The triangles on the grid below represent a translation. On a coordinate plane, triangle A B C is shifted 5 units up to form triangle A prime B prime C prime. Which translation is shown on the grid? a horizontal translation only a vertical translation only a horizontal translation followed by a vertical translation a vertical translation followed by a horizontal translation Mark this and return

The ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on is 0.75.

The Fibonacci series is the sequence of numbers (also called Fibonacci numbers), where every number is the sum of the preceding two numbers, such that the first two terms are '0' and '1'. In some older versions of the series, the term '0' might be omitted. A Fibonacci series can thus be given as, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .

1) To represent any (n+1)th term in this series, we can give the expression as, Fₙ=Fₙ₋₁+Fₙ₋₂.

2) A sequence in which every number in the Fibonacci sequence is the sum of two numbers preceding it in the sequence.

Yes, the Fibonacci sequence written using a formula that connects successive terms of the sequence.

3) The Fibonacci sequence in nature:

A perfect example of this is the nautilus shell, whose chambers adhere to the Fibonacci sequence's logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space.

4) The ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on.

Now, the ratio is 3/2 ÷ 2/1

= 3/2 × 1/2

= 3/4

= 0.75

Therefore, the ratio of consecutive terms of the Fibonacci sequence 2/1, 3/2, 5/3, 8/5, 13/8 and so on is 0.75.

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''The planets farthest from the Sun have the coolest surface temperatures" is the accurate statement.

The amount of energy received from the Sun decreases with increasing distance, so the planets farthest from the Sun receive the least energy and therefore have the coolest surface temperatures.

This can be seen in our solar system, where the outer planets (Mars, Jupiter, Saturn, Uranus, and Neptune) are colder than the inner planets(Mercury, Venus, and Earth)

Therefore, the statement "The planets farthest from the Sun have the coolest surface temperatures" is accurate.

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On solving the provided question, we can say that none of the segments are parallel or perpendicular, and they are all different lengths. The image is a quadrilateral scalene figure.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

FG: slope: -4/5, length: √41 ≈ 6.40

GH: slope: -5, length: √26 ≈ 5.10

HI: slope: -1, length: 3√2 ≈ 4.24

IF: slope: 4, length: √17 ≈ 4.12

None of the segments are parallel or perpendicular, and they are all different lengths. The image is a quadrilateral scalene figure.

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The value of x in the quadrilateral is 112 degrees and the angle relationship is vertical angles.

A quadrilateral is a plane figure that has four sides , and also has four corners or vertices. The sum of angles in a quadrilateral is 360 degrees. Examples of quadrilateral are parallelograms, rectangle, square, rhombus etc.

The quadrilateral above has two diagonals that intersect each other. The diagonal AC and BD intersect each other at a points.

The relationship formed are vertically opposite angles. Vertically opposite angles are congruent.

Hence, the sum of angles in a point is 360 degrees.

Let's find x as follows;

2x + 68 + 68 = 360

2x = 360 - 136

2x = 224

x = 224 / 2

x = 112 degrees.

Therefore,

x = 112 degrees

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Answer:

[tex] y = - \frac{5}{4}x - \frac{5}{2} [/tex]

Step-by-step explanation:

Don't know if it's right but yeah that's what I got.

The area of this rectangle is 4 * √11 square units

The perimeter of a regular hexagon can be divided equally into the lengths of its six sides.

So, the length of each side of the hexagon is 12 / 6 = 2 units.

Since the hexagon is inscribed in a rectangle, the length of the rectangle is equal to the length of two sides of the hexagon, or 2 * 2 = 4 units.

Let's call the height of the rectangle "h."

Then, the length of one side of the equilateral triangle is 2 units and the height is h, so using the Pythagorean theorem:

h^2 + (2/2)^2 = (2 * √3)^2

h^2 + 1 = 12

h^2 = 11

h = √11

So, the area of the rectangle is equal to its length multiplied by its width:

4 * √11 square units

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Answer:

-75

I hope this helps,but I think to answer this question you have to replace the x with 2

The rquired equation of the line is x + 2y = - 10

The slope-intercept form of a line is given by

Where m = slope and c = y-intercept  

Note: The slope of two parallel lines will have the same slope

Here we have

The point (-6, -8) and the line x - 2y = 6 --- (1)

Let the equation y = mx + c ---- (2)  is the equation of the line  that passes through (-6, -8) and parallel to x - 2y = 6  

As we know the parallel  lines will have the same slope

=> Slope of line (1) = Slope of line (2)

Here x - 2y = 6

=> 2y = - x + 6

=>  y = -x/2 + 3  which is in the form of y = mx + c

=> Slope of line = - 1/2

Therefore, the Slope of lines (2) = -1/2

=> y = (-1/2)x + c

=> 2y = -x + 2c --- (3)

Given that line passes through (-6, -8)

=> 2(-8) = - (-6) + 2c

=> - 16 = + 6 + 2c

=> 2c = -10

=> c = -5

=>  y = -x/2 + (-5)

=>  y = -x/2 - 5

=> 2y = - x - 10

=> x + 2y = - 10

Therefore,

The required equation of the line is x + 2y = - 10  

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As a fraction: 26/32 = 13/16

As a decimal: 26/32 = 0.8125

As a percent: 26/32 * 100 = 81.25%

Answer:

The third option

Step-by-step explanation:

The location of the waterfall on the graph will be (3,1). Instead of going down down,  Rodrigo goes 4 units upward direction.

Coordinates are defined as a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).

Given that the location of the entrance is at (6, 5).

To reach the waterfall, you need to go 3 km to the left and 4 km down from the park entrance.

The x-coordinate decreases to the left side of a point and increases to the right side of a point.

The y-coordinate decreases to a downward point and increases upward a point.

The x-coordinate of the waterfall is 6 - 3 =3

The y-coordinate of the waterfall is 5 - 4 = 1.

The coordinate that represents the location of a point is (3,1).

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Answer: The result can be shown in multiple forms.

Inequality Form:

x>−5

Interval Notation:

(−5,∞)

Step-by-step explanation:

Answer:because if we plug this in it will be -7 > -5, this is false because this is saying that -7 has a greater value that -5.

Step-by-step explanation:

hope the helps<3

Answer:

its 47.8 degrees

Step-by-step explanation:

The greatest common factor is 3x.

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common.

For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

Given:

3x³+18x²-12x

First, factorize each term of Expression

3x³ = 3. x . x . x

18x² = 3 . 3 . 2. x .x

12x =

So, 3x³+18x²-12x

= 3. x . x . x + ( 3 . 3 . 2. x .x ) - (2 . 2. 3 . x)

= 3x ( 3x² + 6x - 4)

Hence, the GCF is 3x.

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Answer:

450 plus whatever other costs there are if there are any

Step-by-step explanation:

300+150=450 so it is 450 plus any other ammount of money you must pay if any

The measure of the angles of the parallelogram are: x = 90 degrees, y=   122degress and z=90 degrees

A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides

Remember that the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

This implies that y + 58 = 180

Making y the subject of the relation

y=180-58

y=122⁰

Also, since the other two opposite angles are not given, then it means that x=y = 180/2 = 90

this therefore means that x= 90, y= 122 and z= 90 degrees

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slope

it has 3 on side and i have done this plenty of tjmes to know

Answer:

5 jackets

Step-by-step explanation:

Answer:

The owner must buy 6 jackets

Step-by-step explanation:

$45x [tex]\geq[/tex] $250

x [tex]\geq[/tex] 250/45

x  [tex]\geq[/tex] 5.55555.....

There can't be a decimal amount of jackets

The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15

What is equation of a straight line ?

Equation of straight line as follows , y = mx + b

where m is the slope of line.

Given equation ,

x - 5y = 75

and the points are (0,-3)

First lets find the slope of a line

we get,

x - 5y = 75

5y = x - 75

y = 1/5 x  - 15

m = 1/5

Here the point (0,-3) and slope m = 1/5
Therefore,

The equation of the line

y + 3  = 1/5  (x-0)

5y + 15 = x

5y - x + 15

Therefore, The equation in standard form when the line is passing through point (0,-3) and parallel to x - 5y = 75 is 5y - x + 15

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Answer:

Answers Below

Step-by-step explanation:

[tex]area = \frac{1}{2} (p \times a)[/tex]

[tex]perimeter = 5s[/tex]

The ratio of the side lengths, yellow to green

We see yellow is 36 and green is 60, so we just put that slash mark in between as indicated in the directions, giving us

36/60. We can reduce this to it's simplistic form of 3/5

The ratio of the perimeters, yellow to green.

To find the perimeter, we multiply the side by 5

Yellow; 36x5= 180

Green; 60x5= 300

We put that ratio slash... 180/300. Reducing it comes out to 90/150 > 30/50 > 3/5 also...

And that's because the polygons are similar.

Since the polygons are similar... what would be the ratio for the areas...

Yep, 3/5

Last is to find the area of the green.

The yellow is 45 and the ratio is 3/5. We can write the equation as a ratio

[tex] \frac{45}{x} = \frac{3}{5} [/tex]

Now if we cross multiply;

[tex](45)(5) = 3x > 3x = 225[/tex]

Last but not least, divide by 3

[tex]x = 75[/tex]

Making the area of the green 75

Step-by-step explanation:

you made so many typos.

let's see :

the point-slope form of a line is

y - y1 = a(x - x1)

"a" being the slope, (x1, y1) being a point on the line.

in our case

y - -16 = 1/2 × (x - 16)

y + 16 = x/2 - 16/2 = x/2 - 8

y = x/2 - 24

or

y = (1/2)x - 24

The solution of the system of equation -6x + 2 = -2^{x + 2} + 6 is equal to the ordered pair (0, 2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

f(x) = -6x + 2     ......equation 1.

g(x) = -2^{x + 2} + 6     ......equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (0, 2)

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The table D represents the relationship between the number of minutes and the number of gallons of water in the pool.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A pump fills a pool at a constant rate.

At the end of 12 minutes,

it has filled 3 gallons of water.

From the given choices:

The table D represents the relationship between 12 minutes and 3 gallons of water in the pool.

Therefore, the table D is the correct table.

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Answer: irrational numbers

Step-by-step explanation:

By definition, natural numbers are rational numbers.

Henry has to choose bank Z.

Two or more expressions with an Equal sign is called as Equation.

Given there are three banks Bank X, Bank Y and  Bank Z

For bank X, No monthly fees if balance stays above $500, otherwise $7 per month.

No monthly fees if check card is used less than 6 times per month

$5 monthly fee, No minimum balance, $25 minimum balance, No minimum balance

Has Henry has  about $300 in his account at any given time during the month. He limits his ATM visits to one per week and is interested in banking online options he has to choose bank Z.

Hence, Henry has to choose bank Z.

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Answer: Bank Z

Step-by-step explanation:Bank Z is his best option

The value of x is 24.2.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

Base = 22

Hypotenuse = x

Cos Ф = Base / Hypotenuse

Now,

Cos 24 = 22 / x

0.91 = 22/x

x = 22/0.91

x = 24.18

x = 24.2

Thus,

x is 24.2.

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The number of hits by each player are 1195 and 1470 hits, respectively

Let's call the number of hits that Ricky got "x".

Then, Pedro got x + 275 hits.

The total number of hits for both players is x + (x + 275) = 2665

Solving for x, we get 2x + 275 = 2665

Subtracting 275 from both sides,

We get 2x = 2665 - 275 = 2390

Dividing both sides by 2,

We get x = 2390 / 2 = 1195

So Ricky got 1195 hits and Pedro got 1195 + 275 = 1470 hits.

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The equation is 3 = 3x + (-3) which represents the given statement "3 is the same as the sum of times a number and -3".

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

Let the x represents the number.

The statement is given in the question, as follows:

3 is the same as the sum of times a number and -3

As per the given statement, we can write the algebraic form as

3 = 3x + (-3)

Thus, the equation is 3 = 3x + (-3) which represents the given statement.

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a) 17210368 different ways can the program select which students will answer the five questions

b) 11,793,600 different ways.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Given:

Each of the 28 students in her class is equally likely to be chosen every time she runs the program.

a) The number of ways can the program select which students will answer the five questions

= [tex]28^5\\[/tex]

= 17210368

b) using Permutation

[tex]P^{28}_2[/tex] = 28! / (28-5)!

      = 28! / 23!

      = 28 x 27 x 26 x 25 x 24 x 23! / 23!

      = 11,793,600

So, there are 11,793,600 different ways.

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