Triangle ABC has vertices A = (1, 5), B = (3, 2), and C = (4, 7). Triangle A'B'C' is formed when triangle ABC is shifted using the rule (x, y) --> (x-3 , y-1). What are the coordinates of triangle A'B'C' ?

The HCF of the polynomials x6 - 3x4 + 3x2 - 1 and x3 + 3x2 + 3x + 1 as calculated from the data given is found to be as (x + 1)3.

We will solve the given functions, to get their HCF.

   f(x) = x6 - 3x4 + 3x2 - 1  

⇒ x6 - x4 - 2x4 + 2x2 + x2 - 1

⇒ x4(x2 - 1) - 2x2(x2 - 1) +1(x2 + 1)

⇒ (x2 - 1)(x4 - 2x2 + 1)

⇒ (x + 1)(x - 1)(x4 - 2x2 + 1)

⇒ (x + 1)(x - 1)(x2 - 1)2

⇒ (x + 1) (x - 1) (x + 1)2 (x - 1)2

⇒ (x + 1)3(x - 1)3    

Similarly ,

g(x) = (x + 1)3      

Therefore,

The HCF of f(x) and g(x) is the common factor of equations obtained by solving these functions which is , (x + 1)3.

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Answer: The perimeter of a shape is the sum of all its sides.

From the diagram, we can see that the shaded shape is composed of a square and a rhombus.

The square has 4 sides of equal length, which is the same as the length of one of the diagonals of the rhombus.

The rhombus has 4 sides with two sides of equal length (the diagonals) and two sides of equal length (the parallel sides).

We can call the length of the diagonals of the rhombus as "d" and the length of the parallel sides of the rhombus as "s".

So, the perimeter of the shaded shape is:

Perimeter = 4s + 4d

It is not possible to find the perimeter with out knowing the length of the sides of the rhombus and the square.

Step-by-step explanation:

Therefore ,light of this, the solution to the triangle issue given is ABC, which is equivalent to XYZ.

A triangular is a polygon since it has number of sides and three vertices. This geometric form is essential. Triangle ABC is still a triangles whose corners are located at points A, B, then C. In geometric shapes, a single planar and triangle are produced when four components are not coherent. Due to their three sides and top right corner, triangles are included in polygons.

Here.

Given :

ABC and XYZ are the same, hence ∠ A = ∠ X.

∠ B and ∠ Y mean the same thing.

"∠ Z" = "∠ C," and

The value of line ab matches that of xy.

Both line bc and yz can be substituted.

XZ corresponds to line ac.

To come up with a solution, Cpct was used.

Triangle segments that match each other are congruent.

The solution to the triangle problem is ABC is equal with XYZ as a result.

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The rectangle of perimeter 174 unit that encloses the largest area is a square. [tex]\frac{87}{2}[/tex] unit on a side.

The perimeter of rectangle is 174, let the length of rectangle is x and the width of rectangle is y.

so, the perimeter of rectangle is.

Perimeter=2(x+y)

174=2(x+y)

x+y=87

y=87-x

now the area of rectangle is.

A=x × y

substitute value of y,

[tex]A=87x-x^2[/tex]

This is a quadratic equation whose graph is parabola. because the value of a is negative. the vertex is always located at the point x=-b/2a.

[tex]x=\frac{87}{2}[/tex] unit

[tex]y=87-\frac{87}{2}[/tex]

[tex]y=\frac{87}{2}[/tex]

the rectangle of perimeter 174 unit that encloses the maximum area is a square 87/2 unit on a side.

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The error made by Elijah is ABC Triangle has one included angle between two sides but in triangle DEF Angle is not included between two sides, so that triangles is not similar .

What is side angle side congruent triangles?

If all three corresponding angles and all corresponding sides are equal, two triangles are said to be congruent.

Triangles are said to be congruent according to Side Angle Side if any pair of corresponding sides and their included angle are also congruent.

Here in given triangles ΔABC and ΔDEF,

The error made by Elijah is that for two triangles are congruent there must be two sides and one included angles are needed .

But  in that case ABC Triangle has one included angle between two sides but in triangle DEF Angle is not included between two sides .

Hence  the error made by Elijah is ABC Triangle has one included angle between two sides but in triangle DEF Angle is not included between two sides, so that triangles is not similar .

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Answer:

hope I'm right-

Step-by-step explanation:

first row: 0.3

second row: 0.2

last row: 0.1

The value of function ƒ(10) is 340 if given ƒ(x) = 4x² – 4x – 20.

The concept of a function is used by mathematicians to describe a variety of operations, including addition and multiplication, transformations of geometric figures, relationships between variables, and many other things.

A function is a set of guidelines for matching things with one another. A function pairs the inputs with the outputs and has inputs and outputs. This pairing is subject to a crucial limitation: Each input can only be coupled with one output.

The value of x = 10

4x² – 4x – 20

Lets solve

ƒ(10) = 4(10)² – 4(10) – 20

ƒ(10) = 400 – 40 – 20

ƒ(10) = 340

Thus, The value of function ƒ(10) is 340 if given ƒ(x) = 4x² – 4x – 20.

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The log function is also called Logarithmic functions.

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The area of trapezoid abcd is 164 cm2 with an altitude is 8cm, ab is 10 cm, and cd is 17 cm and bc=10cm

The area of a trapezoid can be calculated if the length of its parallel sides and the distance between them are given. The formula for the area of a trapezoid is expressed as,

A = ½ (a + b) h

where (A) is the area of a trapezoid, 'a' and 'b' are the bases and 'h' is the height.

Given that Area of trapezoid A=164 and the altitude is 8 cm, ab is 10 cm, and cd is 17cm.

Substitute these values in the formula:

164=8(BC+AD)/2

8(BC+AD)=328

BC+AD=41

Drop perpendiculars from B to AD and from C to AD and let them hit AD at E and F respectively. Note that each of these perpendiculars has a length of 8.

From the Pythagorean Theorem, AE=6 and DF=15 thus AD=BC+21. Substituting back into our original equation we have

BC+BC+21=41

2BC=20

BC=10cm.

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Answer:

6/8 = 9/12

Step-by-step explanation:

6/8 = 3/4

9/12 = 3/4

So, the answer is

6/8 = 9/12

the answer is 7x I'll save you some time by not explaining

Answer: 4

Step-by-step explanation:

y wouldn't it be 4

so 2+2=4

ex: ii + ii = iiii (2+2 = 4)

Answer:

4

Step-by-step explanation:

2+2= 4

1+1=2 and 1+1=2

so if you add it together

you get 4

The greatest possible widths of the fields will be -

W₁ = 180/L₁    &    W₂ = 288/L₂    &    W₃ = 84/L₃

Given is that a farmer wants to plant three rectangular fields so that the widths are the same. The areas of the​ fields, in square​ yards, are given by the expressions 10x²y​, 6xy⁴ ​and 14xy.

Rectangle { 1 } -

L₁ x W₁ = 10x²y

W = 10x²y/L₁

If x = 3 and y ​= 2, we can write that -

W₁ = (10 x 9 x 2)/L₁

W₁ = 180/L₁

Rectangle { 2 } -

L₂ x W₂ = 6xy⁴

W₂ = 6xy⁴/L₂

If x = 3 and y ​= 2, we can write that -

W₂ = (6 x 3 x 16)/L₂

W₂ = 288/L₂

Rectangle { 3 } -

L₃ x W₃  = 14xy

W₃ = 14xy/L₃

If x = 3 and y ​= 2, we can write that -

W₃ = (14 x 3 x 2)/L₃

W₃ = 288/L₃

W₃ = 84/L₃

The greatest possible widths of the fields will be -

W₁ = 180/L₁    &    W₂ = 288/L₂    &    W₃ = 84/L₃

Therefore, the greatest possible widths of the fields will be -

W₁ = 180/L₁    &    W₂ = 288/L₂    &    W₃ = 84/L₃.

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The equation of a sphere if one of its diameters has endpoints: (-6, 4, 0) and (0, 0, 6) will be (x+3)2+(y-2)2+(z-3)2=22

d2 = (xf-xi)2 + (yf-yi)2 +(zf-zi)2

d2 = (-6-0)2+(4-0)2+(0-6)2

d2=36+16+36=88

d=sqrt(88)

The radius is half the diameter

r=d/2

r=sqrt(88)/2

Use the center equation to get the diameter's middle.

(xf-xi)/2, (yf-yi)/2, (zf-zi)

(-6-0)/2, (4-0)/2, (0-6)/2

(-3,2,-3) Center

Apply the sphere equation now.

(x-xc)2+(y-yc)2+(z-zc)2=r2

(x+3)2+(y-2)2+(z-3)2=(sqrt(88)/2)2

(x+3)2+(y-2)2+(z-3)2=88/4

(x+3)2+(y-2)2+(z-3)2=22

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Answer: 3

Step-by-step explanation: 77 - 2 = 75, 75/25 = 3

Answer: 6 + 2x

Step-by-step explanation:

Combine like terms:

= 6 + 2x

Suitable choices are (1), (2), (7), and (8). In a plane, lines that are consistently spaced apart from one another are referred to as parallel. Parallel lines don't ever intersect.

Given:

A and B are parallel lines.

Think of a | b and 'd' as a transversal,

Statements

Reasons

1. [tex]$\angle B X Z=\angle A Z P=58^{\circ}$[/tex]

Corresponding angles are equal

[tex]$\therefore \mathrm{m} \angle 2=58^{\circ}$[/tex]

2. [tex]$\angle B Y C=\angle X Y Z=(4 x-10) \cdot$[/tex] Vertically opposite angles are equal

Now, consider a | b and ' c ' be a transversal then,

Statements

Reasons

1. [tex]$\angle X Y Z=\angle Q Z U=(4 x-10)^{\circ}$[/tex]

Corresponding angles are equal  [tex]$\therefore \mathrm{m} \angle 1=(4 x-10)^{\circ}$[/tex]

2. [tex]$\angle P Z A+\angle P Z Q+\angle Q Z U=180^{\circ}$[/tex]

Sum of angles on a straight line is [tex]$180^{\circ}$[/tex]

3. [tex]$58^{\circ}+(3 x-1)^{\circ}+(4 x-10)^{\circ}=180^{\circ} \quad$[/tex]

Substitution property

4. [tex]$47^{\circ}+7 x=180^{\circ}$[/tex]

Combining like terms

5. [tex]$7 x=180^{\circ}-47^{\circ}$[/tex]

Subtraction property of equality

[tex]$\therefore 7 x=133^{\circ}$[/tex]

6. [tex]$x=19^{\circ}$[/tex]

Division property of equality

Plug in x = 19

in [tex]$(3 x-1)^{\circ}$[/tex]

and [tex]$(4 x-10)^{\circ}$[/tex]

we get [tex]$(3 x-1)^{\circ}=(3(19)-1)^{\circ}=56^{\circ}$[/tex]

[tex]$(4 x-10)^{\circ}=(4(19)-10)^{\circ}=66^{\circ}$[/tex]

So, [tex]$(3 x-1)^{\circ} \neq(4 x-10)^{\circ}$[/tex]

Hence, options (1), (2) , (7) and (8) are correct.

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8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.

We can begin solving the problem by using the proportion:

(18 muffins) / (15 muffins) = (x muffins) / (7 muffins)

where x represents the number of Susan's muffins that weigh the same as 7 of Tom's muffins. To solve for x, we can cross-multiply and then divide:

18 muffins * 7 muffins = 15 muffins * x

x = (18 * 7) / 15

x = 8.4

Therefore, 8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.

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The slope of the given coordinate points is -2. Therefore, option D is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (2, -8) and (-4, 4).

Here, substitute (x₁, y₁)=(2, -8) and (x₂, y₂)=(-4, 4) in slope formula, we get

m= (4+8)/(-4-2)

m= 12/(-6)

m= -2

Therefore, option D is the correct answer.

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The value of x in simplest radical form is 8√3.    

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root.  

The radical and root of a number are the same thing.      

Here we have

Given triangle is a right-angled triangle

From trigonometric ratios,

Sin θ = [ Opposite side ]/[ Hypotenuse ]

=> Sin 30° = [ Opposite side ]/[ 16 ]  

As we know, Sin 30° = 1/2

=> [ Opposite side ]/[ 16 ] = 1/2

=> Opposite side = 8 units      

By the Pythagorean theory,

Hypotenuse² = Opposite side² + Adjacent side²  

=> 16² = 8² + x²  

=> 256 = 64 + x²

=> x² = 192  

=> x = √64 × 3  

=> x = 8√3      

Therefore,

The value of x in simplest radical form is 8√3.

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{(−2, 2), (−7, 7), (−1, 1), (−8, 8)} it is a function as every input has a single output. Therefore, option C is the correct answer.

In math, a relation defines the relationship between sets of values of ordered pairs. The set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.

A) {(1, −7), (2, −8), (−2, 7), (1, 8)}

Since the element  1 corresponds to two different images i.e., -7 and 8. So, this relation is not a function.

B) {(−2, 1), (−7, −1), (2, 8), (−7, −8)}

Since the element -7 corresponds to two different images i.e., -1 and -8. So, this relation is not a function.

C) {(−2, 2), (−7, 7), (−1, 1), (−8, 8)}

It is a function as every input has a single output.

So, -2, -7, -1 and -8 are the elements of the domain of the given relation.

D) {(−2, 1), (−2, 2), (−2, 7), (−2, 8)}

Since the element -2 corresponds to different images i.e., 1, 2, 7 and 8. So, this relation is not a function.

Therefore, option C is the correct answer.

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Answer: 15 laps in 12 seconds

Step-by-step explanation:

15 divided by 12 is 5/4 which is also 1.25

12 divided by 10 is 6/5 which is also 1.2

1.25 is greater then 1.2

While both star clusters and galaxies are assumed to have formed simultaneously from a collapsing ball of gas as linear equation .

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.

Here,

Given:

Both contain stars that are held together by gravity. Part of the Local Group of galaxies is the Milky Way galaxy, which houses our solar system.

The Milky Way, the Magellanic Clouds (big and small), and the Andromeda Galaxy are the largest. The average galaxy is also bigger than a star cluster. The cities where star clusters reside are like galaxies, according to Geller.

"Galaxies can contain thousands or more star clusters, numerous molecular clouds, dark matter, and other things," the author writes.

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The complete question is "Establish a linear equation between the following Solar system, Star cluster, Galaxy and Galaxy cluster. "

The number of feet in 1 centimeter is 14 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, in the scale drawing, the length of the cafeteria is 14 centimeters. the length of the actual cafeteria is 210 feet.

Here, 14 centimeters = 210 feet

1 centimeter =210/14 feet

1 centimeter =14 feet

Therefore, the number of feet in 1 centimeter is 14 feet.

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The percent of adults who are developmentally disabled by the criterion of an IQ score below 70 is approximately 2.28%

We can use the standard normal distribution in order to find the probability of an IQ score below 70.

We know the mean IQ score is 100 and the standard deviation is 15, so we can use the formula:

z = (70 - 100) / 15

z = -2

Using a normal probability table, we find that the probability of a score less than -2 is approximately 0.0228.

Therefore, we get that approximately 2.28% of adults are considered developmentally disabled by the criterion of an IQ score below 70.

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The solution of the system of linear equations 2x + y = 5 and 3x - 2y = 4 is x = 2, y = 1.

To find the solution of the pair of equations, 2x + y = 5 and 3x - 2y = 4, we can use different methods.

You can use elimination method to solve the system of linear equations. The elimination method consists of eliminating one of the variables by adding or subtracting the equations.

Multiply the first equation by 3 and the second equation by 2.

6x + 3y = 15

6x - 4y = 8

Subtract second equation from first:

7y = 7

y = 1

Substitute this value of y in the first equation:

2x + (1) = 5

2x = 4

x = 2

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Answer:

1 and - 2

Step-by-step explanation:

f(0) is asking what is the value of y when x = 0

locate x = 0 ( the origin), go vertically up the y- axis to meet the line at (0, 1)

then f(0) = 1

f(x) = 5 is asking what is the value of x when y = 5

locate y = 5 on the y- axis, go horizontally across to meet the line at (- 2, 5 )

then f(x) = 5 when x = - 2

The solution to the system of equation y = 9x + 2 and 7y = 63x + 14 is x = -1 and y = -7

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

y = 9x + 2

multiply the equation by 7:

7y = 63x + 14

-63x + 7y = 14          (1)

And:

-2x + 7y = -47     (2)

To solve by elimination method, subtract equation 2 from 1 to get:

-61x = 61

x = -1

Put x = -1 in the equation:

y = 9x + 2

y = 9(-1) + 2 = -9 + 2 = -7

The solution to the equation is x = -1 and y = -7

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Answer:

([tex]-\frac{7}{12}[/tex],-1)

Step-by-step explanation:

If you have 25 members and wish to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

In the given question,

If you have 25 members and wish to pick a president, secretary, and treasurer, then we have to find how many ways can we choose the officers, if individual members may hold more than one office.

We have a total of 25 members.

They have a total of 3 positions president, secretary, and treasurer.

When the one position of president was filled then there were left 24 members for the secretary position.

When the one position of secretary was filled then there were left 23 members for the treasurer position.

So the possible ways to fill the position are found by multiplying 25,24 and 23. So

Possible ways=25*24*23

Possible ways=13,800

Hence, if you have 25 members, and wish to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

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