A circular mirror has a radius of 14 inches. What is the area of the mirror? Use 3.14 for π (pi). Round to the nearest tenth.

The equivalent expression is (3⁴/7³)³ = 3¹²/7⁹

Define Power Rule for Exponents

The Power Rule for Exponents:  (aⁿ)ˣ= aⁿ*ˣ .

To raise a number with an exponent to a power, multiply the exponent times the power.

Negative Exponent Rule: x⁻ⁿ = 1/xⁿ.

Given expression is,

(3⁴/7³)³

We need to find equivalent expression,

⇒ (3⁴/7³)³

first, split up exponent 3 to both Numerator and denominator as ,

⇒ (3⁴)³ / (7³)³

Now, power of a power can be done as product as,

⇒ 3¹² / 7⁹

Hence,the equivalent expression is (3⁴/7³)³ = 3¹²/7⁹

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The graph of the given function is attached below.

What is a absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x > 0 and f(x) = -x if x 0.

Given function is g(x)= - 2|x -5|-4.

Finding some points on the graph:

Putting x = 5

g(5)= - 2|5 -5|-4

g(5) = -4

Putting x = 0

g(0)= - 2|0-5|-4

g(0) = -2 ×5 - 4

g(0) = -14

Putting x = 10

g(10)= - 2|10 -5|-4

g(10) = -2 ×5 - 4

g(10) = -14

The points on the graph are ( 5,-4), (0,-14), (10,-14).

Plot the points and joint them.

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Answer:

-3/2

Step-by-step explanation:

Let's call the number we're trying to find "x". When we double x and then subtract 3, we get 2x-3. The statement says that this is the same as if we had quadrupled x, which would be 4x. We can set these two expressions equal to each other to create an equation:

2x - 3 = 4x

We can solve this equation by first adding 3 to both sides to get rid of the negative number:

2x - 3 + 3 = 4x + 3

This simplifies to:

2x = 4x + 3

We can now subtract 4x from both sides to get rid of the 4x term:

2x - 4x = 4x + 3 - 4x

This simplifies to:

-2x = 3

Finally, we can divide both sides by -2 to solve for x:

(-2x) / (-2) = 3 / (-2)

This simplifies to:

x = -3/2

Therefore, the number we were trying to find is -3/2.

Answer:

Let's call the number we're trying to find "x". If we double x and then subtract 3, we get the expression 2x - 3. If we quadruple x instead, we get the expression 4x. We are looking for a value of x that makes these two expressions equal, so we can set them equal to each other and solve for x:

2x - 3 = 4x

To solve this equation, we can first combine like terms on each side by adding 3 to both sides and then dividing both sides by 2:

2x - 3 + 3 = 4x + 3

2x = 4x + 3

Combining like terms on the left side gives us:

2x - 4x = 4x + 3 - 4x

0 = 3

This equation is clearly false, since no value of x can make 0 equal to 3. Therefore, there is no solution to this problem, and the original number cannot be determined.

In general, if you are trying to solve a problem involving algebraic equations and you end up with a false equation (like 0 = 3 in this case), it means that there is no solution to the problem. This can happen for a variety of reasons, but in this case it is because the original problem statement was not possible or did not make sense.

Step-by-step explanation:

To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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The set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.

You must take the following actions to determine the standard deviation of a set of observations:

Mean: (32 + 28 + 29 + 30 + 31) / 5 = 30

Deviations: 32 minus 30 = 2, 28 minus 30 = 2, 29 minus 30 = 1, 30 minus 30 = 1, etc.

Squared deviations are as follows: 22 = 4, (-2)2 = 4, (-1)2 = 1, and 02 = 0.

Sum of squared deviations: (Sum of squared deviations) / (number of observations) = 10 / 5 = 2

Standard deviation is square root of sum of squared deviation.

so, [tex]\sqrt{2}[/tex] is 1.41.

As a result, the set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.

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Answer:

There isn't enough information to solve for x.

Step-by-step explanation:

The way the statement of similarity is written, we get this proportion:

TY/CH = TL/CK = YL/HK

Replace segment names with lengths:

TY/10 = 25/CK = (4x - 1)/(x + 5)

There isn't enough information to solve for x.

Answer:

u =10 v=13

in order in order for the triangles to be congruent the sites with vehicle in this case if the you equals to 10 in the both sides then the sides opposite to the right angle will be equal and if the is equal to 13 it will mean that the sides along with the right angle would be equal which makes a triangle congruent

Answer:

$12

Step-by-step explanation:

given:

Stefan sells jin a bicycle for $114 and a helmet for $18.

we're gonna add to get the total cost 114 + 18 = $132

The total cost is 110% of what he spent originally to buy the bike and helmet.

divide 110% by 100 to get the answer in decimal which if you calculate is 1.1

now we're gonna make a simple equation and assume what Stefan spends originally is x

1.1 * x = 132

1.1x = 132

(now we want x to be alone so we can find its value so divide both sides by 1.1 (division is the opposite of multiplication if, for example, we have 1.1 - x   1.1 is positive so take it to the other side it'll be negative))

after dividing x=120

therefore, he originally spent $120

and to find how much money Stefan made we're gonna subtract 132-120 = $12

Stefan made $12

Yes, it is generally considered appropriate for a 12-year-old to learn algebra. Algebra is a branch of mathematics that involves working with variables and equations to solve problems. It is usually introduced to students in middle school or junior high school, which is around the age of 12 or 13.

According to studies, depending on the teaching technique and intellectual maturity: between 5 and 13. Algebra is a theoretical algebra with fewer techniques for demonstrating tangible lessons.

A youngster who develops abstract comprehension at a young age might learn extremely quickly, but a pupil who has difficulties with abstract notions may struggle well into their adolescence.

It is crucial to recognize that each student learns at a different rate and may have distinct arithmetic talents and weaknesses. It is critical that students receive the necessary support and adjustments in order to study algebra and excel in their math studies.

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An object is moved rigidly when it is transferred from one location to another without affecting its size or shape.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

An object is moved rigidly when it is transferred from one location to another without affecting its size or shape. Only a precise movement may generate a correspondence between two forms, and only then can two shapes match.

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Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]

When the vector of constants to the right of the equals sign is not zero, an equation system is said to be non-homogeneous. A broad description of the solutions to a non-homogeneous system is presented in this solution.

General solution for the equation: [tex]y''-y'=t[/tex] , [tex]yp(t)=-t[/tex]

Consider the equation [tex]y''-y'=t[/tex]. The corresponding homogeneous equation has the associated auxiliary equation  [tex]r^2-1=0[/tex] which has [tex]r= -1[/tex]  and [tex]r=1[/tex]  as solutions.

The solution of an n[tex]^{th}[/tex]-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.

Hence the general solution for a homogeneous equation is [tex]y(t)=-t+c_{1}e^t+c_{2}e^-t[/tex]

Combining the general solution [tex]y(t) = c_{1}e^t+c_{2}e^t[/tex] of  [tex]y"-y'=0[/tex]  with the particular solution [tex]y_{p}(t)=-t[/tex] of [tex]y"-y'=t[/tex], we find that the general solution to [tex]y"-y'=t[/tex]  is  [tex]y(t)=c_{1}e^-t+c_{2}e^t-t[/tex]

The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]

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Answer:

Equations of parallel and perpendicular lines The equation of a straight line is represented as \ (y=ax+b\) which defines the slope and the \ (y\)-intercept. Here \ (a\) represents the slope of the line. Since two parallel lines never intersect and have the same slope, their slope is always equal.

Step-by-step explanation:

Answer: 12 m

Step-by-step explanation:

The multiplicative rate of change of the exponential function represented in the table is given as follows:

1.5.

For an exponential function, when x is increased by one, the output variable y is multiplied by a constant, called multiplicative rate of change of the exponential function.

Then, given a table of values, the rate of change is obtained by the division of two outputs(output with the greater input divided by output with the smaller input) when their inputs have a difference of 1.

Thus, for the table, the rate of change is obtained as follows:

6.75/4.5 = 1.5.

(the difference of the inputs is of 2 - 1 = 1).

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Answer: One solution

Step-by-step explanation:

We can solve this question using Linear equations . The answer for the question is Option B.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

So in the given question the motorboat is 55 km from the shore.

  SO y =55 when x=0

  where y is the distance and x is time.

   after 12 minutes it is 19km from the sea shore.

  So y=-3x +55 is the equation.

We can solve this question using Linear equations . The answer for the question is Option B.

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Answer:

Domain:

[tex]0 \leqslant x \leqslant 4[/tex]

Range:

[tex]0 \leqslant x \leqslant 64[/tex]

Answer:

  b)  process b

Step-by-step explanation:

You have 2 of machine A, each of which can do its process in 1 minute; 1 of machine B, which takes 2 minutes to do its process; and 3 of machine C, each of which takes 3 minutes to do its process.

In 6 minutes, the 2 of machine A can produce 2 × 6/1 = 12 units.

In 6 minutes, the 1 of machine B can produce 1 × 6/2 = 3 units.

In 6 minutes, the 3 of machine C can produce 3 × 6/3 = 6 units.

Process B produces the fewest units in equivalent time, so process b is the bottleneck.

__

Additional comment

The production quantity of a given machine is ...

  (production time)/(time/unit) = units

This will be multiplied by the number of machines doing the process.

For comparison purposes, we used a production time of 6 minutes here.

A point in mathematics is symbolised by a dot (.) and used to indicate an accurate location in space. It lacks all three dimensions—length, breadth, and height. It has no size, in other terms.

Different Points

In geometry, there are several distinct kinds of points:

Converging Points

Collinear refers to something that is parallel. If three or more points lie on a single straight line, they are said to be collinear.

Incongruent Points

If three or more points do not lie on the same line, they are said to be non-collinear. There isn't a single straight line that can be drawn that goes through each of these points.

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The interpretation of the x-intercept in the context of the given problem is: B. After 16 months, the business will have $0 remaining in their technology budget.

To find the x-intercept of an equation, substitute the value of y = 0, and solve for x. It is the value of x when y or the output = 0.

Given the equation, T(x) = −135x + 2160, where T(x) is the amount of money remaining in the budget for technology, and x is the number of months, the x-intercept would be the number of months that the business will have $0 in their budget for technology.

To find the x-intercept, substitute T(x) = 0, into T(x) = −135x + 2160:

0 = −135x + 2160

135x = 2160

Divide both sides by 135

135x/135 = 2160/135

x = 16

This means after 16 months, the technology budget that the company will have remaining is $0.

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A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .

A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.

Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.

In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.

A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).

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(4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .

What does greater than (>) mean ?

Greater than means that the variable or number is more than the given limit. On the other hand, greater than or equal to states that the number or variable is either equal to or more than the given limit. The greater-than symbol is represented as >, whereas the greater than or equal to sign is represented as ≥.

Given :

(4,3)

(4,4)

(0,-4)

(4,3.9)

(0,0)

Since , all the ordered pairs are in the (x,y) form , we can clearly see that (4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .

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Answer: The first one is correct

Step-by-step explanation: 4x(-2)=-8; The car used 8 gallons of gasoline.

Answer:

Step-by-step explanation:

A direct variation is a linear relationship between variables so they have a constant ratio. It is a special case of the slope-intercept form y =mx +b, where b = 0.

The set of all the real numbers are written as R.

The term set in set theory can be written as the well-defined collection of objects called elements or members of the set.

Here we have to find the way to write all real numbers.

Here we have considered that all the real numbers are collectively put on to the set.

And the set that contain all the real numbers are called R.

We all know that the real number contain all the number like negative , positive numbers.

So, Here we consider that if the domain of a function is all real numbers, then here we can represent this using interval notation as (−∞,∞).

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Using the concept of functions option A [tex](f-g)(y)=2y^{2}-3y-1[/tex] is true by solving both the functions f(y) and g(y).

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. A relation f between a set A (the function's domain) and a set B is how a function is defined in mathematics (its co-domain). For any A and B, f = {(a, b) | for all a ∈ A, b ∈ B}

According to the given question we have given two functions f (y) and g (y), then:

(f - g) (y)=f(y)-g(y)

We have:

[tex]f(x)=5y^{2} -2y+1[/tex]

[tex]g(y)=-3y^{2}-y-2[/tex]

Subtracting both the above functions we have:

[tex](f-g)(y)=2y^{2}-3y-1[/tex]

Hence option A [tex](f-g)(y)=2y^{2}-3y-1[/tex] is true by using the concept of functions.

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