definition for piecewise function

Yes , it is true that two pairs of adjacent sides of a kite are equal .

A quadrilateral with two pairs of adjacent sides equal in length is called a kite. Kites also have one pair of opposite angle equal as shown in the figure below.

Hence , the given statement is true .

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If [tex]f,g[/tex] are inverses of one another, then

[tex]f\circ g(x) = g\circ f(x) = x[/tex]

Given [tex]f(x)=x^2-1[/tex] and [tex]g(x)=\sqrt{x-8}[/tex], then

[tex]f\circ g (x) = f(g(x)) = f(\sqrt{x-8}) = \left(\sqrt{x-8}\right)^2 - 1 = \boxed{x - 9} \neq x[/tex]

so right away we know [tex]f[/tex] and [tex]g[/tex] are not inverses.

In the other direction, we come to the same conclusion.

[tex]g\circ f(x) = g(f(x)) = g(x^2 - 1) = \sqrt{(x^2-1)-9} = \boxed{\sqrt{x^2 - 9}} \neq x[/tex]

The two similar triangles in this problem are given by:

C. QRS and TUV

Similar triangles share these two features:

Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:

3/6 = 2.4/4.8 = 1.8/3.6.

Hence option C is correct.

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Answer:

180-(35+95)=50

Step-by-step explanation:

Any triangle in the world sum of its angle equal 180

The image of D (1, 2) is D' ( 2, 7).

The image of E (-3 -5) is E' ( -10, 0).

The image of F (4, -1) is F' ( 11, 4).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given points are;

D (1, 2), E(-3, -5) and F(4, -1)

Now, The rule is to find the image of points is;

(x, y) → (3x - 1, y + 5)

Hence,

The image of D (1, 2) = (3 * 1 - 1, 2 + 5)

                               = (3-1, 7)

                               = (2, 7)

The image of E (-3 -5) = (3*-3 - 1, -5 + 5)

                                 = (-9-1, 0)

                                 = (-10, 0)

The image of F (4, -1) = (3*4 - 1, -1 + 5)

                                = (12-1, 4)

                                = ( 11, 4 )

Therefore, The image of D (1, 2) is D' ( 2, 7).

The image of E (-3 -5) is E' ( -10, 0).

The image of F (4, -1) is F' ( 11, 4).

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The probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450

Alphonso can pick a ticket from 50 tickets in 50 ways;

When Alphonso pick a ticket, then Cordell can pick a ticket in 49 ways;

Total number of ways = 50 × 49 = 2450;

Alphonso can get ticket 14 and Cordell can get ticket 23 in only one way;

So, the probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450;

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The drawing shows a series of transformations and the sequence that moves Triangle I to Triangle II to Triangle III is translation followed by reflection.

A reflection in arithmetic is a form of geometrical transformation, wherein an item is flipped to create a reflect or congruent image. The bisector of the plane is referred to as the definition on the line of reflection, and it is perpendicular to the preimage and photograph.

In the coordinate plane we will draw the translation if we recognize the path and how far the figure have to be moved. To translate the factor P(x,y) , a units right and b units up, use P'(x+a,y+b) .

A translation is a form of transformation that takes every factor in a figure and slides it the equal distance in the equal path.

Here, the image is first translated and then rotated.

Therefore, the drawing shows a series of transformations and the sequence that moves Triangle I to Triangle II to Triangle III is translation followed by reflection.

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The sign of the other integer is positive. Value of other integer is greater than 5.

When we add two numbers of the same sign, final number has the same sign of the initial numbers

For example, we add 3 and 8,

3+8= 11

Both the numbers 3 and 8 are positive so our result is also positive.

On the other hand when we add -3 and -8, then the result will be

-3 +(-8)= -11

Both the numbers are negative, so our result also negative.

When two numbers of different sign are being added then the sign of the larger number decide the sign of the final number

For example, we add -3 and 8.

-3+8= 5

8 is larger than 3, and has positive sign, so the result will also be positive.

Suppose other number is x.

-5+x>0 (As the sum is positive)

Add 5 on both the sides

-5+x+5>0+5

x>5

As we can see the number is greater than 5 and has a positive value.

Final answer: The sign of the other integer is positive. Value of other integer is greater than 5.

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The fluid force against the window is equal to 931.5 lb.

Given the following data:

Generally speaking, the fluid force that is exerted on the fish tank by the seawater is due to the liquid pressure acting over the given area. Also, the fluid force that is exerted on the fish tank is directly proportional to the depth of seawater.

The depth of seawater is given by:

Depth = 28.5 - 1.5

Depth = 27 inches.

Next, we would convert the unit of the depth of seawater and width of viewing portion in inches to feet:

1 inch = 12 feet

Depth = 27 inches to feet = 27/12 = 2.25 feet.

Width = 69/12 = 5.75 feet.

Now, we can calculate the fluid force against the window by using this formula:

Fluid force = (density × depth × width)/2

Fluid force = (64 × 2.25² × 5.75)/2

Fluid force = 1863/2

Fluid force = 931.5 lb.

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Complete Question:

The viewing portion of the rectangular glass window in a fish tank is 69 inches wide and runs from 1.5 inches below the water's surface to 28.5 inches below the surface. Find the fluid force against this portion of the window. The weight-density of seawater is 64 lb/ft. What is the fluid force against the window?

By inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.

We are given the arithmetic series as;

5, 10, 15, 20, .......

From the formula of the nth term of an arithmetic series, we know that;

a_n = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

Thus, for this series, it is clear that the common difference is 5. Thus the fifth term is;

a_5 = 5 + (5 - 1)5

a_5 = 5 + 20

a_5 = 25

Thus, by inductive reasoning we can say that the conclusion is based on observing the four numbers in the sequence.

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The distance of each of the paths are as follows;

25) Distance of Low Trail is; d = 17.1 km

26) Distance of willow walk is; d = 20.6 km

27) Distance of Pond Walk is; d = 8.5 km

28) Distance of Meadow Trail is; d = 22.8 km

The formula for distance between two coordinates is;

d = √[(x1 - x2)² + (y1 - y2)²]

25) Distance of Low Trail is;

d = √[(14 - 12)² + (-2 - 15)²]

d = 17.1 km

26) Distance of willow walk is;

d = √[(10 + 4)² + (12 - 1)²]

d = 20.6 km

27) Distance of Pond Walk is;

d = √[(-4 + 12)² + (12 - 15)²]

d = 8.5 km

28) Distance of Meadow Trail is;

d = √[(14 + 4)² + (12 + 2)²]

d = 22.8 km

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Answer:

3.5 × 10 to the 8th power

Step-by-step explanation:

Answer:

8.9 cm

Step-by-step explanation:

We have
[tex]\overline {UV} = 16.8 cm\\\\\overline {WV} = 7.9 cm\\\\ Since all lines are scalars, \overline{WV} = \overline{VW}\\\textrm{We see that \overline{UW} + \overline{WV} = \overline{UV}\\\\\overline {UW} \\ = \overline {UV} - \overline {WV} = 16.9 - 7.9 = 8.9 cm}[/tex]

Items purchased:

x packs of pencils,

twice as many packs of erasers, total number of eraser packs = 2x

three times the number of tape rolls, number of tape rolls = 3x

total expenditure = x m + 2xn + 3xp = x(m + 2n + 3p)

We now have two possibilities:

1- All three goods are the same price:

cost of one pencil pack = cost of one eraser pack = cost of one roll of tape = m

x m + 2xm + 3xm = 6xm

total amount spent

2- The three goods are not the same price:

m = the cost of one pencil pack

n = the cost of one pack of erasers

One roll of tape costs p.

total expenditure = x m + 2xn + 3xp = x(m + 2n + 3p)

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

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Answer:

see explanation

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = lw ( l is the length and w the width )

using the property [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then

A = 2[tex]\sqrt{7}[/tex] × 10[tex]\sqrt{7}[/tex]

  = 2 × 10 × [tex]\sqrt{7}[/tex] × [tex]\sqrt{7}[/tex]

  = 20 × 7

  = 140 ft²

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

the perimeter (P) is calculated as

P = 2(l + w)

  = 2(2[tex]\sqrt{7}[/tex] + 10[tex]\sqrt{7}[/tex] )

 = 2(12[tex]\sqrt{7}[/tex] )

 = 24[tex]\sqrt{7}[/tex] ft

Answer:

Step-by-step explanation:

Answer: 144

Step-by-step explanation:

Answer:

47 , 52

Step-by-step explanation:

Answer:

first figure area is 47 square units

second figure area is 52

Answer:  

> y²⁴- 256 = 0

> (y⁴)

x-256 = 0

or

x= 256

Step-by-step explanation: i have no idea if i am right but pls lmk if i am wrong have a good day/night (: <3

The height of the tree in Jasmines drawing is; 6.25 inches tall

The scale factor used by Louis is; 3in : 10 ft

The scale factor used by Jasmine is; 5in : 20ft

We are told that the tree in front of the school in Luis's drawing is 7.5 inches tall. Thus;

True height of tree in Louis drawing is; (7.5 * 10)/3 = 25 ft

Thus, height of tree in Jasmines drawing = (25 * 5)/20 = 6.25 inches tall

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Step-by-step explanation:

I assume the grid units are single units (1, 2, 3, ...).

to be a function every value of x must have exactly one value of y.

but that is violated at x = 2. at that point y can be either +3 or -3 (indicated by the 2 points at x=2).

so, no, it is not a function.

the domain is the interval or set of all valid x (input) values.

since we have no continuous curve but single points, it is a set :

x € {-4, -3, -2, 1, 2, 3, 6}

the range is the interval or set of all valid y (function result) values. again, it is a set for the same reasons :

y € {-3, -2, 0, 1, 3, 4}

Answer:

10

Step-by-step explanation:

10*10*10=1000

10^3=1000

Answer: You're dividing, and the answer is 1/2, 1/4, 1/3, 1/8

Step-by-step explanation:

The intersection of the two planes is a Line.

According to the statement

We have to find that the Intersection of the planes.

So, For this purpose, we know that the

An intersection is a single point where two lines meet or cross each other.

From the given information:

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors.

And then the intersection of the plane becomes:

Then

The intersection of two planes is a line. If the planes do not intersect, they are parallel.

They cannot intersect at only one point because planes are infinite.it means parallel planes have no intersection point.

So, The intersection of the two planes is a Line.

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Answer:

Range is 21

I believe

Step-by-step explanation:

Answer:

4.88

Step-by-step explanation:

2+2+4+4+5+5+6+7+9=44

44÷9=4.88

Answer=4.88

Answer:

1 2/15 inches

Step-by-step explanation:

First you need to make the denominator of the two fractions match.

4/5 and 1/3

the least common multiple of these is 15

4/5 becomes 12/15

1/3 becomes 5/15

add them together

17/15

subtract 15 from 17 because 15/15 is one

we get 2

put 2 as the numerator and 15 as the denominator

Answer:

37.5

Step-by-step explanation:

5x5 = 25. That's your square. For the triangle, 5x5 = 25. 25/2 = 12.5 25+12.5 = 37.5.

Answer:

She made 118% profit.

Step-by-step explanation: