Use the properties of exponents to simplify the following expressions

1. 5³⋅5⁴

5⁷
5¹²
5⁻¹
5

2. (2⁸)²

2¹⁶
2⁶
2¹⁰
2⁴

3. Anything raised to a power of zero is always:

0
itself
1
negative

4. n²⋅n⁴⋅n⁵

n²²
n¹³
n⁴⁰
n¹¹

5. 8⁷ ⁄ 8²

8⁵
8¹⁴
8⁹
1⁵

6. 3⁻⁴

3^4
-3^4
1 ⁄ 3^4
1 ⁄ 12

7. 7⁰

0
7
-7
1

8. Fill in the blank with the correct exponent to make the statement true.
3^16 = (3^8)(3^_ )

2
4
8
1

9.Which is equivalent to 5 x 5 x 5 x 5

5^3
4^5
5^4
5^5

10. Which is equivalent to 3^4Respuesta necesaria. Opción única.

27
81
9
12

The true statement regarding the number line and the absolute value is given as follows:

The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.

The number line gives the heights relative to the sea level, and thus their signal are interpreted as follows:

The absolute value of a number represents the distance that the number is from the origin. In the context of this problem, it will give the distance of the measure from the sea level of 0 ft.

The height is given as follows:

1.25 ft.

Which is a positive measure, hence the correct option is given by the third option.

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The longer leg is the one that faces the 60-degree angle.

Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.

Triangle Properties 30-60-90

A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.

The shorter leg is the one that faces the 30-degree angle.

The longer leg is the one that faces the 60-degree angle.

The hypotenuse is the side that faces the right angle of 90 degrees.

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As x approaches positive infinity, m(x) approaches positive infinity.

As x approaches negative infinity, m(x) approaches negative infinity.

An expression, rule, or law in mathematics that establishes a connection between one variable (the independent variable) and another variable (the dependent variable).

A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.

If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.

A function is a rule that is applied to a number, known as an input, in order to produce a result, known as an output.

when [tex]$x^n$[/tex] ( n is odd number and n > 0), a > 0 and c is any constant,

[tex]$$x \rightarrow \infty, a x^n+c \rightarrow+\infty[/tex]

[tex]$x \rightarrow-\infty, a x^n+c \rightarrow-\infty$[/tex]

The complete question is;

The function f(x) = x^3 has been transformed, resulting in function m.

m(x) = 1\3x^3 + 6

As x approaches positive infinity, m(x) approaches___

As x approaches negative infinity, m(x) approaches___

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Answer:−

-9−27x

Step-by-step explanation:

Answer:

dude my brain cells are perishing

-2/3 is your answer my guy

have fun

Step-by-step explanation:

The given expression [tex]\sqrt{3}x^{2} -2x[/tex] is a polynomial as the power of x are 2 and 1 which are whole numbers .

What are Polynomials ?

The Polynomials are defined as an expression that are composed of variables, constants and exponents, which are combined using mathematical operators .
For Example : [tex]x^{2} +4x[/tex] .

The Expression can be called as a polynomial if the power of variable present in the expression is a whole number .

The expression is given as : [tex]\sqrt{3}x^{2} -2x[/tex] ,

we can see that , in the first term the power of x is 2 , which is a whole number , and

in the second term the power of x is 1 , which is also a whole number .

Therefore , the expression [tex]\sqrt{3}x^{2} -2x[/tex] is a polynomial .

The given question is incomplete , the complete question is

Is [tex]\sqrt{3}x^{2} -2x[/tex] a polynomial ?

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Three types of triangles according to scalene, isosceles and equilateral triangle.

What is meant by scalene?

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For the rate of change of 4 the two points will be A(2,8) and B(4,16).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the rate of change of the linear function is 4. The coordinates of the two points will be calculated as,

Rate of change = ( y₂ - y₁ ) / ( x₂ - x₁ )

Rate of change = ( 16 - 8 ) / ( 4 - 2 ) = 8 / 2 = 4

Compare the coordinates,

( x₁, y₁ ) = ( 2, 8 )

( x₂, y₂ ) = ( 4, 16 )

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The six different types of graphs are frequency distribution graphs, exponential graphs, logarithmic graphs, trigonometric graphs, and statistical graphs (such as bar, pie, and line graphs).

A vertical and horizontal line connect at the origin to form a simple two-dimensional graph. The x axis is horizontal, whereas the y axis is vertical. The x and y axes in basic line graphs are each subdivided into uniformly spaced subdivisions and given integer values.

There are eight primary types of graphs: linear, power, quadratic, polynomial, and they all aid in organising the presentation of data or information.

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Answer:

below

Step-by-step explanation:

Isosceles triangle have TWO equal legs....so

Leg      + leg        + base = perimeter

(4x-4)   +  ( 4x-4)   + x  = 37

9x -8 = 37

9x = 45

x = 5

Any values of x will result in a real value of the quadratic equation f(x), which is written as f(x). Your minimum score is therefore (3,1).

A function's acceptable range of values is referred to as its domain. These numbers serve as representations of the x-values of a function like f. (x). The set of potential values that a function can be applied to is known as its domain. When the x value is inserted, the method returns the value that is contained in this set. A function's definition is Y = f, where x is the independent variable and y is the dependent variable (x). If it is possible to successfully use a value of x to generate a single value of y using the value of x, that value of x .

given

Let y = f(x) be a function where x and y are the independent and dependent variables.

then that selected x-value is said to belong to the domain of f.

Any values of x will result in a real value of the quadratic equation f(x), which is written as f(x). Your minimum score is therefore (3,1).

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The number of people that will attend each game is given as follows:

The number of attendees will be of 500 on the 857th game, which does not make sense in the context of this problem, as a football team plays at most nine home games during a season. (taking the NFL in context).

The logarithmic function for this problem is defined as follows:

[tex]a(g) = 10 - \log_3{(g + 1)}[/tex]

Hence the number of people that will attend the second home game, when g = 2, is given as follows:

[tex]a(2) = 10 - \log_3{(2 + 1)}[/tex]

a(2) = 10 - 1

a(2) = 9.

Hence 9,000 people, as a(g) is measured in thousands.

The number of people that will attend the eight home game is given as follows:

[tex]a(8) = 10 - \log_3{(8 + 1)}[/tex]

a(8) = 10 - 2

a(8) = 8. (8,000, considering the unit of a(g)).

The game in which 500 people will attend is obtained as follows:

[tex]0.5 = 10 - \log_3{(g + 1)}[/tex]

[tex]\log_3{(g + 1)} = 9.5[/tex]

Applying the cube to both sides, we have that:

g + 1 = 9.5³

g = 857.

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16 is a scale factor of 3 4

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Check to see if there is a constant rate of change to determine if a table of values represents a linear function. You're looking at a linear function if there is! You can learn how to determine whether a table of values represents a linear function in this tutorial.

If an equation is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Identities and conditional equations are the two types of equations.

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There were 24 photos of Simon's motorbike in the album originally.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Let x be the number of photos of Simon's motorbike in the album originally.

We know that the number of photos of his car became 12, so the number of photos of his car originally was 8.

We also know that the ratio of the number of photos of his car to his motorbike became 3:5.

So the number of photos of his car and his motorbike originally was x-4.

We can set up the following equation:

12/(x-4) = 3:5

We can cross-multiply and simplify to get:

3x - 12 = 60

3x = 60 + 12

3x = 72

x = 72/3

x = 24

Hence, originally there were 24 photos.

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We can form a triangle with sides 6cm, 7cm, and 2cm.

Now, According to the question:

We know that:

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

We have the sides:

6cm, 7cm, 2cm

Here,

6 + 7 > 2

Hence, we can form a triangle with sides 6cm, 7cm, and 2cm.

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Answer:

right 2 up 8 units

Step-by-step explanation:

the (x-2) is basically the opposite of what u think so it goes right

and +8 is normal so its up 8

The height of the tree is 17.32 feet.

Height is the measurement of a person's or object's vertical distance from the ground. It is usually expressed in units of meters or feet. Height is an important factor in determining physical characteristics, such as BMI, or Body Mass Index. Height can also be used to estimate the age of a person, and to measure the effects of a growth-promoting treatment. Height is also used in many sports, as it is often an advantage for athletes.

Using the tangent formula, the height of the tree is approximately 17.32 feet. To calculate this, take the tangent of 70 degrees (which is 1.19175) and multiply it by the 10 feet of distance.

The result is 11.9175 feet, which when rounded to the nearest hundredth is 17.32 feet.

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One Kung Pao chicken contains 1620 calories. One Big Mac contains 500 calories.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Assume that one Kung Pao chicken content x calories and one Big Mac content y calories.

Given that one Kung Pao chicken and two Big Macs provide 2620 calories.

Two Kung Pao chickens and one Big Mac provide 3740 calories.

Now using the variable finding calories:

One Kung Pao chicken and two Big Macs provide x + 2y calories.

Two Kung Pao chickens and one Big Mac provide 2x + y calories.

The system of equations is:

x + 2y = 2620  ......(i)

2x + y = 3740  .....(ii)

Using the elimination method to solve the given equations.

Multiply equation (i) by 2 and subtract it from equation (ii)

2x + y = 3740

2x + 4y = 5240

(-)  (-)      (-)

_____________

      -3y = -1500

Divide both sides by -3:

y = 500.

Putting y = 500 in equation (i)

x + 2(500) = 2620

x + 1000 = 2620

x = 1620

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Answer:

1/2

Step-by-step explanation:

I think it is 1/2 Sorry If i am Wrong

If A alone can do a piece of work in 6 days and B alone in 8 days, then A and B undertook to do it for $3200 and complete the work in 3 days with the help of C, then C would be paid 400 dollars.

Therefore the answer is $400.

This is a work and time problem that can be solved using the concept of rate of work. Let's call the amount to be paid to C as "x".

A can do 1 piece of work in 6 days. Therefore, his rate of work is 1/6.

B can do 1 piece of work in 8 days. Therefore, his rate of work is 1/8.

Amount of work A and B can do in 3 days is

= 3×(1/6) + 3×(1/8)

= 3×(1/6)×(4/4) + 3×(1/8)×(3/3)

= 12/24 + 9/24

= 21/24

= 7/8

So amount of work C doing is

= 1 - 7/8

= 1/8

As C do 1/8 amount of work, the amount C would receive is

= 3200 × (1/8)

= 400

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Expression and polynomial are both mathematical terms that are used to represent mathematical equations.

An expression is any combination of symbols, numbers, and operations that represent a value or a quantity. Expressions can be represented as algebraic equations, numerical equations, or verbal phrases. A polynomial is a specific type of expression that is composed of one or more terms with each term containing a power of a single variable. A polynomial can be represented with a single variable or multiple variables.

A formula is an expression or equation that represents an idea or a relationship between two or more variables. A calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.

In summary, an expression is any combination of symbols, numbers, and operations that represent a value or quantity, while a polynomial is a specific type of expression composed of one or more terms with each term containing a power of a single variable. A formula is an expression or equation that represents an idea or relationship between two or more variables, while a calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.

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In Class 8, equality is likely to be defined as a state of being where all individuals are treated fairly and have the same rights, opportunities, and access to resources, regardless of factors such as race, gender, socioeconomic status, and other characteristics. Equality is often contrasted with inequality, which is a state of being where individuals or groups have unequal access to resources and opportunities.

In class 8, students may learn about different types of equality, such as:

Political equality: This refers to the idea that all individuals have an equal say in the political process and equal representation in government.

Social equality: This refers to the idea that all individuals have the same rights and opportunities, and are treated with the same respect and dignity, regardless of their background or characteristics.

Economic equality: This refers to the idea that all individuals have access to the same economic opportunities and resources, regardless of their background or characteristics.

Educational equality: This refers to the idea that all individuals have access to quality education, regardless of their background or characteristics.

Equality of opportunity: This refers to the idea that all individuals have an equal chance to succeed and reach their full potential, regardless of their background or characteristics.

In class 8, students may also learn about the importance of equality and the ways in which inequality can negatively impact individuals and society. They may also learn about different strategies for promoting equality and reducing inequality in society.

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The simplified form of the  (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2 expression is Negative StartFraction 1 Over 16 a squared b squared EndFraction. Option A

Index forms of a number can simply described as can be defined as that number written as an exponential expression.

They are also referred to standard form and scientific notation.

These index forms could also be written as single numbers raised to an exponent.

From the information given, we have that;

1//4 ab superscript negative 2

This is represented as;

(1/4 ab)⁻²

Now, expand the  bracket, we have;

(16 a⁻²b⁻²)

This is further simplified to

1/16 a²b²

Hence, the expression is 1/16 a²b²

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There are seven images are formed If two plane mirrors are positioned at an angle of 45°.

The formula for the number of images formed by two plane mirrors placed at a certain angle is

⇒360/n

where n=angle between the mirrors

The most important thing to remember is that every time the number of images formed is only ODD numbers, if the result is even then you need to subtract 1 from that.

if it is odd u need not subtract, since the number of images ever formed is only odd.

so for an angle, of 45° the number of images formed are:

⇒360/45=8

in this case, since the images formed are even u need to subtract 1 from it i.e

8–1=7

So, the number of images formed is 7.

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The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1 so options (A), (B), and (E) will be correct.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint. The hint which is present in a given pattern hides in the pattern only.

Given the two patterns.

In the first pattern, each term become by adding 5 so option (A) is correct.

In the second pattern, each term become by adding 10 so option (B) is correct.

The term in the second pattern becomes by multiplying 2 in pattern 1

For example 5× 2 = 10 and 10 × 2 = 20 so option (E) will be correct.

Hence, "The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1".

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