Determine whether the relation is a function
Explain why or why not.
1. (9, -1) (4,2) (5,3) (8, -1) (3, 0)

Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Step-by-step explanation:

There are four basic properties of numbers: commutative, associative, distributive, and identity.

1.Commutative Property

a. Addition

. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8       or       5 + 3 = 8

b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15       or       5 x 3 = 15

2.Associative Property

a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13   or   (6 + 4) + 3 = 13

b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72   or   (6 x 4) x 3 = 72

3.Distributive Property

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45   or   5 x 7 + 5 x 2 = 45

4.Identity Property

a. Addition. The sum of any number and zero is that number.

12 + 0 = 12

b. Multiplication, The product of any number and one is that number.

18 x 1 = 18

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The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).

To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.

If w = 7 and l = 9

A = l × w = 8 × 6 = 48

If w = 8 and l = 8

A = l × w = 8 × 8 = 64

So, the second case would obtain a larger area.

Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.

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Answer: 12 inches

Step-by-step explanation:

Answer: 15 cm

Step-by-step explanation:

The range and the domain of the function f(x) =  1 - x^2 is less than or equal to 1 and all values of x are a real number (R).

Domain: x ∈ R

Range: f ( x ) ≤ 1, ∈ R

f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).

x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.

Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.

So, the range of f(x)≤ 1, and the domain is all real values ( R ).

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The exponential decay formula can take one of three forms:

f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]

Where,

a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality

What is Exponential Decay ?

Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.

The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:

f (x) = abx

f (x) = a (1 – r)x

P = P0 e-k t

Where,

a (or) P0 = Initial amount

b = decay factor

e = Euler’s constant

r = Rate of decay (for exponential decay)

k = constant of proportionality

x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).

In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as

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The straight line has the equation, y = 5x - 4.

A straight line is made up of an infinite number of points that are joined on both sides of the point.

Any straight line's slope 'm' is given by:

m = y2 - y1 / x2 - x1

In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.

The obtained points from the graph are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

   = 5/1

   = 5

Because it intersects the y-axis at the point where the intercept C = -4,

The line's equation will be:

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, the equation for the straight line shown below is y = 5x - 4.

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The used postulate is explained below.

What is congruent triangles?

Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.

When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.

This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.

Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.

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Answer:

3

Step-by-step explanation:

Hope this helps..

The rate of change in the given interval would be 1.25 ft/s.

What is the rate of change?

The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.

By observation, we can take the points from the graph in between the given interval.

The points would be (3, 2.5) and (5, 4)

Then the rate of change = y2 - y1/ x2 - x1

                                         = 4 - 2.5/5 - 3

                                         = 2.5/2

                                         = 1.25 ft/s.

Hence, the rate of change in the given interval would be 1.25 ft/s.

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B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)

1000 + 25 + 200 = 1225

Total 56 pencils are needed for the exam.

Multiplication is one of the arithmetic operation used to find total numbers of items or things.

Given,

Total students in the classroom = 28

Total number of pencils needed by each student for the exam=2 pencils

Total number of pencils needed for the exam are,

= Total student ×  Number of pencils needed by each student

= 28 × 2

= 56 pencils

Hence , The total number of pencils needed by the students for the exam would be 56 .

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Answer:

B) x + 1

Step-by-step explanation:

Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.

Eg: 5 , 6 , 7 ,.....

6 = 5 + 1

7 = 6 + 1

So, if first number is x, then the next number will be x + 1

The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

The various types of inverse function are:

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The length of the line segment will be 4 units. Then the correct option is A.

The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,

D² = (2 - 2)² + (2 + 2)²

Simplify the equation, then we have

D² = (2 - 2)² + (2 + 2)²

D² = (4)²

D = 4 units

The length of the line segment will be 4 units. Then the correct option is A.

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The missing diagram is attached below.

An isosceles triangle therefore has both two equal sides and two equal angles.

What is traiangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the previous illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg).

An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces. The isosceles right triangle is yet another unique instance of an isosceles triangle.

The Pythagorean theorem can be used to determine the height of the isosceles triangle shown in figure:

[tex]h = \sqrt{b^2-\frac{1}{4}a^2 }[/tex]

Consequently, the region is given by:

A=1/2ah

A = [tex]\frac{1}{2}a\sqrt{b^2-\frac{1}{4}a^2 }[/tex]

[tex]A = \frac{1}{2}a^2\sqrt{\frac{b^2}{a^2}-\frac{1}{4} }[/tex]

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The center is (6, 1) of the given circle with the equation  x²+y²-12x-2y+12=0.

Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.

A circle is a closed shape that can be created by following a moving point in a plane while maintaining a constant distance from another point.

The Greek word kirks, which means hoop or ring, is whence the word circle gets its form.

So, we have the equation: x²+y²-12x-2y+12=0

Compared to the circle's basic equation:

2 + y² + 2gx + 2fy + c = 0

2g = -12, 2f = -2, c = 12

g = -6, f = -1

Centre = (-g, -f)= (6, 1)

Now, fill in the square:
x² - 12x + 36 + y² - 2y + 1 = -12 + 36 + 1

(x - 6)² + (y - 1)² = 25

(x - 6)² + (y -1)² = 52

When compared to the equation for a circle with the centers at (h, k) and radius "r," Centre = (h, k) = (6,1).

Therefore, the center is (6, 1) of the given circle with the equation  x²+y²-12x-2y+12=0.

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Correct question:
What is the center of a circle whose equation is x²+y²-12x-2y+12=0?

Answer:

6,1

Step-by-step explanation:

trust me

The equation that best defines the length of the equal piece is 4x+2¹-12

We should know that an equation is a mathematical model that shows the equality of two sides of an expression

Based on the given condition 12-24=4*x

Applying multiplicative distribution -12=4x

Rearrange the equation 4x=-12

Calculate the product of the quotient x=-3

Now 24feet divided by -3 =-4

Since it deals with length =4

In conclusion the equation that determines the length of each equal piece is  4x+2¹-12

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Answer:

To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.

Step-by-step explanation:

The inverses of the functions  y= x⁹ and y= x¹¹ are functions.

The inverses of the functions y = x⁴ and y= x⁸ are not functions.

(a )Consider ,the inverse of the function is a function

(2 ) y= x⁹

The inverse of the function is given by,

x = [tex]\sqrt[9]{y}[/tex]  

Here y is an element of the real numbers.

i.e. y ∈R

So, this is a function.

(4) y= x¹¹

The inverse of the function is given by,

x = [tex]\sqrt[11]{y}[/tex]

Here y is an element of the real numbers.

i.e. y ∈R

Similarly , this is a function.

(b ) Consider ,the inverse of the function is a not a function

(1  )y = x⁴

The inverse of the function is given by,

x =  [tex]\sqrt[4]{y}[/tex] (y ≥0)

It is of one- one correspondence,

when y = 4 ,

x = ±√2

Thus, it is not a function.

(3)  y= x⁸

The inverse of the function is given by,

x = [tex]\sqrt[8]{y}[/tex]

Likewise , this is not a function.

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The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

we know that

The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.

therefore

Is the point of concurrency of the angle bisectors of the triangle

Part 2)

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

therefore

Is a segment drawn  from a vertex to the midpoint of the opposite side

Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

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Answer:

A

Step-by-step explanation:

The volume in cubic inches is [tex](36)(18)(6)=3888[/tex].

This is equal to [tex]3888/12^3=2.25[/tex] cubic feet.

The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.

Given, a destroyed angle

A destroyed angle is called a figure in Geometry also known as Rectangle.

A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.

So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.

Therefore, the destroyed angle is a rectangle.

Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.

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There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume

The volume of cube is calculated by using a × a × a = a³ where "a" is the edge.

The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches

The volume of the smallest cube = 3.375inches³

The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches

The volume of the largest cube = 421.875inches³

Thus, the number of the smallest cubes it would take to fill the largest cube is derived by

421.875inches³/3.375inches³ = 125.

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From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|

What is graph of a function?

The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.

Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.

Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|

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The value of the variables x and y are,

11) x = 13,  y = 18.4

12) x = 6.9,  y = 8.

What is right angle triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

11)Let the given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]

Using this to find the value of y.

[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]

So, the values of x and y are x = 13 and y = 18.4.

12) The given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]

Now to find the value of x.

[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]

Hence, the values of x and y are, x = 6.9 and y = 8.

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Isosceles triangle problem can be solved by given steps

what is isosceles triangle ?

An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.

explanation:

In isosceles triangle

1. Two sides of the triangle are congruent

2. The angle opposite those sides are congruent

x + 72 +72 = 180

             x  = 180 -144

             x = 36

Hence the isosceles triangle problem can be solved by above steps and explanation

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Answer:

Step-by-step explanation:

1) 4 1/4 + 5 1/2

= 9 3/4

2) 10 4/5 - 6 1/5

= 4 3/5

3) 3 1/4 - 1 3/4

= 1 1/2

4) 3 2/5 + 7 7/10

= 11 1/10

5 ) 10 3/13 + 2 10/13

= 13

Answer:

1

Step-by-step explanation:

Its for sure 1

1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches  form a right triangle.

What is Right traingle?

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),

assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;

The Pythagoras Theorem is:

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

Making substitutions and applying the math results in:

[tex]15^2 + 36^2= 39^2[/tex]

225 + 1296 = 1521

1521 = 1521

Therefore, it is a right traingle.

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First, 108/9=12

This means that are 12 groups of people.

If there are 8 students in each group, 12 x 8 = 96.

96 should be your answer.