The graph shows the amount of book sales
over several days. Determine if the
relationship is proportional. Find and
interpret the slope. Then find the unit rate
and compare it to the slope.

Answer:

m<8=1024

Step-by-step explanation:

Since they are asking for m<8, we do 128*8=1024.

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.

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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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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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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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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We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.

An discriminant value definition ?

The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

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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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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:

3

Step-by-step explanation:

Hope this helps..

The probability for each event are

[A] -  36/1320

[B] -  36/1320

[C] -  36/1320

[D] -  The probability doesn’t change in any order.

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.

[A] -

{3/12} x {3/11} x {4/10} =

36/1320

[B] -

{3/12} x {4/11} x {3/10}

36/1320

{C} -

{4/12} x {3/11} x {3/10}

36/1320

D) The probability doesn’t change in any order.

Therefore, the probability for each event are -

[A] -  36/1320

[B] -  36/1320

[C] -  36/1320

[D] -  The probability doesn’t change in any order.

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The equidistant point of  the triangle is point O , which is shown below.

In the question ,

we have to find the equidistant point in the triangle ,

We know that the equidistant point from the vertices of the triangle is the circumcenter ,

let the circumcenter be point O .

The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .

We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .

So ,we draw OA ,OB and OC .

we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.

that means , OA = OC and OC = OB .

which means OA = OB .

we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.

So, we can say that point O is on the perpendicular bisector of AB .

and

Since OA = OB = OC , the point O is equidistant from A , B and C .

Therefore , the equidistant point of the triangle is the circumcenter (point O) .

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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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