What is the distance between the points (2, 1) and(6, 7)?

Answers

Answer 1

Answer:

[tex]\displaystyle d = 2\sqrt{13}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Point (2, 1)

Point (6, 7)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]:                                                         [tex]\displaystyle d = \sqrt{(6 - 2)^2 + (7 - 1)^2}[/tex][√Radical] (Parenthesis) Subtract:                                                                   [tex]\displaystyle d = \sqrt{4^2 + 6^2}[/tex][√Radical] Evaluate exponents:                                                                       [tex]\displaystyle d = \sqrt{16 + 36}[/tex][√Radical] Add:                                                                                                 [tex]\displaystyle d = \sqrt{52}[/tex][√Radical] Simplify:                                                                                           [tex]\displaystyle d = 2\sqrt{13}[/tex]

Related Questions

Find the greatest common factor of 8a and 6a? ​

Answers

Answer:

2a.

Step-by-step explanation:

6 = 2 * 3

8 = 2 * 2 * 2   - 2 is common to both sets of factors.

So the GCF of 6 and 8 is 2.

For the 2 a's it is a.

I need help on this too please it’s hard

Answers

Answer:

Y=x

Step-by-step explanation:

The y and x values are the same

Answer:

y = x

Step-by-step explanation:

a 45° line with the origin passing through the origin has the equation y=x.

Have a nice day.

brainliest answer po yung tama
nk tym for nega NEED HELP PK TALAG​

Answers

A

A

B

C

A

D

B

C

May choices po yan saamen

Step-by-step explanation:

Love you

what is the value of this expression

log2^8 + log3(1/3)​

Answers

Answer:

2

Step-by-step explanation:

log2^8 + log3(1/3)

=>3 + (-1)

=>2

Find the explicit general solution to the following differential equation.

(8+x) dy/dx = 5y

The explicit general solution to the equation is y:_______

Answers

Answer:

y = (8+x)^5 + C

Step-by-step explanation:

Given the differential equation

(8+x) dy/dx = 5y

Using the variable separable method

(8+x) dy = 5ydx

dx/8+x = dy/5y

Integrate both sides

[tex]\int\limits^ {} \, \frac{dx}{8+x} = \int\limits^ {} \, \frac{dy}{5y} \\ln(8+x) = \frac{1}{5}lny\\5ln(8+x)= lny\\ln(8+x)^5 = lny\\ (8+x)^5 = y\\Swap\\y = (8+x)^5 + C[/tex]

This gives the required solution

The explicit general solution to the following differential equation[tex](8+x)\dfrac{dy}{dx} = 5y[/tex]  is [tex](8+x)^5 +C[/tex], where [tex]C[/tex] is a constant.

The relationship between the unknown function and its derivative is called the differential equation.

The differential equation in which variables are separated from each other is called the variable separable method.

Now, separate the variables using the variable separable method:

[tex](8+x){dy} = 5y \ dx[/tex]

[tex]\dfrac{dx}{8x} = \dfrac{dy}{5y}[/tex]

Integrating both sides,

[tex]\int \dfrac{dx}{x+8} = \int \dfrac{dy}{5y}\\log(x+8) = \dfrac{1}{5} log y\\ 5 log(x+8) = log y\\log(x+8)^{5} = log y \ \ \\y = ( x+8)^{5} +C[/tex]

Thus, the explicit general solution to the equation is [tex](8+x)^5 +C[/tex].

Learn more about differential equations here:

https://brainly.com/question/33814182

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Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.2 feet. A sample of 41 men's step
lengths is taken
Step 2 of 2: Find the probability that the mean of the sample taken is less than 2.2 feet. Round your answer to 4 decimal places, if necessary,

Answers

Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 2.5 feet and a standard deviation of 0.2 feet.

This means that [tex]\mu = 2.5, \sigma = 0.2[/tex]

Sample of 41

This means that [tex]n = 41, s = \frac{0.2}{\sqrt{41}}[/tex]

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}[/tex]

[tex]Z = -9.6[/tex]

[tex]Z = -9.6[/tex] has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

For the data set 4, 5, 10, 11, 15, the mean, x, is 9. What is the standard
deviation?
The formula for the sample standard deviation is a -
Jo-;2(x-
z(x -- Hoje
Use the table to help you.
4.
5
10
11
15
X-8
(x - x?
-5
25
-4
16
1
1
2
4.
6
36
Sum= 82
Round your answer to the nearest tenth.

Answers

Answer:

4.53

Step-by-step explanation:

Given the data :

4, 5, 10, 11, 15

The mean = 9

The standard deviation of a sample :

s = √[Σ(x - mean)²/(n-1)]

s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]

s = √(25+16+1+4+36)/4

s = √20.5

s = 4.527

s = 4.53

Answer:

4.5

Step-by-step explanation:

5.1.3

Find the value for the side marked below.
Round your answer to the nearest tenth.
50°
122
y
y = [?
Enter

Answers

Answer:

y = 189.8

Step-by-step explanation:

Apply trigonometric function to find y.

Reference angle (θ) = 50°

Adjacent side = 122

Hypotenuse = y

Apply CAH, since the Hypotenuse and the Adjacent are involved.

Thus:

Cos θ = Adj/Hypo

Plug in the values

Cos 50° = 122/y

y*Cos 50° = 122

y = 122/cos 50°

y = 189.8 (beater tenth)

What is the system of equations represented by the tables?
O A. y=2x-1
y = -x + 3
B. y = x + 2
y = x-1
O c. y=-3x-1
y = 3x + 2
O D. y = 2x-3
y = -x + 2

Answers

Answer:

C.

y = -3x - 1

y = 3x + 2

Step-by-step explanation:

Find the slope (m) and y-intercept (b) of each table to write an equation for each.

✔️First table:

Find the slope (m) = change in y/change in x

Using any two pair of values, say (0, -1) and (1, -4),

Slope (m) = (-4 - (-1))/(1 - 0) = -3/1

m = -3

Find the y-intercept:

y-intercept is the value of y when x = 0

From the table, y = -1 when x = 0. Therefore,

y-intercept (b) = -1

To write an equation for table 1, substitute m = -3 and b = -1 into y = mx + b

Equation for table 1:

y = -3x - 1

✔️ Second table:

Find the slope (m) = change in y/change in x

Using any two pair of values, say (0, 2) and (1, 5),

Slope (m) = (5 - 2)/(1 - 0) = 3/1

m = 3

Find the y-intercept:

y-intercept is the value of y when x = 0

From the table, y = 2 when x = 0. Therefore,

y-intercept (b) = 2

To write an equation for table 1, substitute m = 3 and b = 2 into y = mx + b

Equation for table 1:

y = 3x + 2

characteristics of the median

Answers

Answer:

Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.

Median is not dependent on all the data values in a dataset. The median value is fixed by its position and is not reflected by the individual value. The distance between the median and the rest of the values is less than the distance from any other point. Every array has a single median.

The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 9 vans and 14 buses with 710 students. High School B rented and filled 13 vans and 5 buses with 371 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

Answers

Answer:

Buses - 43 people

Vans - 12 people

Choose the Athat seems to be congruent to the given one.
R.
F
D
B
AEGFA
OEGD
o CGD
BGC

Answers

Answer:

a. ∆EGF ≅ ∆EGD

Step-by-step explanation:

Congruent triangles would have the same side lengths and the same measure of angles.

From the figure given:

EG in ∆EGF ≅ EG in ∆EGD

GF in ∆EGF ≅ GD in ∆EGD, also

EF ≅ ED.

The three angles in ∆EFG are also congruent to the three angles in ∆EGD.

Therefore, ∆EGD is congruent to ∆EGF.

∆EGF ≅ ∆EGD

A team of researchers wants to determine whether pet owners are generally more satisfied with their lives than non-pet owners. To test their theory, the researchers randomly select 500 pet owners and 500 non-pet owners from several major metropolitan areas in the country. The researchers then interview the individuals, asking them a series of questions. Each response is assessed with a point value that is later translated to a satisfaction indicator. Of the pet owners surveyed, 380 of the 500 were found to be satisfied with their lives, while 336 of the 500 non-pet owners were found to be satisfied.
Would this study be considered an experiment or an observational study?

Answers

Answer:

observational study

Step-by-step explanation:

Kaleigh wants to buy a car that costs $17360. She deposits $14,000 in a savings account that earns 8% simple interest. How long was Kaylee leave the money in the savings account to be able to buy the car?

Answers

Answer:

Kaylee must leave the money in the savings account for 3 years.

Step-by-step explanation:

Given that Kaylee wants to buy a car that costs $ 17,360, and she deposits $ 14,000 in a savings account that earns 8% simple interest, to determine how long was Kaylee leave the money in the savings account to be able to buy the car must be made the following calculation:

14,000 + (14,000 x 0.08 x X) = 17360

1,120X = 17,360 - 14,000

X = 3,360 / 1,120

X = 3

Therefore, Kaylee must leave the money in the savings account for 3 years.

help me find the perimeter of this square. if you can do it step by step please!

Answers

Answer:

396

Step-by-step explanation:

It's a square.

That means that all four sides are equal.

So the two expressions you have been given are equal.

2.5x + 76.5 = 12x - 9            Subtract 2.5x from both sides.

-2.5x               -2.5x  

          76.5 = 9.5x - 9          Add 9 to both sides

           9                 9

          85.5 = 9.5x              Divide by 9.5

       85.5/9.5 = x

x = 9

That is just the value for x. It is not the answer

Side = 12x - 9

Side = 12*9 - 9

Side = 108 - 9

Side = 99

The perimeter = 4 * Side

The perimeter = 4 * 99

Perimeter = 396

If a franchise company wanted to determine why sales were higher at some locations rather than others, what statistical process would be most appropriate? Group of answer choices Regression with sales as an independent variable Regression with sales as the dependent variable Use a confidence interval with the posted speed as the mean Hypothesis testing with a null hypothesis that the sales are less than or equal to the highest sales Hypothesis testing with a null hypothesis that the sales are more than the highest sales

Answers

Answer: Regression with sales as the dependent variable

Step-by-step explanation:

Since the franchise company wanted to determine why sales were higher at some locations rather than others, the statistical process that would be most appropriate is regression with sales as the dependent variable.

Regression will be used in determining the strength of the relationship that exist between one dependent variable and the independent variables. In this case, the dependent variable is sales.

Name two characteristics of the Fibonacci Series that you observed. ​

Answers

Answer:

See the answers below

Step-by-step explanation:

Name two characteristics of the Fibonacci Series that you observed. ​

If we take a closer look at the Fibonacci series, we will notice the following characteristics

1.The next number is the sum of the two preceding numbers

2. Another interesting characteristic is evidenced in the convergence of the sequence

A cyclist travels at a rate of 12 kilometers per hour. What is the rate in kilometers per minute? How many kilometers will the cyclist travel in 20 minutes? Do not round your answer.

Answers

Answer:

0.2&4

Step-by-step explanation:

There are 60 minutes in one hour, so 12 divided by 60 is the answer.

0.2   kilometers * 20 = 4

An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A

Answers

Answer:

[tex]P(x\geq 1) = 0.923[/tex]

Step-by-step explanation:

From the question we are told that:

Percentage of student to get A [tex]P(A)=\%5=0.05[/tex]

Sample size [tex]n=50[/tex]

Generally Number of student to get A is

[tex]N_a=n*P(A)[/tex]

[tex]N_a=50*0.05[/tex]

[tex]N_a=2.5[/tex]

Therefore

Probability that one student gets an A grade is mathematically by

  [tex]^nPC_xP^x(1-P)^{n-x}[/tex]

 [tex]P(x\geq 1)=1-P(x<1)[/tex]

 [tex]P(x\geq 1) =1-P(x=0)[/tex]

 [tex]P(x\geq 1) =^50C_0(0.05)^0(0.95)^50[/tex]

 [tex]P(x\geq 1) = 0.923[/tex]

The perimeter of a rectangle is 12cm the area is 5cm square what is the length of the sides?

Answers

Answer:

l=5, w=1

Step-by-step explanation:

5*1=5 for area

5+1+5+1=12 for perimeter

PLEASE HELP ASAP
Add the complex numbers: (4 + 8i) + (–2 – i)

Answers

Answer:

2 + 7i

Step-by-step explanation:

(4 + 8i) + (-2 - i)

open the brackets

4 + 8i - 2 - i

add or subtract like terms

2 + 7i

Answer:

2+7i

Step-by-step explanation:

Open the brackets.

4+8i-2-i

You will get…

2+7i

Can someone tell me if its A,B, or C? Thanks besties.

Answers

Answer:

... ..... C is the answer

Find the 23rd term of the arithmetic sequence with the terms a1 27 and d = 16.​

Answers

Answer:

379

Step-by-step explanation:

a23 = 27 + (23-1)(16)

= 27 + (22)(16)

= 27 + 352

= 379

A professor has been teaching introductory statistics for many years and the final exam performance has been very consistent from class to class and the scores have been normally distributed. Overall, the whole data base (i.e. population) of final scores has a mean (μ) of 24 points (out of a maximum of 30 points) and a standard deviation (Ï) of 5 points. The professor would like to revise the course design to see if student performance on the final could be improved.

The new course design was implemented in the most recent academic year. There were 100 students and the average final exam score was 24.7. The professor would like to run a hypothesis test to see if this sample of students in the recent academic year performed significantly better than the past population. In other words, the hypothesis was a comparison between the population taking the course with the new design (represented by the sample of 100 students) with the population taking the course with the old design. The professor is predicting an increase of final score with the new design, so the hypotheses should be directional, and the test should be one-tailed. The significance level is set at α = .1.

Required:
a. Identify the dependent variable for this study.
b. State the null hypothesis and alternative hypothesis using both words and symbol notation

Answers

Answer:

a) Independent variable - Design of the course

Dependent variable - Final score of the students

b)  H0 - Final score >24.7

Alternate hypothesis - Final score is less than or equal to 24.7

Step-by-step explanation:

a) Independent variable - Design of the course

Dependent variable - Final score of the students

b) Null Hypothesis : Performance of student taking course with the new design is better as compared to the population of student taking the course with the old design.

H0 - Final score >24.7

Alternate hypothesis - Final score is less than or equal to 24.7

The harmonic mean of two real numbers x and y equals 2xy/(x + y). By computing the harmonic and geometric means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.

Answers

Answer:

Conjecture :  2xy / ( x + y ) ≤  √xy

Step-by-step explanation:

Harmonic mean of  x and y = 2xy/( x + y )

Formulate a conjecture about their relative sizes

we will achieve this by computing harmonic and geometric means

Geometric mean = √xy

harmonic mean = 2xy/( x + y )

Conjecture :  2xy / ( x + y ) ≤  √xy

attached below is the proof

(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x) is an exsample of

Answers

this is an example of linear equations is one variable

What value of y makes the sentence true?
y + 3 = 30
Type your answer in the box below.
I
y =

Answers

y = 27
Subtract 3 from both sides to get y by itself.

Hey there!

y + 3 = 30

SUBTRACT 3 to BOTH SIDES

y + 3 - 3 = 30 - 3

CANCEL out: 3 - 3 because that gives you 0

KEEP: 30 - 3 because that gives you the value of y

y = 30 - 3

30 - 3 = y

y = 27

Answer: y = 27

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

What’s an example for y=1/2x-6 real world problems

Answers

Max is participating at a school bake sale. Each cookie he sells costs 50 cents. Unfortunately, it took 6 dollars to buy the materials for the cookies. Find how much money would it take for Max to break even.

Answer:

Step-by-step explanation:

4 years ago when Mary was 6, she was one half the age of her brother.  

 How old is her brother now?

Solution :

Let brother's age be = x

Four years ago, brothers age was = (x - 4)

Four years ago Mary was = 6

She was half the age of her brother

                                                   [tex]6 = \frac{1}{2} (x - 4)[/tex]

work out 8^2/3
^2/3 means to the power of 2/3

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

4

»»————- ★ ————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\[/tex]

[tex]-----------[/tex]

[tex]\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

4

Step-by-step explanation:

[tex]8^{\frac{2}{3} }[/tex]

=[tex](2)^3*\frac{2}{3}[/tex]

=[tex](2)^\frac{3*2}{2}[/tex]

=[tex](2)^\frac{6}{3}[/tex]

=[tex]2^2[/tex]

=4

How tall is the table?
120cm
90cm
I

Answers

The table is 120 cm tall

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

https://brainly.com/question/16513646

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