the first equation and solve for y.

y = 5 - 2x

y = 5 - 2(2)

y = 5 - 4

y = 1

Hence, the solution of the given system of equations is (2, 1).

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Answer:

[tex]192x ^{3} y ^{3} [/tex]

After dilation, the co-ordinate of point A will be (-4,4) while B will be (2,4) and of C will be (-2,0).

The distance between the point of dilation and the point you are dilating must be multiplied by three if the point you are dilating is directly above the point of dilation and you are dilating by 3. You inserted your new point there.

The x-value of each point will be multiplied by 2 to enlarge the image by a factor of two. The x and y values of each point will be multiplied by 2 to enlarge the figure by a factor of 2.

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The classification of the transformations based on the properties are presented as follows;

[tex]\begin{array}{|c|c|c|} & \mathbf{Preserves \ length} & \mathbf{Does \ not \ preserve \ lengths} \\\mathbf{Preserves \ angle \ measure} & Reflection\ Rotation &Translation \ followed \ by \ dilation \\&&Dilation \ with \ K > 1\\\mathbf{Does \ not \ preserve \ angle \ meas} & & \\\end{matrix}[/tex]

The transformations that preserves the lengths of the original figure or pre-image and also preserves the angle measure is a rigid transformation.

Rigid transformations includes; Reflections, rotations, and translations

Transformations that preserves the angle of measure but in which the lengths of the preimage is not preserved are non-rigid transformations

Non rigid transformations includes; Dilation with a scale factor

Transformations that does not preserve the angle measure includes; Shear transformation

A translation and a dilation transformation does not preserve the lengths of the original figure.

The classification of the transformations based on their properties are therefore presented as follows;

[tex]{}[/tex]                               Preserves lengths      Does not preserve lengths

Preserves               Reflection              [tex]{}[/tex]    Translation followed by dilation

angle measure       Rotation                   [tex]{}[/tex]  with k > 1

                                                          [tex]{}[/tex]        Dilation with k > 1

Does not              

Preserve angle

measure

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Answer:

Scale Factor: 2

Step-by-step explanation:

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Hope this was helpful! Thank you & have an awesome day! =)

Answer:

15 ft

Step-by-step explanation:

Using sinus law

sin(A) /a = sin(B) /b = sin(C) /c

Where smale letters indicate the sides

For this question :

(sin(90)*12)/sin(53)=15

Answer:

9.58

Step-by-step explanation:

Sin=opposite/hypotenuse

sin53=12/length of slide

Length of slide=12sin53

=9.58

Answer:

b = -10

c = 25

Step-by-step explanation:

Since the only solution to x is 5 that mean answer will look something like this:

(x-5) (x-5) = 0

x(x-5) -5(x-5)

x^2 -5x -5x + 25

x^2 -10x + 25

This is same as x^2 + bx + c = 0

where b is -10 and c is 25

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]2(x-2)^2=8(7+y)\hspace{5em}\stackrel{\textit{quick switcheroo}}{2(y-2)^2=8(7+x)} \\\\\\ (y-2)^2=\cfrac{8(7+x)}{2}\implies (y-2)^2=4(7+x)\implies (y-2)^2=28+4x \\\\\\ y-2=\pm\sqrt{28+4x}\implies \boxed{y=2\pm\sqrt{28+4x}}\qquad \impliedby f^{-1}(x)[/tex]

On solving the provided question, we can say that - the each angle of pentagon is x = 108

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

since all sum of pentagon is 540

so, 5x = 540

x = 108

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Answer:

The distance between the yacht from the ship is about 33.6 km.

Step-by-step explanation:

The diagram is attached below.

Point A is the shipe, Point B is the tugboat, and Point C is the yacht.

Since the tugboat is 28 km away, and the scale being used is 1 cm : 4 km, the tugboat is 7 cm away from the ship at a 210° bearing on the diagram.

Likewise, the yacht is 6 cm away from the tugboat at a 210° bearing.

To find the distance between the yacht to the ship, we need to determine the value of x.

To do so, we can use the Law of Cosines:

[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]

First, we need to determine ∠B.

A has a bearing of 210°. 180° is covered by QI and IV. So, the small angle in QIII is 30°.

By Alternate Interior Angles, the angle in QI (inside the triangle) of Point B must also be 30°.

And since Point B has a bearing of 310°, 270° is covered in total by QI, QIV, and QIII. So, 40° is left in QII.

Therefore, 50° is the measure of the angle in QIII within the triangle of Point B.

Thus, ∠B measures 50° + 30° = 80°.

So, ∠B measures 80°. We also know that a = 6 and c = 7. Substitute:

[tex]b^2=(6)^2+(7)^2-2(6)(7)\cos(80)[/tex]

Simplify and take the square root of both sides. So:

[tex]b=\sqrt{85-84\cos(80)}[/tex]

Approximate using a calculator:

[tex]b=8.3912...\approx 8.39\text{ cm}[/tex]

Since 1 cm : 4km, to find the distance in km, we simply need to multiply by four. So:

[tex]\Rightarrow b=4(8.3912...)=33.5651\approx 33.6\text{ km}[/tex]

The distance between the yacht from the ship is about 33.6 km.

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{35}{m}=\cfrac{m}{7}\implies 245=m^2\implies \sqrt{245}=m\implies \sqrt{7^2\cdot 5}=m\implies 7\sqrt{5}=m[/tex]

She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.

Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.

number of bracelets sold for $12 each=9

number of bracelets sold for $8 each=14

Total profit=9x12+8*14=$220

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Answer:

there r more students who way 60-69 kilograms and there r less students who way 90-100 kilograms

Step-by-step explanation:

Answer:

m∠A=126°

Step-by-step explanation:

Supplementary means that they add up to 180°.

Therefore we can do 180-54 to get 126° for the m∠A.

Hope this helped! :)

Answer: 7 hours! you do 74-18 to get 56 then you divide 56 by 8 to get 7.

Step-by-step explanation:

hope this helps!!

Answer:

:) 17

Step-by-step explanation:

68 = 4 x L

68 div by 4 = 17

the length is 17

Answer:

C

Step-by-step explanation:

If the space the battery will be in is 4 centimeters wide, then 4 cm is the width of the rectangle. The length is the area divided by the width. Since we know the area is 68, and the width is 4, divide 68 by 4 and you get 17. So C is the correct answer :)

35-55-90 is a right-angle triangle because one of the angles is 90 degrees.

The explanation for a right triangle says that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or simply, a right triangle.

The right triangle formula can be presented in the following way: The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

In a right triangle we have: (Hypotenuse)² = (Base)² + (Altitude)²

Properties of Right Triangle:

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Answer:

(2,4)

Step-by-step explanation:

x=2

y=4

The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. 

 we have

 y = x² + 3x + 2   .............(a)

 y = 2x + 3    ...................(b)

To solve the system of equations equate equation A to equation B

  x² + 3x + 2 = 2x + 3

 Group terms that contain the same variable

   x² + 3x + 2 - 2x - 3 = 0

  x² + x - 1 = 0

The formula to solve a quadratic equation of the form ax² + bx+ c  is equal to

     in this problem we have

       x² + x - 1 =0

 so,   a= 1

        b = 1

        c = -1

substitute in the formula

  x = -1 ± √1² - 4(1)(-1)/2(1)

  x = -1 ±√5/2

  x = -1+√5/2 = 0.618

   x = -1 - √5/2  =  - 1.618

  Find the values of y

 for  x = 0.618

    y = 2(0.618) + 3 = 4.236

  for  x = - 1.618

   y = 2(-1.618) + 3  = -0.236

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The complete question is -

At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?

Answer:

Hi how are you doing today Jasmine

Adam and William

 Allen and Owen

Answer:

1)33.4096

2) 113.1

3) 268.08

4) 904.78

Step-by-step explanation:

Volume = 4/3π*r cubed

So, let's say π = 3.14

1) Radius =2

4/3*3.14 = 4.1762

4.1762*2*2*2

4.1762* 8

=33.51

2) Radius = 3

113.1

3) Radius = 4

268.08

4) Radius = 6

904.78

I hope this helps

Sorry if it's wrong, I am just 4th grade :(

Answer:

[tex]\boxed {\boxed {\sf 14.2 \ cm}}[/tex]

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:

Substitute these values into the formula.

[tex](9 \ cm)^{2} +(11 \ cm)^{2} =c^{2}[/tex]

Solve the exponents.

[tex]81 \ cm^{2} +(11 \ cm)^{2} =c^{2}[/tex]

[tex]81 \ cm^{2} +121 cm^{2} =c^{2}[/tex]

Add the values on the left side.

[tex]202 \ cm^{2} =c^{2}[/tex]

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

[tex]\sqrt {202 \ cm^{2} }=\sqrt{c^{2} }[/tex]

[tex]\sqrt {202 \ cm^{2} }=c[/tex]

[tex]14.2126704036 \ cm =c[/tex]

We are told to round to the nearest tenth.

The 1 in the hundredth place tells us to leave the 2 in the tenth place.

[tex]14.2 \ cm= c[/tex]

The hypotenuse is equal to 14.2 centimeters.

Answer:

D.   49/4

Step-by-step explanation:

Complete the square by squaring half the coefficent of the x term

(-7/2)² = 49/4

Answer:

60 kkkkkkkkkkkkkkkkkkkkkk

Answer:

a = 60

Step-by-step explanation:

First off this is a straight angle so it will add up to 180 degrees we already have 30 and the other angle between a and 30 is a 90 degree angle so now we just have to subtract those from 180 to get the answer! so... 90 + 30 = 120 180 - 120 = 60

So 60 is the answer hope that helps!

Answer:

14t²+42t

Step-by-step explanation:

So you're basically going to use distributive property.

(2t+6)+7t is the same as, (2t)7t + 6(7t).

2t(7t)= 14t² and 6(7t)= 42t.

Combine the two answers and you get 14t²+42t.

14t²+42t is the simplest form you can get to.