Applying the Pythagorean Theorem

What is the value of x?

x = ?

The value of 6315 ×41 is 260391.

Multiplication is a method of finding the product of two or more numbers

We have to find the product of 6315 times of forty one

 6351

×     41

_______

    6351

25404+

__________

260391

Hence, the value of 6315 ×41 is 260391.

To learn more on Multiplication click:

https://brainly.com/question/5992872

#SPJ1

To find the equation of a circle passing through three points, we can make use of the formula for the circumcenter of a triangle, which is the point where the perpendicular bisectors of the sides of the triangle intersect. The circumcenter is the center of the circle, and the distance from the circumcenter to any of the three points is the radius of the circle. Let's follow these steps to find the equation of the circle:

Step 1: Find the midpoint and slope of the line joining two of the points, say (1, 7) and (8, 6). The midpoint of this line is (4.5, 6.5), and the slope is -1/7.Step 2: Find the equation of the perpendicular bisector of the line joining (1, 7) and (8, 6). Since the slope of this line is -1/7, the slope of the perpendicular bisector is 7 (the negative reciprocal of -1/7). The midpoint (4.5, 6.5) lies on the perpendicular bisector, so we can find the equation of the perpendicular bisector in point-slope form:

y - 6.5 = 7(x - 4.5)Simplifying, we get:

y = 7x - 28

Step 3: Repeat steps 1 and 2 for the other two pairs of points, say

(1, 7) and (7, -1), and (8, 6) and (7, -1).  We obtain the equations:

y = 4x + 3, and y = -5x + 46 respectively.

Step 4: Solve the system of equations

y = 7x - 28, y = 4x + 3, and y = -5x + 46

to find the point where the perpendicular bisectors intersect, which is the circumcenter of the triangle formed by the three points. We get the solution x = 5, y = 4. Therefore, the center of the circle is (5, 4), and the radius is the distance from (5, 4) to any of the three points. Let's use (1, 7) to find the radius:

Radius = \(sqrt((5 - 1)^2 + (4 - 7)^2) = sqrt(17)\)The equation of the circle is then\((x - 5)^2 + (y - 4)^2 = 17\).

For more questions on perpendicular bisectors

https://brainly.com/question/30151766

#SPJ8

\((f-g)(-4)=f(-4)-g(-4)=[3(-4)^2 +5]-[-2(-4)+2]=\boxed{43}\)

-3 is not an irrational number, but it is a real number, a rational number, an integer, and a whole number.  

What are whole numbers and rational numbers?

All numbers, including integers, fractions, decimals, and irrational numbers, that can be represented on a number line are considered real numbers.

In summary, real numbers include rational and irrational numbers, and integers include whole number and their negatives.

When two integers are compared, a number can be stated as a ratio, such as -3/1, 1/2, or 5/7. Writing rational numbers as recurring or ending decimals is an option.

Numbers that can't be stated as a ratio of two integers, like 2 or, are referred to as irrational numbers. It is impossible to write irrational numbers using repeating or ending decimals.

Positive and negative whole numbers, as well as zero, are considered integers. Since whole numbers are non-negative integers, they contain zero and only positive values.

Learn more about Decimals here:

brainly.com/question/29765582

#SPJ9

Answer:

A

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

"Employee #1" took test 2023

Answer:

The second box plot represents the data

Step-by-step explanation:

A box and whisker plot gives you the five-number summary of the data, which includes:

the minimum (lowest value of the data)

the maximum (highest value of the data)

Q1 (25% of the data lies below this point)

Q3 (75% of the data lies below this point), and

the median (the middle of the data).

The two ticks at the far left and far right of the box-and-whisker plot are the minimum and maximum respectively.  From the data, we see that the minimum is 5 and the maximum is 10.

Although both plots have a minimum value of 5, only the second plot has the accurate maximum at 10.

Answer:

Well, if b = 2, then 12 - b = 10

Step-by-step explanation:

hope this helps, lol! <3

Answer: Graph A

Step-by-step explanation:

Graph A. If you find the y-intercept by plugging in 0 for x, you get 2.5 = y, so therefore graph A is correct.

Answer:

38

Step-by-step explanation:

Answer: The correct answer is:  " 38 " .

_____________________

Step-by-step explanation:

_____________________

We are given the following expression:

_____________________

–32 – (–52) – (15 – 33) ;

_____________________

Let us begin by consider the expression given in parentheses:

_____________________

" (15 – 33) " ;  Note that:  " 15 – 33 =  - 18 " ;

_____________________

Now, let us rewrite the entire given expression—substituting "(-18)" for:

 "(15 – 33)" ; as follows:

_____________________

  "  –32 – (–52) – (-18) " ;

_____________________

Now, this is an entire expression on its own, i.e. there is no expression contained within this expression.  The operations are only subtraction; so we can work from "left to right" in terms of simplifying this expression.

 As such: Let us being with:

 _____________________

   " –32 – (–52) " ;

 Note that "subtracting a 'negative value' is the same as "adding that particular value's positive counterpart" ;

As such:

   " –32 – (–52) =

        –32 + (⁺52)  =  

                  –32 + 52 =  

                   52 + (-32) = ?

          Note that adding a "negative value" is the same as "subtracting that value's positive counterpart" ;

        As such:  " 52 + (-32) =  52 – 32 = 20 " :

_____________________

Now, we can rewrite the expression:

_____________________

  " 20  – (-18) " ;  

Note that subtracting a "negative value" is the same as "adding that value's positive counterpart" :

        As such:  " 20  – (-18) = 20 + (⁺18) = 20 + 18 = 38 .

_____________________

 The correct answer is:  " 38 " .

_____________________

Hope this is helpful to you!

 Best wishes in your academic pursuits—

      and within the "Brainly" community!

_____________________

Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

for such more question on expression

https://brainly.com/question/16763767

#SPJ8

Greece is different from most other countries in southern Europe because its most popular religion is not Catholicism. Option B

Catholicism refers to the traditions, beliefs, and behaviors of the Catholic Church

Greece is predominantly an Orthodox Christian country, whereas most other countries in southern Europe, such as Italy, Spain, and Portugal, are predominantly Catholic.

Learn more about Catholicism at:https://brainly.com/question/929974

#SPJ1

The quadratic equation can be written as follows:

y = 5(x - 3)² + 50.

The quadratic function in the context of this problem is defined as follows:

y = 5x² - 30x + 95

The coefficients of the quadratic function are given as follows:

a = 5, b = -30 and c = 95.

Then the x-coordinate of the vertex is given as follows:

h = -b/2a

h = 30/10

h = 3.

The y-coordinate of the vertex is given as follows:

h = 5(3)² - 30(3) + 95

h = 50.

Hence the equation is:

y = 5(x - 3)² + 50.

The quadratic function in the context of this problem is defined as follows:

y = 5x² - 30x + 95

More can be learned about quadratic functions at https://brainly.com/question/31895757

#SPJ1

9514 1404 393

Answer:

  x = 1

Step-by-step explanation:

The diagram is intended to show you that the whole is the sum of the part:

  11 = (10x -1) +(2x)

  11 = 12x -1 . . . . . . . collect terms

  12 = 12x . . . . . . . . add 1 to both sides

  1 = x . . . . . . . . . . . divide both sides by 12

The value of x is 1. The lengths of the segments are 9 and 2.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

for such more question on combinations

https://brainly.com/question/28065038

#SPJ8

The t-statistic for these two sample is 3.80 with 73 df

T-value is a ratio of the difference between the mean of two samples sets an the variation exist within the sample sets .
The numerator value is difference of mean of two samples.

According to the question,

We have two different sample

Sample 1

n1 = 35 (sample size)

x1 = 13.6 (sample mean)

s1 = 5.8 (standard deviation)

Sample 2

n2 = 40

x2 = 10.1

s2 = 8.5

To calculate the t-value of difference of sample means

\(t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{\frac{s_1^2}{n_1} - \frac{s_2^2}{n_2}}}\)

Substituting all the values

=> \(t = \frac{13.6-10.1}{\sqrt{\frac{5.8^2}{35} - \frac{8.5^2}{40}}}\)

Solving ,

=> t = 3.5 / 0.9192

=> t = 3.807

With degree of freedom = n1 + n2 - 2

=> df =73

To know more about t-statistics here

https://brainly.com/question/28000141

#SPJ4

Answer:

an inequality is a relation that states that two or more numbers or mathematical expressions are inequal to each other. It makes that comparison that they are not equal. In the real world they are used in budgeting, in counting materials for manufacturing goods, and in business

Step-by-step explanation:

The slope of the line according to the graph will be -2 which is denoted by m.

What is slope?

The ratio of how much y grows as x grows by a certain amount is known as slope of line. The slope of a line tells  how steep it is, or how much y rises as x rises. Everywhere along the line, the slope remains constant (the same).

What is slope formaulae?

the slope of line is denoted by m.

              m=(y2-y1)/(x2-x1)

The points on the graph are (x1,y1)=(3/2,0)

                                                (x2,y2)=(0,3)

According to the formulae,

                                slope(m)=(y2-y1)/(x2-x1)

                 substitute the values above

                                      =>(3-0)/(0-3/2)

                                     =>3/(-3/2)

                                       =>-2

To know more about lines visit:

https://brainly.com/question/17731558

#SPJ1

PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

For similar question on annual interest rate.  

https://brainly.com/question/29059795  

#SPJ11

Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

Answer:

He has to pay 14427.21 rupees.

Step-by-step explanation:

1. 13% of 16583 = 2155.79

2. 16583 - 2155.79= 14427.21

3. Has to pay 14,427.21 rupees

Answer:

C

Step-by-step explanation:

Riding at a constant rate of 15 miles per hour means that the line must be drawn through (1,15) and (2,30).

In one hour, he has traveled 15 miles and in 2 hours, he has traveled 2 times 15 = 30 miles.

The graph which shows the distance that Carmen travelled is option C.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Given that,

Carmen rode his bicycle at a constant rate of 15 miles per hour.

This means that Carmen is riding bicycle at 15 miles for 1 hour, 30 miles for 2 hours, etc.

The general equation for the situation is,

y = 15x

where y is the distance travelled and x is the time taken.

The graph of this function will be a proportional graph passing through points (0, 0), (1, 15), (2, 30), (3, 45), ...

The correct graph is picture number 3.

Hence the correct option is C.

Learn more about Linear functions here :

https://brainly.com/question/20106471

#SPJ2

Answer:

Slope = 6, y intercept = -7, x intercept = 7/6

Step-by-step explanation:

Slope = 6

y intercept = -7

x intercept = 7/6

The size of the crowd that is 5 feet deep on both sides of the street along a 2.7 -mile section of a parade route is 74,131 people.

The number of people that can fit comfortably in a 5 feet by 5 feet area = 13.

Therefore;

The ratio of the number of people per unit area = 13/(5 × 5) = 13/25

The area A occupied by the crowd = 5 feet × 2.7 mile × 2

2.7 miles = 14,256 feet

∴ A = 5 feet × 14,256 feet × 2 = 1,42,560ft²

We then have:

\(\frac{number\ of\ people}{1,42,560} = \frac{13}{25}\)

∴Number of people = 13/25 × 1,42,560 = 74,131.2 ≈ 74,131 people

To know more about estimate size of crowd , check out:

brainly.com/question/29281093

#SPJ1

9514 1404 393

Answer:

  20

Step-by-step explanation:

4 and 5 have no common factors*, so their least common multiple is their product:

  4 × 5 = 20

The LCM of 4 and 5 is 20.

_____

* We're concerned with integer factors greater than 1. Of course, 1 is a factor of everything, We could say this as "no common prime factors". For computing the LCM, we really want the GCF (greatest common factor) for use in the formula ...

  LCM(m, n) = mn/GCF(m, n)

Answer:

Step-by-step explanation:

When x=-2; y = -16+12= -4. This means a=-4

When x=-1; y= -2+3 = 1. This means b= 1.

When x=2; y = 16 +12 = 28 . This means c= 28

When x=4; y= 128+48 = 176. This means d= 176

The linear function parallel to the line represented by y = 3x/4 - 1/2 is given as follows:

y = 3x/4 + 1/2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

When two lines are parallel, they have the same slope.

The slope of the line y = 3x/4 - 1/2 is given as follows:

m = 3/4.

Hence the equation of the parallel line is given as follows:

y = 3x/4 + 1/2.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1