There are two points of the form (x,-4) that have a distance of 10 units from the point (3,2). Give the x value for one of those points.​

Answers

Answer 1

Answer:

x = - 5

Step-by-step explanation:

[tex]Let \ (x _ 1 , y _ 1 ) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ points. \\\\The \ distance \ between \ the \ points \ be ,\ d = \sqrt{(x_2 - x_1)^2 + ( y _ 2 - y_1)^2}[/tex]

Given : d = 10 units

         And the points are ( x , - 4) and ( 3 , 2 ).

Find x

[tex]d = \sqrt{( 3 - x)^2 + ( -4 - 2)^2} \\\\10 = \sqrt{( 3 - x)^2 + ( -6)^2} \\\\10^2 = [ \ \sqrt{( 3 - x)^2 + 36} \ ]^2 \ \ \ \ \ \ \ \ \ [ \ squaring \ both \ sides \ ] \\\\100 = ( 3 - x )^2 + 36\\\\100 - 36 = ( 3 - x )^ 2\\\\( 3 - x ) = \sqrt{64}\\\\3 - x = \pm 8\\\\3 - x = 8 \ and \ 3 - x = - 8\\\\-x = 8 - 3 \ and \ -x = - 8 - 3\\\\-x = 5 \ and \ -x = - 11\\\\x = - 5 \ and \ x = 11\\\\[/tex]

Check which value of x satisfies the distance between the points.

x = 11

[tex]d = \sqrt{(3-11)^2 + (-2--4)^2} = \sqrt{(-8)^2 + (-2+4)^2}= \sqrt{64+4} = \sqrt {68} \ units[/tex]

does not satisfy.

x = - 5:

[tex]d = \sqrt{ (3 -- 5)^2 + ( - 4 - 2)^2} = \sqrt{8^2 + 6^2} = \sqrt{100} =10 \ units[/tex]

Therefore , x = - 5


Related Questions

A, B and C are collinear points. B is between A and C. AB=12 BC=18 AC=3x Find X.

Answers

Answer:

[tex]x =10[/tex]

Step-by-step explanation:

Given

[tex]AB = 12[/tex]

[tex]BC = 18[/tex]

[tex]AC = 3x[/tex]

Required

Solve for x

Since B is in between both points, then:

[tex]AC = AB + BC[/tex]

This gives

[tex]3x = 12 + 18[/tex]

[tex]3x = 30[/tex]

Divide by 3

[tex]x =10[/tex]

Help and explain !!!!!!

Answers

Answer:

x = -4   or   x = 5

Step-by-step explanation:

To solve the absolute value equation

|X| = k

where X is an expression in x, and k is a non-negative number,

solve the compound equation

X = k or X = -k

Here we have |2 - 4x| = 18

In this problem, the expression, X, is 2 - 4x, and the number, k, is 18.

We set the expression equal to the number, 2 - 4x = 18, and we set the expression equal to the negative of the number, 2 - 4x = -18. Then we solve both equations.

2 - 4x = 18  or  2 - 4x = -18

-4x = 16   or   -4x = -20

x = -4   or   x = 5

Answer:

x = -5 . x= 4

Step-by-step explanation:

because |4| = 4 and |-4| = 4

you can see that TWO inputs can get an output of (lets say) 4

The absolute value function can be seen as a function that ignores negative signs

so to get an OUTPUT of "18" using the absolute value function

there are really two ways of getting there

"2-4x = 18"  AND "2-4x = -18"

if you solve both of those you will find that -5 and 4 will

produce the 18 and -18

Order the following integers from smallest (left side) to biggest (right
side):
20, 0, 22, -35, 100, -59

Need help please

Answers

-59, -35, 0, 20, 22, 100

LOOK AT THE BOTTOM PLEASE MAKE SURE YOU ARE RIGHT

Answers

Answer:

reflection

Step-by-step explanation:

B is the mirror image of A across a line between the two images

3.6 subtract by 1.487 is egual to ______.Pls write in step by step.​

Answers

Answer:

2.113

Step-by-step explanation:

 

               [tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]

In the diagram, the measure of angle 3 is 76°. A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8. What is the measure of angle 4?

Answers

Answer:

104

Step-by-step explanation:

180-76=104

Answer:

104

Step-by-step explanation:

heres my proof. have a nice day :)

A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the other students. Find the probability that, in exactly one of the two classes, all 8 students pass.

Answers

Answer:

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability that all students pass in a class:

Class of 8 students, which means that [tex]n = 8[/tex]

Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]

This probability is P(X = 8). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]

Find the probability that, in exactly one of the two classes, all 8 students pass.

Two classes means that [tex]n = 2[/tex]

0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].

This probability is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

I need help with these questions

Answers

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Which operation must you use to find the water temperature after the submarine’s final dive? Which word or words in the problem signify this operation?

Answers

Answer:

the temperature drops 2 degrees F

Step-by-step explanation:

Answer:

The problem states that the temperature drops 2 degrees F.  The word drops signifies that I should subtract 2 1/5 degrees F from 63 1/4 F.

Step-by-step explanation:

Show all the steps to solve the following
942.6 - 19.734

Answers

Answer:

922.868

Step-by-step explanation:

1. Thousandth place of 942.6002. Subtracting

[tex]942.600-19.732=922.868[/tex]

An amusement park offers 2 options on tickets into the park. People can either buy 5 admission tickets for $130 or buy 1 admission ticket for $30. How much money will a group of 5 people save by buying 5 admission tickets for $130?

Answers

Answer:

You could save $20

Step-by-step explanation:

For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130

Answer:

20 dollars

Step-by-step explanation:

for the first deal is 5 for $130

and the second is for $30

$30 times 5 (the number of people) = $150

$150-$130= is 20

answer: $20

Pls answer? Last one for today!

Answers

Step-by-step explanation:

You look for the common factor of both of them which in this case is 5, therefore it's

5(x+7)..just divide 5 in 5x and in 35

Please help me i will give you brainly please

Answers

Answer:

19. 3x+5/2x+7 =5

or, 3x+5=5×(2x + 7)

or, 3x + 5 = 10x + 35

or, 5 - 35 = 10x - 3x

or, -30 = 7x

or, -30/7 = x

21. let x be the other number

we know,

or, x × 1/7 =2

or, x/7 =2

or, x = 14

therefore, the other number is 14.

Know idea how to get an answer to this

Answers

Step-by-step explanation:

k=8.6

i think it is the right answer

Two events A and B are​ _______ if the occurrence of one does not affect the probability of the occurrence of the other.

Answers

Answer:

Independent

Step-by-step explanation:

From the word independent, which means being able ot stand alone, that is the absence or presence of one has no impact on the outcome of each phenomenon. Two events A and B are said to be independent, if the occurence of one has no bearing on the probability or chance that B will occur. This means that each event occurs without reliance on the occurence of the other. This is different from mutually exclusive event whereby event A has direct bearing in the probability of the occurence of event B.

In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 526 and the standard deviation was 101. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.

Answers

Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.

Answer:

- 0.0943

- 0.386

30.185

Step-by-step explanation:

Given :

ACT:

Mean score, m = 22.5

Standard deviation, σ = 5.3

SAT :

Mean score, m = 526

Standard deviation, σ = 101

1.)

Zscore for ACT score of 22:

Since the distribution is normal ; we use the relation ;

Zscore = (score - mean) / standard deviation

Score = 22

Zscore = (22 - 22.5) / 5.3 = - 0.0943

B.)

Zscore for SAT of 487

Zscore = (score - mean) / standard deviation

Score = 487

Zscore = (487 - 526) / 101 = - 0.386

C.)

ACT score, for ACT Zscore of 1.45

Zscore = (score - mean) / standard deviation

ZScore = 1.45

1.45 = (score - 22.5) / 5.3

1.45 * 5.3 = (score - 22.5)

7.685 = score - 22.5

Score = 7.685 + 22.5

Score = 30.185

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $2000. What is the probability of randomly selecting one employee who earned less than or equal to $45,000

Answers

Answer:

The probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621

Step-by-step explanation:

We are given that

Mean,[tex]\mu=50000[/tex]

Standard deviation,[tex]\sigma=2000[/tex]

We have to find the probability of randomly selecting one employee who earned less than or equal to $45,000.

[tex]P(x\leq 45000)=P(\frac{x-\mu}{\sigma}\leq \frac{45000-50000}{2000})[/tex]

[tex]P(x\leq 45000)=P(Z\leq-\frac{5000}{2000})[/tex]

[tex]P(x\leq 45000)=P(Z\leq -2.5)[/tex]

[tex]P(x\leq 45000)=0.00621[/tex]

Hence,  the probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621

Instructions: Drag and drop the correct name for each angle. Each angle has more than one name so be sure to identity all the correct names

Answers

Answer/Step-by-step explanation:

Recall: an angle can be named in three different ways:

i. Using one letter which is the vertex of the angle. i.e. if the vertex of the angle is A we can name the angle as <A.

ii. Using the number of the labelled angle. i.e. is the angle is labelled 2, we can name it <2

iii. Using the three letters of the angles with the vertex angle in the middle. i.e. if the three points that form an angle are A, B, C and the vertex is B, we can name the angle as <ABC.

✔️Let's name the each angle given according:

1. <G, <3, and <FGH

2. <D, <4, and <CDE

3. <S and <TSR (the number seems blur and difficult to read. Whatever number is used to label the angle is what you'd use in naming the angle)

were should i go shopping for fidgets

Answers

Answer:

Amazon

Step-by-step explanation:

You can shop from Etsy/Amazon

Find the quotient of the following

Answers

Answer:

you simply have to do ide the coefficients and subtract the power

Plsss help Get brainiest if right!!

Anita can paint 25 wooden slats in 5.5 hours. If she continues to
work at the same speed without any breaks, how many slats can
she paint in 9.9 hours?

Answers

Hello!

25 wooden ..... 5.5 hours

x wooden ..... 9.9 hours

_____________________

25/x = 5.5/9.9

25 × 9.9 = x × 5.5

247.5 = x × 5.5

x × 5.5 = 247.5

x = 247.5 : 5.5

x = 45 wooden

Good luck! :)

Answer:

45

Step-by-step explanation:

In questions such as these it is implied Anita can and does work at a constant rate. Therefore, we can set up the following proportion:

[tex]\frac{25}{5.5}=\frac{x}{9.9}[/tex], where [tex]x[/tex] represents the number of wooden slats she can paint in 9.9 hours.

Multiplying both sides by 9, we get:

[tex]x=\frac{9.9\cdot 25}{5.5},\\x=\boxed{45}[/tex]

Martina made$391for17hours of work. At the same rate, how many hours would she have to work to make$253? a 11 hours b 9 hours c 22 hours d 33 hours

Answers

Answer:

11 hours is right answer i hope it will help you

Find the value of x in each case:

Answers

Answer:

36

Step-by-step explanation:

2x is an exterior angle

Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).

Put symbolically

<LEG = <EGF + <EFG

<EFG = 180 - 4x           In this case you need to find the supplemtnt

<LEG = x + 180 - 4x

2x = 180 - 3x                Add 3x to both sides

5x = 180                       Divide by 5

x = 36

SCALCET8 3.9.013. A plane flying horizontally at an altitude of 2 mi and a speed of 570 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station. (Round your answer to the nearest whole number.)

Answers

Answer:

DL/dt = 529 miles/h

Step-by-step explanation:

The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t  point C) shape a right triangle wich hypothenuse L is:

L²  =  d² + x²

d is the constant distance between the plane and the ground

Then differentiation with respect to time on both sides of the equation

2*L*dL/dt  = 2*d* Dd/dt  + 2*x*dx/dt

But   Dd/dt  =  0

L*dL/dt  =  x*dx/dt

x =  5 miles       dx/dt  =  570 m/h        L  = √ d² + x²    L  √ (5)² + (2)²

L = √29      L  = 5.39 m

5.39 *DL/dt  =  5*570 m/h

DL/dt  =   5*570/5.39   miles/h

DL/dt  =  528.76  miles/h

DL/dt = 529 miles/h

You are hanging a picture on a wall that is 56 1/4 inches long. If the picture frame is 18 2/3 inches long, how much wall space is left? Write your answer as a mixed number.

Answers

Answer:

[tex]37 \frac{7}{12}[/tex] inches.

Step-by-step explanation:

Let's start by converting all of these mixed numbers to improper fractions to handle them a little better.

56 × 4 = 224 ⇒ 224 + 1 = [tex]\frac{225}{4}[/tex]

18 × 3 = 54 ⇒ 54 + 2 = [tex]\frac{56}{3}[/tex]

So, we have our improper fractions. Now, we need to convert each to twelfths so we can subtract.

225 × 3 = 675

56 × 4 = 224

[tex]\frac{675}{12} - \frac{224}{12}[/tex] = [tex]\frac{451}{12}[/tex]

[tex]\frac{451}{12} = 37 \frac{7}{12}[/tex]

So, the answer is [tex]37 \frac{7}{12}[/tex] inches.

If I=square root-1 then i^2=

Answers

Answer:

i^−3 = i

i^−2 = −1

i^−1 = −i

i^0 = 1

i^1 = i

i^2 = −1

i^3 = −i

i^4 = 1

i^5 = i

i^ 6 = −1

See the pattern

(2cosA+1) (2cosA-1)=2cos2A+1 prove that

Answers

Step-by-step explanation:

To prove that: (2cosA+1) (2cosA-1) = 2cos2A+1

We try to solve one side of the equation to get the other side of the equation.

In this case, we'll solve the right hand side (2cos2A + 1) of the equation with the aim of getting the left hand side of the equation  (2cosA + 1)(2cosA - 1)

Solving the right hand side: 2cos2A + 1

i. We know that cos2A = cos(A+A) = cosAcosA - sinAsinA

Therefore;

cos2A = cos²A - sin²A

ii. We also know that: cos²A + sin²A = 1

Therefore;

sin²A = 1 - cos²A

iii. Now re-write the right hand side by substituting the value of cos2A as follows;

2cos2A + 1 = 2(cos²A - sin²A) + 1

iv. Expand the result in (iii)

2cos2A + 1 = 2cos²A - 2sin²A + 1

v. Now substitute the value of sin²A in (ii) into the result in (iv)

2cos2A + 1 = 2cos²A - 2(1 - cos²A) + 1

vi. Solve the result in (v)

2cos2A + 1 = 2cos²A - 2 + 2cos²A + 1

2cos2A + 1 = 4cos²A - 2 + 1

2cos2A + 1 = 4cos²A - 1

2cos2A + 1 = (2cosA)² - 1²

vii. Remember that the difference of the square of two numbers is the product of the sum and difference of the two numbers. i.e

a² - b² = (a+b)(a-b)

This means that if we put a = 2cosA and b = 1, the result from (vi) can be re-written as;

2cos2A + 1 = (2cosA)² - 1²

2cos2A + 1 = (2cosA + 1)(2cosA - 1)

Since, we have been able to arrive at the left hand side of the given equation, then we can conclude that;

(2cosA + 1)(2cosA - 1) = 2cos2A + 1

Answer:

[tex]\boxed{\sf LHS = RHS }[/tex]

Step-by-step explanation:

We need to prove that ,

[tex]\sf\implies (2 cosA +1)(2cosA-1) = 2cos2A+1[/tex]

We can start by taking RHS and will try to obtain the LHS . The RHS is ,

[tex]\sf\implies RHS= 2cos2A + 1 [/tex]

We know that , cos2A = 2cos²A - 1 ,

[tex]\sf\implies RHS= 2(2cos^2-1)-1 [/tex]

Simplify the bracket ,

[tex]\sf\implies RHS= 4cos^2A - 2 +1 [/tex]

Add the constants ,

[tex]\sf\implies RHS= 4cos^2-1 [/tex]

Write each term in form of square of a number ,

[tex]\sf\implies RHS= (2cos^2A)^2-1^2 [/tex]

Using (a+b)(a-b) = a² - b² , we have ,

[tex]\sf\implies RHS= (2cosA+1)(2cosA-1) [/tex]

This equals to LHS , therefore ,

[tex]\sf\implies \boxed{\pink{\textsf{\textbf{ RHS= LHS }}}} [/tex]

Hence Proved !

Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.

PLEASE HELP NEED ASAPPPPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRRR

Answers

Answer:

The answer is

[tex]y = 3[/tex]

[tex]y = - 4[/tex]

Step-by-step explanation:

We must find a solution where

[tex] \frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]

Consider the Left Side:

First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get

[tex] \frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1} [/tex]

Which equals

[tex] \frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)} [/tex]

Add the fractions

[tex] \frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]

Simplify the right side by multiplying the fraction

[tex] \frac{6y}{(y + 1)(y + 2)} [/tex]

Set both fractions equal to each other

[tex] \frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)} [/tex]

Since the denomiator are equal, we must set the numerator equal to each other

[tex]6y = {y}^{2} + 7y - 12[/tex]

[tex] = {y}^{2} + y - 12[/tex]

[tex](y + 4)(y - 3)[/tex]

[tex]y = - 4[/tex]

[tex]y = 3[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{6}{y+1}+\frac{y}{y-2}=\frac{6}{y+1} \times \frac{y}{y-2} \\multiply ~by~(y+1)(y-2)\\6(y-2)+y(y+1)=6y\\6y-12+y^2+y=6y\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\\y=-4,3[/tex]

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour. What is the probability that no requests for assistance are in the system

Answers

Answer:

0.1667

Step-by-step explanation:

We are given;

Arrival rate, λ = 10 requests per hour

Service rate, μ = 12 requests per hour

From queuing theory, we know that;

ρ = λ/μ

Where ρ is the average proportion of time which the server is occupied.

Thus;

ρ = 10/12

ρ = 0.8333

Now, the probability that no requests for assistance are in the system is same as the probability that the system is idle.

This is given by the Formula;

1 - ρ

probability that no requests for assistance are in the system = 1 - 0.8333 = 0.1667

2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?

15.9
59
77
96.8

Answers

Answer:

[tex]x = 77[/tex]

Step-by-step explanation:

Given

[tex]First \to Second[/tex]

[tex]35 \to x[/tex]

[tex]20 \to 44[/tex]

[tex]20 \to 44[/tex]

Required

Find x by SSS

Represent the triangle sides as a ratio

[tex]35 : x = 20 : 44[/tex]

Express as fraction

[tex]\frac{x}{35} = \frac{44}{20}[/tex]

Multiply by 35

[tex]x = \frac{44}{20} * 35[/tex]

[tex]x = \frac{44 * 35}{20}[/tex]

[tex]x = \frac{1540}{20}[/tex]

[tex]x = 77[/tex]

Answer:

ccccccccccccccccccccccccccc

Step-by-step explanation:

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