Why might squaring a number and taking the square root of a number be thought of as opposite operations?

The measure of segments mAG, mAC, and mBC are 11.4, 16.1 and 7.1 respectively,

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Apply Pythagoras theorem in triangle ABG,

mAG = √[7² + 9²]
mAG = √[49 + 81]
mAG = √[130] = 11.4
Apply Pythagoras theorem in triangle BGC,
mBC = √[10² - 7²]
mBC = √51
mBC = 7.1

Now

mAC = mAB  + mBC
mAC = 9 + 7.1
mAC = 16.1

Thus, the segments mAG, mAC, and mBC have measures of 11.4, 11.1, and 7.1, respectively.

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Discontinuity can be determined by looking for sudden changes in values or jumps in the graph of the function. If there is a break or gap in the graph, the function is discontinuous.

Discontinuity occurs when a function fails to be defined at a certain point within its domain, resulting in a sudden change in the graph of the function. Discontinuity can be determined by plotting the graph and looking for sudden changes in values or jumps in the graph. If the graph shows a break or gap, then the function is discontinuous. Discontinuity can also be determined by examining the behavior of the function at a certain point. If the function values diverge as the point is approached from either side, then the function is discontinuous at that point. Additionally, a function can be discontinuous at a point if it does not obey the rule of continuity, which is that the function's value must be equal to the limit of the function as the point is approached from both sides. If the limit does not exist at a point, then the function is discontinuous at that point.

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The customer can afford to buy 2 whole bags of candy.

In this problem, the customer started with $52.02 in his pocket and spent $37.85 on items, leaving him with $14.17 to spend on candy. Each bag of candy costs $5.50, so the customer can afford to buy $14.17 / $5.50 = 2.6 bags of candy. However, since the customer can only buy whole bags of candy, he can only afford to buy 2 whole bags of candy. This is the final answer to the problem.

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The simple interest is $6,240.00.

The term simple interest refers the interest that is only calculated on the initial sum borrowed or deposited.

Here we need to find  the simple interest on $6000 from 16 may 2010 to 9 October 2010 at 10% per annum.

While we looking into the given question, we know te following values,

Principal amount = $6000

Time period = 16 may 2010 to 9 October 2010

The number of days between 16 may 2010 to 9 October 2010 is

=> 146 days.

Here we have the interest for 1 year,

So, the time period is written as,

And then we have to put time into years for simplicity,

146 days / 365 days/year = 0.4 years.

And the interest rate = 10%

Here we have to convert R percent to r a decimal

r = R/100 = 10%/100 = 0.1 per year.

Now, we have to apply the values on the formula, then we get by solving our equation:

A = 6000(1 + (0.1 × 0.4)) = 6240

A = $6,240.00

Therefore, the total amount accrued, principal plus interest, from simple interest on a principal of $6,000.00 at a rate of 10% per year for 0.4 years (146 days) is $6,240.00.

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The ratio in which P (1,2) divides AB at (2,1) and (7,4) is 1:6.

Ratio is the term for the proportion between two or more things in terms of number, amount, or size.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

Given,

Point P → (1, 2)

Point A → (2, 1)

Point B → (7, 4)

Let m1:m2 be the ration

The formula that is used is:

[tex]x=\frac{m1x2+m2x1}{m1+m2} ; y=\frac{m1y2+m2y1}{m1+m2}[/tex]

Now we have been given the Point P → (1, 2), hence x = 1 and y = 2

Also, (x₁, y₁) = (2, 1) and (x₂, y₂) = (7, 4)

[tex]1=\frac{7m1+2m2}{m1+m2} ; 2=\frac{4m1+m2}{m1+m2}[/tex]

m₁ + m₂ = 7m₁ + 2m₂

0=6m1-m2

m2=6m1

1/6=m1/m2

The ratio in which P divides AB is 1:6.

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The side-side-side (SSS) theorem states that if three sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent.

In other words, if the lengths of the sides of two triangles are the same, then the triangles must be the same shape and size.

For example, consider two triangles ABC and DEF. If we know that

we can use the SSS theorem to conclude that triangle ABC is congruent to triangle DEF.

It is important to note that the SSS theorem is only applicable if the three sides of each triangle are equal in length. If the sides are not equal, the theorem does not apply and we cannot use it to prove the congruence of the triangles.

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Therefore, the formula for solving the area of quadrilateral is given by

area of quadrilateral = 1/2(sum of perpendicular drawn from residual two vertices).

What is quadrilateral?

A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. It is made up of four linked non-collinear points. The sum of the internal angles of quadrilaterals is always 360 degrees.

According to the given question:

When the diagonal and the sum of the lengths of the perpendiculars traced from the remaining two vertices are known,

The area of the quadrilateral can be calculated as follows:

Area of quadrilateral = (1/2) diagonal length sum of the lengths of the perpendiculars drawn from the residual two vertices.

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The median of 4 and 7 is 5.5.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.

The mean of these middle values is (4+7)/2 = 11/2= 5.5

Thus, the median of 4 and 7 is 5.5.

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For a total of 8 sales the employee earns about 57 tokens

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

If the employee by amount of sales obtains a greater benefit each time, which is stipulated as follows:

We must put together an equation that relates the amount of sales with the amount of  tokens.

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To solve a binomial expression, use the FOIL (First, Outer, Inner, Last) method to multiply the two terms together. Then use the distributive property to simplify the expression and combine like terms.

1.Identify the two terms of the binomial expression and write them in the correct order.

2. Use the FOIL method to multiply the two terms together:

the first term of each binomial is multiplied together first.

Outer: Divide the second term of the second binomial by the first term of the first binomial.

Multiplying the first term of the second binomial by the second term of the first binomial yields the inner product.

Lastly, combine the second terms of each binomial.

3. To make the expression simpler, use the distributive property.

4. Combine like terms, if applicable.

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Using the SAS(Side-Angle-Side) Theorem, ASA(Angle-Side-Angle) Theorem, SSS(Side-Side-Side) Theorem and AA(Angle-Angle) Theorem we can easily prove that two triangles are similar.

If two triangles have an equal number of comparable angles and sides, they are said to be similar.

Similar figures are items that have two or more figures with the same shape but varying sizes.

Using the SAS(Side-Angle-Side) Theorem, ASA(Angle-Side-Angle) Theorem, SSS(Side-Side-Side) Theorem and AA(Angle-Angle) Theorem we can easily prove that two triangles are similar.

A portion on one polygon must correspond perfectly to a part in another polygon that is in a similar place. Even though two triangles are oriented differently from one another, you can conclude that their angles match if you can spin them to align in the same direction and notice that their angles are similar.

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The formula in getting possible zeros in rational root theorem is given as ± p / q.

According to rational root theorem if a polynomial expression which is written in descending order of the exponents and has integer coefficients, then any rational zero must be of the form ± p / q

Here, p is a factor of the constant term or the numerator and q is a factor of the leading coefficient or the denominator.

As the name implies, the rational root theorem is used to find the rational solutions to a polynomial equation . Polynomial roots or zeros are the solutions we get when we solve a  polynomial equation. A polynomial does not need required rational zeros only.

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As per the combination method, the number of ways can the ribbons be awarded is 24,024

The general formula to calculate the combination is written as,

nCr = n!/r! (n - r)!

where n refers the set or population and r refers subset of n or sample set

Here we have given that there are 14 dogs in a particular class at a dog show. blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers,

Here we need to find the number of different ways can the ribbons be awarded.

While we looking into the given question, the following details are given in it,

Total number of dogs = 14

Number of ribbons = 5

Which means that the value on n = 14 and the value of r = 5.

As per the given question we know that,

There are 14 possibilities for blue one

And then there are 14 - 1 = 13 possibilities for red ribbon.

And for the next yellow one has 12 possibilities

Then the white one has 11 possibilities.

Therefore, the total number of ways is

=> 14 x 13 x 12 x 11

=> 24024

Therefore, option (c) is correct.

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Answer:

x=4      y=-1

Simplify:

100+43y over 3 = 19

Step-by-step explanation:

-3x-8y=20

-5x+y=19

The solution of the given system of equation is (-19, 55).

In the given question we have to find the solution to the system of equations:

y = -3x-2 and 5x + 2y = 15

We can solve the system of equation using the substitution method.

In substitution method we have to put the the value of one variable from one equation to the other equation.

We have to equations:

y = -3x-2...................................(1)

5x + 2y = 15.............................(2)

Now putting the value of y from the equation 1 in equation 2

5x + 2(-3x-2) = 15

Now solving the equation using the distribution method.

5x - 6x - 4 = 15

Simplifying

-x - 4 = 15

Add 4 on both side we get

-x = 19

Now the value of x is -19.

Now putting the value of x in equation 1

y = (-3)*(-19)-2

y = 57-2

y = 55

Hence, the solution of the given system of equation is (-19, 55).

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The right question is:

What is the solution to the system of equations y = -3x-2, 5x+2y=15?

Answer:

the answer is D i think

Answer:

Step-by-step explanation:

from the drawing BC = EF

we solve with an equation

x - 4 = 19

x = 19 + 4

x = 23

The prediction is not reasonable and The prediction is an interpolation is correct

How to use a regression calculator to make a reasonable prediction given a data table?

Kardal used the trend line to predict that a man 72 inches tall would wear about a size 10. 5 shoe.

Given data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.

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Population parameters are used to estimate sample statistics, and this is true.

Population parameters are used to describe the characteristics of a population, such as the mean, median, and standard deviation, and are used to make inferences about a population. Sample statistics, on the other hand, are used to describe the characteristics of a sample of a population. For example, a sample statistic could be the mean of a sample of people's heights.

To estimate sample statistics, population parameters must first be known. For example, the sample mean can be estimated using the population mean. If the population means are unknown, then the sample means can be estimated using the sample mean.

In conclusion, population parameters are used to estimate sample statistics, and this is true. Population parameters provide useful information about a population that can be used to make inferences about a sample. Knowing the population parameters allows researchers to make more accurate estimates of sample statistics, which in turn can be used to make more reliable inferences about a population.

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As per the given equation, the length of the arc of the curve from point p to point q is 1.8973

Here we have given the equation y = 1/2 x².

Then the the length of the arc of the curve from point p to point q is calculated by using the formula,

=> [tex]\int\limits^q_p {\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]

Here we have to extract the value of (x1, x2) from the given coordinates, then we get,

=> (x1, x2) = (-3, 3)

Now, we have to find the derivative of y, then we get he value as,

=> dy/dx = x

So, the length is calculated as,

=> [tex]\int\limits^3_{-3} {\sqrt{1+x^2} } \, dx[/tex]

As per the power rule of derivative, then reduced form of the equation is written as.

=> [x/√x²+1]₋₃³

When we apply the value of x as the given limit, then  we get,

=> [3/√3²+1] - [(-3)/√(-3)²+1]

=> [3/√10] + [3/√10]

=> 6/√10

=> 1.8973

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Main five functions of the roots are as follow:

1.Anchorage of the plant

2. Absorption of water

3. Absorption of minerals or food

4. Preventing soil erosion

5. Transportation of food.

Five function of the roots of the plants:

Therefore, the five functions of the roots of the plants are

1.Anchorage of the plant

2. Absorption of water

3. Absorption of minerals or food

4. Preventing soil erosion

5. Transportation of food.

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Pipe will take 21.5 hours to fill tank completely.

A tank can be partially filled in 1 hour = 1/x if it takes x hours to fill it completely.

If the tank must be emptied in y hours, then the portion drained in an hour is equal to 1/y.

If a pipe can fill a tank and drain it in x and y hours, respectively.

When both pipes are opened simultaneously, the tank's net volume is filled in one hour using the formula (xy) / (y-x), provided y>x.

If a pipe can fill a tank and drain it in x and y hours, respectively.

When both pipes are opened simultaneously, the tank's net volume is filled in one hour using the formula (xy) / (x-y), provided x>y.

Net work completed equals the sum of all inlets' work (Sum of work done by Outlets)

Volume of tank be V

Pipe A and Pipe B together fill (1/9)V in one hour.

Pipe A fills (1/15)V in one hour.

Pipe B fills (1/9 - 1/15)V in one hour.

Solving for pipe B, we get

1/9 - 1/15

[tex]=\frac{15-9}{15*9}\\=\frac{6}{15*9}\\=\frac{2}{45}\\[/tex]

So, tank B will take total 21.5 hours to fill tank individually.

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Answer: x = 32/2

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

12*8=96

96/3= 3 remainder 6

The nature of the roots of 2x² 3x 5 0 are imaginary, as it is not possible to solve for real numbers.

To solve this equation, we first factor out the coefficients (2 and 5). Factoring out 2 gives us x² + 1.5x + 5 = 0. After that, we solve for x using the quadratic formula:

x

= -1.5 ± √(-1.5² - 4(1)(5)) / 2(1). This is reduced to x = -1.5 9.5 / 2, an imaginary number that cannot be solved using real values. This indicates that the equation's roots are fictitious.

x

= -1.5 ± √(-1.5² - 4(1)(5)) / 2(1)

x = -1.5 ± √9.5 / 2

x = -1.5 ± √(9.5)i / 2

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Answer:

highway: 70 × 2 = 140 miles

side roads: 35 × 1 = 35 miles

total distance: 140 miles + 35 miles = 175 miles

im sorry if the answer is wrong :)

The two groups have the same ratio of students with solo to total students.

We should know that ration is the quotient of two numbers. In mathematics ration is defined as  as the number of times one number contains another number

The given parameters are

25 choir students

5 solo students from the choir

20 Orchestra students

4 solo orchestra students

Expressing the ratio of total choir students to total orchestra students and solo choir  students to solo orchestra students we have

25:20 = 5:4

Dividing the left hand side by 5

5:4 = 5:4

In conclusion the ratio of total choir students to total orchestra students and solo choir students to solo orchestra students are the same = 5:4

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The total distance traveled by the cows are 3.58 meters. To calculate that we need to calculate fourth area before.

It sounds like you are trying to solve a problem involving two cows grazing in a field and the area that they graze. Here is a possible solution:

We can use the formula for the area of a quadrilateral to solve for the fourth side:

Area = (1/2) x (12 cm) x (fourth side)

Solving for the fourth side, we get:

Fourth side = (20 cm)/(12 cm) = 1.67 meters

Finally, add up the lengths of the four sides to find the total distance traveled by the cows:

Total distance = (1.67 meters) + (12 cm) + (1.67 meters) + (12 cm) = 3.58 meters

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The correct answer is c.) the probability of getting a number less than 3 is equal to 0.33 but does not change the probability of the next trial.

The probability of getting a number less than 3 on a standard die is always equal to 0.33, regardless of the number of times the die is rolled. The probability of an event occurring does not change based on the number of times the event has occurred in the past. Each roll of the die is an independent event, meaning that the outcome of each roll does not affect the probability of the next roll.

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The solution of the given system of equation is (8, -22).

In the given question we have to find the solution to the system of equations:

y = -4x + 10 and y = -2x - 6

We can solve the system of equation using the substitution method.

In substitution method we have to put the the value of one variable from one equation to the other equation.

We have to equations:

y = -4x + 10...................................(1)

y = -2x - 6.............................(2)

Now putting the value of y from the equation 1 in equation 2

-4x + 10 = -2x - 6

Add 6 on both side we get

-4x + 16 = -2x

Add 4x on both side, we get

2x = 16

Divide by 2 on both side, we get

x = 8

Now the value of x is 8.

Now putting the value of x in equation 1

y = -4(8) + 10

y = -32 + 10

y = -22

Hence, the solution of the given system of equation is (8, -22).

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The right question is:

What is the solution of the system of equations y = -4x + 10 and y = -2x - 6?