Which expressions are equivalent to the one below? Check all that apply.
4^3 x 4^x

Answer:  3.6y^2

Step-by-step explanation:

To calculate this, you simply multiply the two numbers together: 1.2y * 3y = 3.6y^2.

Answer:

[tex] \sf \: c) \: 3.6 {y}^{2} [/tex]

Step-by-step explanation:

Now we have to,

→ find the product of 1.2y and 3y.

Forming the problem,

→ 1.2y × 3y

Then the product will be,

→ 1.2y × 3y

→ (1.2 × 3)(y × y)

→ (1.2 × 3)y²

→ (3.6)y²

→ 3.6y²

Hence, the answer is 3.6y².

Considering the given data which include the domain and the range the possible value of n is

The possible value of n will be n such a way that both the domain and the range are not altered

for a domain of 1, 2, 3, 4, 5, 6, 7, 8 using n, 3n will have a range of

1, 6, 9, 12, 15, 18, 21, 22, 24,

The number 24 is outside the range which is 3, 4, 5, 6, 7, 8,,,,,,,20, 22

n = 8 gave the value of 24 hence 8 cannot be the value of n

n is 1, 2, 3, 4, 5, 6, and 7

written in the form: 1 ≤ n ≤ 7

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The quadratic equations are

a) x² + 5x - 6 = 0  ( the roots are x = -6 , x = 1 )

b) x² - 5x + 6 = 0  ( the roots are x = 2 , x = 3 )

c) x² + 2x - 3 = 0  ( the roots are x = -3 , x = 1 )

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation in the standard form is ax² + bx + c = 0

Now , the value of A is

a)

Let the quadratic equation be x² + 5x - 6 = 0

Now , on simplifying the equation , we get

x² + 5x - 6 = 0

x² - x + 6x - 6 = 0

Taking the common factors in the equation , we get

x ( x - 1 ) + 6 ( x - 1 ) = 0

On factorizing the equation , we get

( x + 6 ) ( x - 1 ) = 0

So , ( x + 6 ) = 0 or ( x - 1 ) = 0

And , x = -6 or x = 1

So , the roots of the quadratic equations are x = -6 or x = 1

b)

Let the quadratic equation be x² - 5x + 6 = 0

Now , on simplifying the equation , we get

x² + 5x + 6 = 0

x² + 2x + 3x - 6 = 0

Taking the common factors in the equation , we get

x ( x + 2 ) + 3 ( x + 2 ) = 0

On factorizing the equation , we get

( x + 3 ) ( x + 2 ) = 0

So , ( x + 3 ) = 0 or ( x + 2 ) = 0

And , x = -3 or x = -2

So , the roots of the quadratic equations are x = -2 or x = -3

c)

Let the quadratic equation be x² + 2x - 3 = 0

Now , on simplifying the equation , we get

x² + 2x - 3 = 0

x² - x + 3x - 3 = 0

Taking the common factors in the equation , we get

x ( x - 1 ) + 3 ( x - 1 ) = 0

On factorizing the equation , we get

( x + 3 ) ( x - 1 ) = 0

So , ( x + 3 ) = 0 or ( x - 1 ) = 0

And , x = -3 or x = 1

So , the roots of the quadratic equations are x = 1 or x = -3

Hence , the quadratic equations are solved

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Answer:

Step-by-step explanation:

Let's call the two numbers x and y, where x is the smaller number and y is the larger number. We are given that x and y differ by 3, which means y - x = 3. We are also given that the product of x and y is 88, which means x * y = 88. We can solve this system of equations by substituting the second equation into the first equation:

y - x = 3

y = x + 3

Substituting this expression for y into the second equation, we get:

x * (x + 3) = 88

x^2 + 3x - 88 = 0

This is a quadratic equation that we can solve using the quadratic formula:

x = (-3 +/- sqrt(3^2 - 41(-88))) / (2*1)

= (-3 +/- sqrt(9 + 352)) / 2

= (-3 +/- sqrt(361)) / 2

= (-3 +/- 19) / 2

= -11/2 or 8/2

Therefore, the two numbers are x = -11/2 and y = 8/2, or x = -5.5 and y = 4. These are the solutions to the original system of equations.

When we multiply 4 with 4 we get 16 again

when we multiply (-4) with (-4) we get 16. so 16 has 2 square root.

There are always two solutions to the square root of a number: a positive response and a negative answer. Because the square of a negative and positive integer is the same, there are two possible solutions.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.

The values that result from multiplying an integer by itself are known as square numbers. Among the attributes are:

When we multiply 4 with 4 we get 16 again

when we multiply (-4) with (-4) we get 16. so 16 has 2 square root.

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The expression representing the height of the box is the difference between the length and width of the box, which is equal to x subtracting two, or x – 1.

The expression representing the height of the box can be determined by subtracting the width of the box from the length. The length of the box is x 6, and the width is x – 2. To calculate the height, we subtract the width from the length: x – (x – 2) = x – x + 2 = 2. Therefore, the expression representing the height of the box is x – 1. This indicates that the height of the box is equal to the length of the box minus one. This calculation can be applied to any rectangular prism to calculate the height.The volume of the box is represented by the function f(x) = x3 5x2 – 8x – 12. To calculate the volume, we can substitute the length and width into the function:

f(x) = (x – 6)(x – 2)(x – 1) = x3 – 8x2 + 11x – 12.

Therefore, the volume of the box is x3 – 8x2 + 11x – 12.

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Answer:

3,4,5,6,7.

Step-by-step explanation:

if yk, yk

Using the concept of proportions, the 20 feet pole will cast an 8ft shadow

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

In this problem, we can find the length of the shadow casted if we write a proportional relationship between the two object.

50 / 20 = 20 / x

Cross multiply both sides and solve for x

50 × x = 20 × 20

50x = 400

x = 400 / 50

x = 8

The shadow  is 8ft

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Either Pythagorean Theorem or the Law of Cosines is used to solve for y in a triangle, you can use either of these equations.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of the triangle is equal to the square of the longest side. This is written as:

                                            a2 + b2 = c2,

where a and b are the lengths of the two shorter sides, and c is the length of the longest side. In this equation, y is the length of the longest side.

The Law of Cosines states that:

                                          a2 = b2 + c2 - 2bc cos A

where A is the angle opposite side a. In this equation, y is side a.

Therefore, to solve for y in a triangle, you can use either the Pythagorean Theorem or the Law of Cosines, depending on the information given.

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The graph of quadratic inequality when plotted represents the parabola.

The quadratic inequality will have a range of solutions, unlike the quadratic equation.

The quadratic inequality could be solved using factorization method for example

The quadratic inequality x²+6x+5 ≤0 can be solved by factorizing but instead of two solutions, there are a range of solutions.

For given equation we need to calculate value of x such that the graph is less than zero.

Hence solution to this inequality can be written as

−5≤x≤−1.

And the graph of given quadratic inequality represents the parabola.

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The complete table for the pie chart is;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            198

Comedy                         5                            90

From the given table used to form the pie chart, we see that;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            

Comedy                         5

We know that the angles in a circle is equal to 360 degrees. Thus;

Angle composed of horror and comedy = 360 - 72 = 288°

Thus;

Angle for horror film = (11/(4 + 11 + 5)) * 360°

= (11/20) * 360°

= 198°

Thus;

Angle for comedy = 288° - 198° = 90°

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Any equation that does not contain a discontinuity, defined as a point where the graph of the equation has a sudden break or jump, is considered continuous. Examples of continuous equations include linear equations, polynomial equations, and exponential equations.

Continuity is an important concept in mathematics and related disciplines. A continuous equation is defined as any equation that does not contain a discontinuity, which is a point where the graph of the equation has a sudden break or jump. Discontinuous equations are equations with discontinuities that cause the graph of the equation to have sudden jumps or breaks. Linear equations, polynomial equations, and exponential equations are all examples of continuous equations, since they do not contain any discontinuities. Continuous equations are important because they are used in many areas of mathematics, such as calculus, to solve problems and understand the behavior of certain function

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Using basic geometry and area formula for calculation of length, Apply fencing on only 3 side , The answer is 109.54 feet.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Area of rectangle is:

A= l x b

area=750 square feet.

for attaining minimum area , these area must be fitted in square,

so, [tex]l = \sqrt {750}[/tex]

=27.38 feet

since, one side is taken by barn, l should be extended 4 times, 2 on 1 side and 2 on sides each.

Total length of fence = 4 * 27.38

= 109.54 feet

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Answer:

To find (g o f)(3), we need to first apply f to 3, which gives us f(3) = 3 * 3 - 2 = 7. Then we need to apply g to the result of f(3), which gives us g(7) = 7^2 = 49. Therefore, (g o f)(3) = 49, so the answer is c.

Step-by-step explanation:

Answer:

64, 2

Step-by-step explanation:

By simplifying [tex]\sqrt{75a^{8}b^{5} }[/tex], we get 5[tex]a^{4} b^{2}[/tex][tex]\sqrt{3b}[/tex].

What is square root?

A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root.

How to find square root?

[tex]\sqrt{75a^{8}b^{5} } =\sqrt{25*3*a^{4}*a^{4}* b^{2} *b^{2}*b }[/tex]

             =[tex]\sqrt{5*5*3*a^{2}*a^{2}*a^{2}*a^{2}*b^{2}*b^{2}*b }[/tex]

             =5×a×a×a×a×b×b[tex]\sqrt{3*b}[/tex]

             =5[tex]a^{4}b^{2}[/tex][tex]\sqrt{3b}[/tex]

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The formula used to calculate the solving the volume of the rectangular prism is equal to ( length × width × height ).

As given in the question,

Given base of the prism is rectangular in shape ,

Area of the base with rectangular base is given by :

area of the rectangle = length × width

Volume of the rectangular prism = base area × height

⇒Volume of the rectangular prism = ( length × width ) × height

Therefore, the formula required to calculate the volume of the rectangular prism is given by ( length × width × height ).

The above question is incomplete , the complete question is:

What is the formula in solving volume of the rectangular prism?

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The given content is an example of sweepstakes.

What is a sweepstake?

A sweepstake is a type of contest in which a prize or prizes are given to the winner or winners. Sweepstakes began as a type of lottery tied to the sale of a product. Sweepstakes became strictly "No purchase necessary to enter or win" and "A purchase will not increase your chances of winning" under these laws, especially because many sweepstakes companies skirted the law by stating only "no purchase necessary to enter," removing the consideration (one of the three legally required elements of gambling) to prevent sweepstakes abuse.

Based on the above definition,

we can conclude that the given question is an example of a sweepstake.

Hence, this is an example of sweepstakes.

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Answer:

X=log 3.2/5 log 21

Step-by-step explanation:

X=0.0764094

Numbers approach negative infinity as they move left on the number line and positive infinity as they move right on the number line. Negative infinity is always less than any number, positive infinity is always greater than any number.

Main Difference:

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Positive curve graphs will be upward-sloping.

Negative curve graphs will be downward-sloping.

Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.

In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

The pair of equations y = -3 and y = 0 have No Solution .

The pair of equations is given as y = 0 and y = -3 .

In order to find number of solutions of the equations ,

we use the graphical method ,

the graph of the equation y = 0 is x axis .

and the graph of the equation y = -3 is a straight line that is parallel to the x axis , as shown in the figure below .

From the graph drawn below , we can see that the two lines are parallel and

We know that , when two lines are parallel they have No Solution .

Therefore , given pair equations have No Solution .

The given question is incomplete , the complete question is

How many solutions does a pair of equations y = -3 and y = 0 has ?

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Answer: i think c or d

Step-by-step explanation:

Answer:

the answer would be D

Step-by-step explanation:

The value of the game would be 13.33 dollars.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Value of the game = E(x)

                               [tex]= [(60\times\frac{5}{6}) + (-10\times\frac{1}{6})]\\\\=50 -1.66\\\\= 48.33[/tex]

P(Plain surface) = 2/6 and

P(Not plain surface) = 1 - 2/6 = 2/3

Let x: Value won/lost in the game

Value of the game

                          [tex]= [(60\times\frac{2}{6}) + (-10\times\frac{2}{3})]\\\\=20 -6.66\\\\= 13.33[/tex]

Hence, the value of the game would be 13.33 dollars.

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Answer:

2x² - 20x - 32 = 0

Step-by-step explanation:

Trip upstream:

distance = 10 km

time = t

current = 4 km/h

speed of boat in still water = x

speed upstream: x - 4

speed = distance/time

distance = speed × time

10 = (x - 4) × t

10 = tx - 4t

t(x - 4) = 10

t = 10/(x - 4)

Trip downstream:

Distance = 10 km

time = 2 - t

current = 4 km/h

speed downstream = x + 4

speed = distance/time

distance = speed × time

10 = (x + 4) × (2 - t)

10 = 2x - tx + 8 - 4t

10 = 2x - 10x/(x - 4) + 8 - 40/(x - 4)

10(x - 4) = 2x(x - 4) - 10x + 8(x - 4) - 40

10x - 40 = 2x² - 8x - 10x + 8x - 32 - 40

2x² - 20x - 32 = 0

We simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.

The collection of all potential inputs for a function is its domain.

For instance, the domain of f(x)=x² and g(x)=1/x are all real integers with the exception of x=0.

The set of numbers x for which a function has a valid definition is known as its domain.

A closed interval is referred to as a function's domain if it is specified over the interval a ≤ x ≤ b.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x).

Simply put, x=g(y) will calculate the function's range after we identify g(y).

Therefore, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.

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Answer:

No

Step-by-step explanation:

5+10<17

All equilateral triangles are similar.

In an equilateral triangle, all the lengths of the sides are equal.

In such a case, each of the interior angles will have a measure of 60°

Since the angles of an equilateral triangle are the same, it is also known as an equiangular triangle.

A property of equilateral triangles includes that all of their angles are equal to 60°

The AAA Triangle Similarity Postulate asserts that if all of the angles in a triangle are equal to the corresponding angles in another triangle, then those two triangles are equal.

Since every equilateral triangle’s angles are, 60°every equilateral triangle is similar to one another due to this AAA Postulate.

=> For congruence of triangles, we need equal sides for two equilateral triangles, but here it has said nothing about sides of both triangles in Congruent. So, this is incorrect. Here, it can be said that all equilateral triangles are similar.

Hence, all equilateral triangles are similar.

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The rational root theorem is the required to represents rational root or zeros or the solution of the given polynomial function with example: g(x) = 4x² - 4x + 1.

As given in the question,

Therefore, the rational root theorem is the required to find the rational root or the solution or the zero of the polynomial function.

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