If the area of an isosceles right triangle is 72, find the length of the hypotenuse.

When the operation is defined on the set of R by a*b-1, it is commutative rather than associative.

In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations. Algebra is used in many equations. When it comes to arithmetic, algebra is used when it's difficult to compute an exact amount.

Given,

a∗b=1+ab,∀a,b∈R

Commutativity a∗b=1+ab

=1+b.a

=b∗a

∵ Set of real numbers is commutative.

So, a∗b=b∗a

∴ is commutative Associativity (a∗b)∗c=(1+ab)∗c

=(1+ab)c

=2+abc

a∗(b∗c)=a∗(1+bc)=1+a∗(a+bc)

=1+a+abc

It is clear that (a∗b)∗c

=a∗(b∗c)

So, * operation is not associative.

So, option (a) is correct.

When the operation is defined on the set of R by a*b-1, it is commutative rather than associative.

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Answer:

1. Convert to decimal notationThe exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times: 4.0

 2. Final result

0.004

Answer:

0.444

9/20.25=0.444

Answer:

Step-by-step explanation:

The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.

The number 1 in exponential form can be written as 1 itself , because 1 is the base and the "number 1" to the exponent of any number will be 1 only .

What is Exponential Form?

The exponential Form of representation is a way of representing the repeated multiplication which involves base and exponents.

For Example : if 3 is multiplied 2 times ,then the exponential form will be [tex]3^{2}[/tex] ;

we have to write the exponential form of the number 1 ;

So , the base of the number is 1 , let x be the exponent ,

So , the exponential form will be ⇒ [tex]1^{x}[/tex] , on substituting any value in x , we will always get the result as 1 .

Therefore , the exponential form of the number 1 is 1 .

The given question is incomplete , the complete question is

How do you write the number 1 in exponential form ?

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To find the ordered pair (x, f(x)) of a function, you must first know the function's equation. The ordered pair is a combination of the input value (x) and the output value (f(x)) of the function.

Here are the steps to find the ordered pair of a function:

f(4) = 2(4) + 3 = 8 + 3 = 11

It's important to note that the ordered pair will be different for every input value (x) you substitute into the function's equation.

For instance, if you want the ordered pair of f(x) = 2x + 3 for x = 5 you will have (5,13) as an ordered pair.

It's also worth mentioning that in some cases you might have functions like[tex]f(x) = (x-2)^2 + 1[/tex], you can use the same process but you will be solving the equation rather than just substituting it.

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A mall city had 5000 population of people in 2005 and 6200 in 2010, then the value of k is,

k = Log( [tex]\frac{\frac{Q(t)}{5000} }{t*log(e)}[/tex] )  ,  k = Log ( [tex]\frac{\frac{Q(t)}{6200} }{t*log(e)}[/tex] )

The value of t corresponds to the last two digits in the year.  

If t=0 represents the year 2000, then

For the year 2005,

t = 5

For the year 2010,

t = 10

First part of the problem.  

Find the value of k using these values.

Q(t) = 5000

t = 5

Q(t) = Qo[tex]e^{kt}[/tex]

Q(t) = 5000[tex]e^{kt}[/tex]

k is an exponential value.  When we solve for an exponential value, we must use logarithms.

First, divide both sides of equation by 5000

[tex]\frac{Q(t)}{5000}[/tex] = [tex]e^{kt}[/tex]

log both sides of the equation.

log(  [tex]\frac{Q(t)}{5000}[/tex] ) = log ([tex]e^{kt}[/tex] )

Next, bring the exponents down as the coefficients of the log.

log(  [tex]\frac{Q(t)}{5000}[/tex] ) = kt * log(e)

Divide by t*Log(e) both sides of equation to obtain k.

Log( [tex]\frac{\frac{Q(t)}{5000} }{t*log(e)}[/tex] )  = k

Now, plug in the values.

Second part of problem.  Find P using these values.

t = 10

Q(t) = Qo[tex]e^{kt}[/tex]

Q(t) = 6200[tex]e^{kt}[/tex]

k is an exponential value.  When we solve for an exponential value, we must use logarithms.

First, divide both sides of equation by 6200

[tex]\frac{Q(t)}{6200}[/tex] = [tex]e^{kt}[/tex]

log both sides of the equation.

log( [tex]\frac{Q(t)}{6200}[/tex] ) = log ([tex]e^{kt}[/tex] )

Next, bring the exponents down as the coefficients of the log.

log( [tex]\frac{Q(t)}{6200}[/tex] ) = kt * log(e)

Divide by t*Log(e) both sides of equation to obtain k.

Log ( [tex]\frac{\frac{Q(t)}{6200} }{t*log(e)}[/tex] ) = k

Now, plug in the values.

Therefore,

A mall city had 5000 population of people in 2005 and 6200 in 2010, then the value of k is,

k = Log( [tex]\frac{\frac{Q(t)}{5000} }{t*log(e)}[/tex] )  ,  k = Log ( [tex]\frac{\frac{Q(t)}{6200} }{t*log(e)}[/tex] )

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We use Section formula for internal division: P(x, y) = x = (m₁x₂ + m₂x₁)/(m₁+ m₂) and y = (m₁y₂ + m₂y₁)/(m₁+ m₂).

Section formula for external division: P(x, y) = x = ((m₁x₂ - m₂x₁)/(m₁+ m₂) , y = (m₁y₂ - m₂y₁)/(m₁+ m₂).

What is the section formula?

In coordinate geometry, the Section formula is used to determine the internal or external ratio at which a line segment is divided by a point. It is used to determine a triangle's centroid, incenter, and excenter. It is employed in physics to identify equilibrium locations, system centers of mass, etc.

Here,

We have to find the use of the section formula.

we concluded that the section formula is used for internal division: P(x, y) = x = (m₁x₂ + m₂x₁)/(m₁+ m₂) and y = (m₁y₂ + m₂y₁)/(m₁+ m₂).

Section formula for external division: P(x, y) = x = ((m₁x₂ - m₂x₁)/(m₁+ m₂) , y = (m₁y₂ - m₂y₁)/(m₁+ m₂).

Hence, the section formula is x = (m₁x₂ + m₂x₁)/(m₁+ m₂) and y = (m₁y₂ + m₂y₁)/(m₁+ m₂).

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The absolute value f(x)=6|x| function as a piecewise-defined function is:

f(x) = { 6x, if x ≥ 0

        { -6x, if x < 0

A piecewise-defined function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

Each sub-function is defined by a separate piece of the overall function, and together they define the entire domain of the function. The sub-functions are typically separated by breakpoints, which are values of the input variable at which the sub-functions change.

|x| can either be -x or x. Thus, the absolute value function f(x) = 6|x|  can be written as:

f(x)= 6x or f(x)= -6x

Therefore, the piecewise-defined function of f(x) = 6|x| will be:

f(x) = { 6x, if x ≥ 0

        { -6x, if x < 0

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If a set of data has a normal distribution with a mean of 50 and a standard deviation of 8. the percent of data within the interval less than 50 is; C. 50%.

Based on the details given the percent of data within the interval less than 50 is not 34% or 68% or 97.5% but rather the percent of data  is 50%.

The reason why it is 50% is that  the mean is 50 in which the data has a normal distribution, 50 is the center of the distribution.  Based on this half the data falls above the mean and half the data falls below the mean.

Therefore the correct option is C.

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i) The mean of x is 68.33 grams.

ii) The standard deviation of x is 2.23 grams.

A standard deviation or (σ ) is a measurement of the data's dispersion from the mean. A low standard deviation indicates that data are concentrated around the mean, whereas a high standard deviation shows that data are more dispersed.

If the standard deviation is close to zero, the data points are close to the mean; otherwise, if the standard deviation is high or low, the data points are, respectively, above or below the mean.

i) Properties of expected values establish that

[tex]$\mathrm{E}(W)=\mathrm{E}(P)+\mathrm{E}\left(X_1\right)+\ldots+\mathrm{E}\left(X_{12}\right)$[/tex]

Because all 12 eggs have the same mean weight, this becomes

[tex]$\mathrm{E}(W)=\mathrm{E}(P)+12 \times \mathrm{E}\left(X_i\right)$[/tex]

We were told that

[tex]$\mathrm{E}(W)=840$ and $\mathrm{E}(P)=20$, so we can solve[/tex]

[tex]$840=20+12 \times \mathrm{E}\left(X_i\right)$ to find $\mathrm{E}\left(X_i\right)=\frac{840-20}{12} \approx 68.33$ grams.[/tex]

ii) Because of independence, properties of variance establish that

[tex]$${Var}(W)={Var}(P)+{Var}\left(X_1\right)+{Var}\left(X_2\right)+\ldots+{Var}\left(X_{12}\right)$$[/tex]

Because all 12 eggs have the same variance of their weights, this becomes

[tex]${Var}(W)={Var}(P)+12 \times {Var}\left(X_i\right)$[/tex]

We were told that

[tex]${SD}(W)=7.9\ \text {and}\ {SD}(P)=1.7$ Therefore, ${Var}(W)=(7.9)^2=62.41$ and ${Var}(P)=(1.7)^2=2.89$[/tex]

We can solve

[tex]$ 62.41=2.89+12 \times {Var}\left(X_i\right)$[/tex]

To find

[tex]${Var}\left(X_i\right)=\frac{62.41-2.89}{12}=4.96$[/tex]

Thus, SD[tex](X_i\right))=\sqrt{(4.96)} \approx[/tex] 2.23 grams.

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2.5 miles Han run after a half hour

it will take 1[tex]\frac{1}{9}[/tex] to meet both

Given that

At 10:00 a. M. , Han and Tyler both tarted running toward each other from opposite end of a 10-mile path along a river.

Han run at a pace of 12 minute per mile.

Tyler run at a pace of 15 minute per mile.

We can say that he is capable of running at a pace of 5 mph. (Since speed is equal to 1/pace, and 12 minutes equal 1 mile and 60 minutes equal 5 miles),

Similar to this, Tyler would run at a speed of 4 miles per hour if he ran a mile at a pace of 15 minutes.

distance = speed * time

The distance covered by Han in half an hour = 1/2 × 5 = 2.5 miles

the time at which Han and tyler will meet,

T= Total distance/ ( the sum of their speed)

T = 10/5+4 = 10/9

T = 1[tex]\frac{1}{9}[/tex] hours is greater than 1 hour

so, they will not meet within 1 hour

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There are several ways to calculate the slope of a line, but the most common ways are:

Rise over Run: This is the most basic and intuitive way to calculate slope. It involves taking the difference in the y-coordinates (rise) and dividing it by the difference in the x-coordinates (run) between two points on the line. The slope is represented by the letter "m" and can be calculated using the following formula: m = (y2 - y1) / (x2 - x1)

For example, if two points on a line are (3,6) and (6,9) the slope can be calculated as: m = (9-6) / (6-3) = 3/3 = 1

Point-Slope Form: This method uses the coordinates of a single point on the line and the slope of the line to find the equation of the line. The slope is represented by the letter "m" and the point by the coordinates (x1, y1). The equation of the line in point-slope form is: y - y1 = m(x - x1)

Slope-Intercept Form: This method expresses the equation of a line in the form of y = mx + b, where m is the slope and b is the y-intercept. To find the slope-intercept form, you need to know the slope and the y-intercept (the point where the line crosses the y-axis) of the line.

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The maximum number of shirts in each row is 14 shirts. The result is obtained by finding the greatest common factor.

The GFC can be found by using factor trees. We will get prime factorization to determine the GFC. Here are the steps.

A salesclerk is displaying 14 polo shirts and 56 team shirts. In each row, there are only one type of shirt. Find the maximum number of shirts in each row so that the length of all rows are equal!

To make the length of all rows equal, we should find the GFC of two kinds of shirts. That would be the maximum number of shirts.

See the factor trees illustration in the attachment!

The prime factorization

The common factors are 2 and 7.

The greatest common factor is

= 2 × 7

= 14

Hence, the shirts displayed would be a maximum of 14 shirts in each row.

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A function's domain is the set of all possible inputs to the function. Domains can be limited if the function is rational and the denominator is 0 for some x value or values.

What are the 3 domain restrictions?

The square root function, log function, and reciprocal function are the three functions with limited domains. Because you cannot take square roots of negative numbers and produce real numbers, the square root function has a limited domain.

To find the domain restriction of an expression, take the expression's denominator. Put that denominator to zero. Solve the resulting equation for the denominator zeroes. The domain consists of all other x-values.

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Answer:

The Last Answer

Step-by-step explanation:

Process of elimination

He wants AT LEAST which means that is will be a less than symbol with a line under it, the last one is the only one with that!

We know that Ron's estimate for the number of messages he sent that day was 40% more than the actual number of messages he sent. To find out how many messages he estimated he sent, we need to undo this percentage increase.

If the actual number of messages Ron sent was 25, and his estimate was 40% more than that, we can use the following equation:

Estimated number of messages = Actual number of messages + (Actual number of messages * 40%)

We can then substitute in the known values and solve for the estimated number of messages:

Estimated number of messages = 25 + (25 * 40%)

Estimated number of messages = 25 + (25 * 0.4)

Estimated number of messages = 25 + 10

Estimated number of messages = 35

Therefore, Ron estimated that he sent 35 messages that day.

It is normal for the cervix to dilate during labor. The cervix opens when there is dilatation. The cervix may begin to shrink or stretch (efface) and open as labor approaches (dilate).

As a result, the cervix is ready for the baby to enter the delivery canal (vagina). Each woman's cervix thins and opens at a different rate. The cervix may begin to slowly efface and dilate over a few weeks in certain women. On the other hand, a first-time mother frequently won't dilate until active labor begins.

Your doctor may use his or her fingers to feel the cervix toward the end of your pregnancy to see how much it has effaced and dilated. To do this, he or she will put on sterile gloves. Your cervix opens (dilates) as your uterus contracts during labor. They also assist in positioning the infant for birth.

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The measure of the arc QP is QP = 66°.

What is inscribed angle?

In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.

Given:

m ∠ RPQ = 57°

We have to find the measure of the arc QP.

Since,

RQ = 2*m ∠RPQ

RQ = 2*(57°)

RQ = 114°

Let

 RP = RQ + QP

180° = 114° + QP

 QP = 180° - 114°

 QP = 66°

Hence, the measure of the arc QP is QP = 66°.

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A) Leaving home in a car and going to a store, shopping for a while, and then coming back home (the direction of the store is positive) figure 2.

B) Rolling a marble down the stairs (the bottom of the stairs is the origin)  figure 6.

C) Rolling a marble towards a table (the direction from which the marble came was the negative direction). figure 1.

The graphs are extremely helpful and widely used data structures. They are applied to a wide range of object relationships and, in reality, are applicable to almost everything.

The graphs represent a generalised structure that allows for the modelling of a very broad range of real-world situations, as we shall see in more detail. Trees are a subset of graphs, and lists are special cases of both trees and thus of graphs.

Since graphs are frequently used in practise, there has been a great deal of research into "graph theory," where there are many known problems for graphs and many well-known solutions to them.

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Casey would pay the same amount to be a member of either gym in 6 months and that amount would be 360 dollars, that is $360.

Let the number of months be x.

In the 1st gym there is a $150 joining fee and cost $35 per month. So after x months the total cost in dollars in first gym is

= 150 + 35x

In the 2nd gym there is no joining fee and cost $60 per month. So after x months the total cost in dollars in second gym is

= 60x

When Casey pay the same amount to be a member of either gym, the total cost of the gym would be equal

150 + 35x = 60x

25x = 150

Dividing by 25

x = 6

The amount she pay to be a member of either gym when there is same amount is

= 60×6

= 360

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Answer: The unit rate is the number of cars washed per minute. To find the unit rate, we need to divide the number of cars washed by the number of minutes.

3 cars / 27 minutes = 1/9 car/minute

To express the unit rate as a shaded fraction of a circle, we can divide the circle into 9 equal parts and shade 1 of those parts to represent the unit rate of 1/9 car/minute.

It is not possible to provide a shaded fraction of a circle here as it is a text based interface.

Step-by-step explanation:

The claim about the function that is false is At x = 1 and x = -1, respectively, the function has a local minimum and a local maximum.

what is function ?

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

Let y=x^x

⇒ dx/dy =x ^x (1+logx)

For increasing function,  dx/dy >0

⇒x ^x (1+logx)>0

⇒1+logx>0

⇒log e

x>log e/e

⇒x> 1/e

Therefore, the function is increasing, when x> 1/e

The claim about the function that is false is At x = 1 and x = -1, respectively, the function has a local minimum and a local maximum.

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According to the condition given in the question that the basket contains red balls and yellow balls weighing 4300 g, the total number of yellow balls in the basket  would be 55.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols, including solving equations and analyzing graphs

An equation is a statement of equality between two expressions, while an expression is a combination of numbers, variables, and mathematical operations. An equation is something that can be solved to find the value of the unknown, while an expression is a combination of numbers and operations that stands on its own.

Let there are R red balls and Y yellow balls in the basket,

As given in the question, each red ball weighs 35 g and each yellow ball weighs 40g, and the total weight of basket is 4300 g,

so, 35 * R + 40 * Y = 4300

Also, there are 60 red balls in the basket , so R =60,

35 * 60 + 40 * Y = 4300

therefore, Y = 55

Hence there are 55 yellow balls in the basket.

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Answer:

No picture is shown?

Step-by-step explanation:

Answer: i think i did it

Step-by-step explanation:

So on solving the provided question, we can say that Area of rectangle, A = 3x*x => x = 5

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here, length is 3 times breadth

so let length = x

breadth = 3x

Area of rectangle, A = 3x*x

A = 3x^2

75 = 3x^2

x = 5

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Answer:

y = 9x

Step-by-step explanation:

Let y = the cost

Let x = the number of hours

It costs $9 and hour to rent 27/3 = 9

The rate of flying explorer A is more than the rate of explorer B.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
Proportionality equation for explorer A,
y=7000x
Rate of flying explore A = 7000

Rate of flying explore B,
Rate = distance / time = 84000 / 20 = 42000

Thus, the rate of flying explorer A is more than the rate of explorer B.

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May ha 4/15 meter of lace while lovie ha 2/7 meter longer Than may lace then 86/105 meter of lace do girl have altogether

Meter Definition

The meter is the standard unit of measuring length in the International System of Units (SI). Its symbol is “m” and it is one of the seven base units of the SI system.

May has 4/15 meters of lace

Lovie has a lace that is 2/7 meters longer

4/5 + 2/7

= 58/105

Therefore the lace they own together can be calculated as follows

= 4/15 + 58/105

= 86/105

Hence together they have 86/105 meters of lace

that is May ha 4/15 meter of lace while lovie ha 2/7 meter longer Than may lace then 86/105 meter of lace do girl have altogether

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Yes your answer was correct.