Solve each formula for the indicated variable. s = (1/2)gt² , for g

Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.

Is a triangle capable of tessellation?

To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.

Every vertex, edge, and tile in a regular tesselation are identical.

However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).

Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.

Each vertex in the semiregular tessellations is the same.

Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)

The Octagon & square tiling (4,8,8) is a very common floor tiling.

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Answer:  The claim is true

The proof is below

=====================================================

A = some nonzero rational number

B = some irrational number

Because value A is rational, this means A = p/q where p,q are nonzero integers.

Let's do a proof by contradiction. The claim is that A*B is irrational, but let's do the opposite and assume A*B is rational. We should get to a contradiction somewhere based on this assumption.

If A*B is rational, then A*B = r/s for some integers r and s

Then we can have the following steps

A*B = r/s

(p/q)*B = r/s

B = (r/s)*(q/p)

B = (rq)/(sp)

B = (some integer)/(some other nonzero integer)

B = some rational number

Recall we made B irrational. There's no way to have B rational and irrational at the same time. This is where the contradiction happens. This causes the original assumption of "A*B is rational" to be false. Therefore, the opposite must be the case and A*B has been proven to be irrational.

Therefore, the product of a rational number and an irrational number is irrational.

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

Example:

5 is rational

sqrt(3) is irrational

5*sqrt(3) is irrational

Answer:

D. 52 45

Step-by-step explanation:

Answer:

6n2-15=150-15

6n2-15=135

6n2=150

divied both side by 6

n2=25

sqrt both side

n=-5 or 5 bc sqrt so 2 answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

Flight speed there = 12 feet / second

Flight speed back = 8 feet / second

Total time = 22 minutes

Time at rest = 18 minutes

Time in flight = 22 - 18 = 4 minutes

Equation

Let the time going to the flowerbed = t

12*t + 8*t + 18 = Distance travelled + time at rest.

Answer

12*t + 8*t + 18 = Distance travelled + time at rest

The mean height of the given sample of values is approximately 65.20.

The heights of the 15 students are as follows:

{59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73}

To find the mean (average) height of the given values, we need to add up all the heights and then divide the sum by the total number of heights:

59 + 61 + 62 + 63 + 63 + 64 + 65 + 65 + 66 + 67 + 67 + 67 + 67 + 69 + 73

= 978

So, the mean height can be calculated as:

Mean height = Total height / Number of heights = 923 / 15 = 65.2

Therefore, the mean height is approximately 65.20.

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The two numbers which are 5 units away from zero on the number line as required in the task content are; -5 and 5.

It follows from the task content that the numbers which are 5 units away from zero on the number line be identified and plotted.

Hence, given that the numbers in discuss are represented by; x; we have;

| x - 0 | = 5

| x | = 5

Ultimately, x = ±5. where +5 is to the right and -5 is to the left of zero respectively.

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The Gary's score after getting stuck in the dust storm will be -35 points.

It is given in the problem that,

The points gained by Gary by jumping over a crater = 20 points

And then,

The points lost by Gary for getting stuck in a dust storm = 45 points

We need to find,

The Gary's score after getting stuck in the dust storm

As in the beginning of the game, Gary's account had 20 points but as he then stuck in the dust storm he lost 45 points, which means he has lost points more than he had. So, now Gary would have negative points left in his account in the game

= 10 - 45

= - 35

Hence, the Gary's score after getting stuck in the dust storm will be -35 points.

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A large ship lowered its anchor, The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in sec) E=-2.4t+75. The anchor drop 12 meters every 5 seconds.

Given that in the picture we can see the question that is

A large ship lowered its anchor,

The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in second).

E=-2.4t+75

According to the function E=-2.4t+75

We assume that [tex]t_{1}[/tex].

So, every 5 second [tex]t_{1}[/tex]=t+5.

So, we get

ΔE=E(t)-E(t+5)

ΔE=-2.4t+75-(-2.4(t+5)+75)

ΔE=-2.4t+75+2.4t+12-75

ΔE=12

Therefore, the anchor drop 12 meters every 5 seconds.

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Answer:

[tex]0 \leqslant c \leqslant 56[/tex]

Step-by-step explanation:

Since candy costs $7 per pound, and Kayla will buy less than 8 pounds, she will spend no more than $7 × 8, or $56.

Answer:

no solution

Step-by-step explanation:

5n + 1 = 5n - 1 ( subtract 1 from both sides )

5n = 5n - 2 ( subtract 5n from both sides )

0 = - 2 ← not possible

this indicates that the equation has no solution

The length of seesaw will be equal to 11 feet.

It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.

We have to find out the length of seesaw.

What do you mean by midpoint of a line segment ?

The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.

As per the question ;

The midpoint of the seesaw is 13.5 feet from the swing set.

and

The swing set is 8 feet from the edge of the seesaw.

So ;

The distance from the midpoint to the edge will be ;

13.5 – 8 = 5.5.

And

The length of the seesaw will be ;

= 2× (5.5)

= 11 feet

Thus , the length of seesaw will be equal to 11 feet.

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The slope of the line that contains the  points G(-4,3), H(-4,7) is not defined.

Slope of a line containing two points (a,b) and (c,d) is denoted  by

[tex]slope=\frac{d-b}{c-a}[/tex]

In the given question

The points given are G(-4,3), H(-4,7)

a=-4, b= 3  and c= -4 and d=7

Substituting the values in formula of slope we get

[tex]slope=\frac{d-b}{c-a}[/tex]

[tex]slope=\frac{7-3}{-4-(-4)}\\ \\ =\frac{4}{-4+4} \\ \\ =\frac{4}{0}[/tex]

Since the division of any number by zero is not defined .

Therefore , the slope of the line that contains the  points G(-4,3), H(-4,7) is not defined.

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an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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As per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.

As given in the question,

Number of elephants in zoo = 2

Sally weighs = 7,645 pounds

Joe weighs = 12, 479 pounds

Total weight of Sally and Joe is equal to

= ( 7,645 + 12,479 ) pounds

= ( 20,124 ) pounds

Therefore, as per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.

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Answer:

where is the equal to sign????

Answer:

  g(f(x)) = 6x -9

Step-by-step explanation:

Given f(x) = 3x –5 and g(x) = 2x +1, you want to find g(f(x)).

A function is evaluated by simplifying the result of substituting the argument for the function's variable.

  g(f(x)) = 2·f(x) +1 = 2(3x -5) +1 = 6x -10 +1

  g(f(x)) = 6x -9

Answer:

X=2

Step-by-step explanation:

Add four to both sides

2x-4=0

2x-4+4=0+4

Add the numbers 2x = 4

2x =4

2x/2 = 4/2

cancel the terms

divide the numbers

= x=2

Answer:

22 :)

Step-by-step explanation:

I've attached an image to help break down the answer. (credit to cymath.com)

Hope this helps!

Answer:

9

Step-by-step explanation:

Since one place to the right is greater than or equal to 5 you round up.

Using the given information, the equation of the circle with center located at point (2 , 1) and passes through the point (6 , 4) is (x - 2)^2 + (y - 1)^2 = 25

Using the distance formula, get the radius of the circle by solving for the distance between the center (2 , 1) and the point (6 , 4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(6 - 2)^2 + (4 - 1)^2

radius= √16 + 9

radius = √25

radius = 5

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (2 , 1)

r = 5

(x - 2)^2 + (y - 1)^2 = 5^2

(x - 2)^2 + (y - 1)^2 = 25

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Answer:

f (x^2-4)  =  2x^2 - 5

Step-by-step explanation:

The line which have a steeper slope is Line 1.

It is given in the question that the points on the line are given by:-

Line 1: (-9,-4) and (7,0)

Line 2:(0,1) and (7,4)

We have to find which line has a steeper slope.

First we will find the slope of each line.

We know that slope of a line with points (a,b) and (c,d) is given by:-

(d-b)/(c-a)

Slope of Line 1:

(0-(-4))/(7-9) = 4/(-2) = -2 (we will take the absolute value)

Slope of Line 2:

(4-1)/(7-0) = 3/7

We know that greater the slope of the line means greater the steep of the line.

As,

2 > 3/7

Hence, Line 1 is steeper than Line 2.

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The naive forecast for day 6 is 94.

The naive forecast for the nth period is calculated as follows.

Forecast period Yn=Yn−1​

Period Sales Naive Forecasts

1         90                   -

2         97                  90

3         92                  97

4         90                  92

5         94                  90

6                            94

Hence, the naive forecast for day 6 is 94.

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The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.

The given arithmetic series is 50+55+60+ . . .

The summation notion of given series is ∑50+5n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=7, [tex]a_{1}[/tex] = 50

To calculate sum of arithmetic series, we need to find [tex]a_{7}[/tex] .

[tex]a_{7} = a_{1} + (n-1)d[/tex]

d = 5 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{7}[/tex] = 50 + (7-1)(5)

[tex]a_{7}[/tex] = 50 + 30 = 80

On substituting values in sum of arithmetic series formula, we get

[tex]S_{7}[/tex] = (7(50 + (80)))/2 = 455

The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.

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Using translation concepts, the function g is given as follows:

g(x) = -|x - 4| + 1

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that function g(x) is the function f(x) vertically compressed by a factor of 2, hence:

g(x) = 0.5f(x)

g(x) = 0.5(-2|x - 4| + 2)

g(x) = -|x - 4| + 1

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The arithmetic mean of two terms in an arithmetic sequence is 42 .

One term is 30 then other term is

42 = (x+30)/2

x=54

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The equation and the solution are 2 = -8 * -x and x = 1/4, respectively

On the model, we have the following representations

[1][1]          [-1][-1][-1][-1][-1][-1][-1][-1][-x]

When represented as an equation, we have the following equation

So, we have

2 = -8 * -x

Evaluate the product in the above equation

So, we have

2 = 8x

Divide both sides of the above equation by 8

So, we have

1/4 = x

Rewrite the above expression as

x = 1/4

Hence, the equation and the solution are 2 = -8 * -x and x = 1/4, respectively

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By elimination, the solution of the system of equations, 6x - 3y = 3 and 5x - 5y = 10, is (-1 , -3).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

First, simplify both equations by dividing the first equation by 3 and the second equation by 5.

6x - 3y = 3 ⇒ 2x - y = 1     (equation 1)

5x - 5y = 10 ⇒ x - y = 2     (equation 2)

Use the elimination method since subtracting the two equations will eliminate the variable y.

2x - y = 1     (equation 1)

 x - y = 2     (equation 2)

x        = -1

x = -1

Substitute the value of x to any of the two equation and solve for y.

6x - 3y = 3     (equation 1)

6(-1) - 3y = 3

-3y = 3 + 6

-3y = 9

y = -3

Hence, the solution of the system of equations is (-1 , -3).

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