Given 4 points A, B, C, D where no 3 points are collinear, any 2 points have a distance greater than 10. Prove that there exist two points out of 4 given points with greater distance 14.

Answers

Answer 1

Answer:

idea how to tell your loved one how you feel? How about a love song?


Related Questions

please help me i will give 20 points for this question ​

Answers

Answer:

1. a. 2

b. -½

c. y - 3 = -½(x - 8) => point-slope form

y = -½x + 7 => slope-intercept form

2. a. -1

b. 1

c. y - 5 = 1(x - 3) => point-slope form

y = x + 2 => slope-intercept form

Step-by-step explanation:

1. (8, 3) and (10, 7):

a. The gradient for the line joining the points:

Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Let,

[tex] (8, 3) = (x_1, y_1) [/tex]

[tex] (10, 7) = (x_2, y_2) [/tex]

Plug in the values

Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]

Gradient = [tex] \frac{4}{2} [/tex]

Gradient = 2

b. The gradient of the line perpendicular to this line = the negative reciprocal of 2

Negative reciprocal of 2 = -½

c. The equation of perpendicular line if it passes through the first point, (8, 3):

Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).

Where,

(a, b) = (8, 3)

Slope (m) = -½

Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).

Thus:

y - 3 = -½(x - 8) => point-slope form

We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:

Thus:

y - 3 = -½(x - 8)

y - 3 = -½x + 4

y - 3 + 3 = -½x + 4 + 3

y = -½x + 7

2. (3, 5) and (4, 4):

a. The gradient for the line joining the points:

Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Let,

[tex] (3, 5) = (x_1, y_1) [/tex]

[tex] (4, 4) = (x_2, y_2) [/tex]

Plug in the values

Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]

Gradient = [tex] \frac{-1}{1} [/tex]

Gradient = -1

b. The gradient of the line perpendicular to this line = the negative reciprocal of -1

Negative reciprocal of -1 = 1

c. The equation of perpendicular line if it passes through the first point, (3, 5):

Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).

Where,

(a, b) = (3, 5)

Slope (m) = 1

Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).

Thus:

y - 5 = 1(x - 3) => point-slope form

We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:

Thus:

y - 5 = 1(x - 3)

y - 5 = x - 3

y - 5 + 5 = x - 3 + 5

y = x + 2

one class collects 8 1/4 pounds of recyclable materials. Another class collects 1 1/2

Answers

Missing material to solve

Step-by-step explanation:

what to find then??.........

Heyyy could someone please help me out?? Would appreciate it. Thanks in advance!!^^

Answers

Answer:

Below,...

Step-by-step explanation:

They are saying that if you add a odd number + a odd number than you'd get a even number,... odd + even = odd,... odd x even = even,... and so on,...

Hope it helps,... Chow!

f(x) = Square root of quantity x plus seven. ; g(x) = 8x - 11 Find f(g(x)). (1 point)
f(g(x)) = 2 Square root of quantity two x plus one
f(g(x)) = 8 Square root of quantity x plus seven - 11
f(g(x)) = 8 Square root of quantity x plus four
f(g(x)) = 2 Square root of quantity two x minus one

Answers

Answer:

2 sqrt(2x-1)

Step-by-step explanation:

f(x) = sqrt(x+7)

g(x) = 8x-11

f(g(x))=

Place g(x) in for x in the function f(x)

f(g(x)) = sqrt( 8x-11 +7)

          = sqrt( 8x -4)

Factor out 4

          = sqrt( 4(2x-1)

          = 2 sqrt(2x-1)

[tex]\\ \sf\longmapsto f(x)=\sqrt{x+7}[/tex]

[tex]\\ \sf\longmapsto g(x)=8x-11[/tex]

g(x) will be put on the place of x

[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}[/tex]

[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}[/tex]

[tex]\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}[/tex]

[tex]\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}[/tex]

The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Answers

Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

Can someone please do this for me please

Answers

Answer:

r=-11

Step-by-step explanation:

7r+2=5(r-4)

7r+2=5r-20

2r=-22

r=-11

I hope it helps you!!have a good day

Martina bought 19 pounds of sugar for $10. How many pounds of sugar did she get per dollar?

Answers

Answer:

1.9 pounds

Step-by-step explanation:

To solve this divide the amount of sugar by the number of dollars:

19 pounds / 10 dollars = 1.9 pounds per dollar

Per 10dollar she brought=19pounds

Per dollar

[tex]\\ \sf\longmapsto \dfrac{19}{10}[/tex]

Write in decimals

[tex]\\ \sf\longmapsto 1.9pounds[/tex]

What is the radius of a hemisphere with a volume of 885 in^3, to the nearest tenth of
an inch?

Answers

Answer:

The desired radius is r = 7.5 inches

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)πr³.  A hemisphere is half a full sphere, so the formula for the volume of a hemisphere of radius r is (4/3)(1/2)πr³, or (2/3)πr³.

We know that the volume of the hemisphere is 885 in³:

885 in³ = (2/3)πr³ and need to solve this first for r³ and then for r.

This is equivalent to:

885 in³ = (2π/3)r³.

We can now isolate r³ by multiplying both sides of this equation by (3 / [2π]):

(3 / [2π])(885 in³) = (3 / [2π])(2π/3)r³ = r³

Then r³ = 422.556 in³

Finally, we find the desired hemisphere radius by taking the cube root of both sides of the above equation:

r = ∛(422.556 in³) = 7.5 in (which is to the nearest tenth of an inch)

The desired radius is r = 7.5 inches

What is the estimated value of 2v12 . 3V5 / V30 . V36

Answers

Answer:

the correct answer is b and I know this because I just had it

two triangles are similar what is x

Answers

Answer:

x = 10

Step-by-step explanation:

smaller triangle / bigger triangle = 20 / 28

hence,

3x / (4x+2) = 20/28

28(3x) = 20(4x+2)

84x = 80x + 40

4x = 40

x = 10

In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them?
-2x + 4y = 10
3x - 2y = -7
A. Multiply the top equation by 2 and the bottom equation by 3.
B. Multiply the bottom equation by 2.
C. Multiply the top equation by -3.
O D. Multiply the top equation by 3 and the bottom equation by -2.

Answers

Answer:

Multiply the bottom equation by 2

if x^2=y^2+z^2

what does x equal?

Answers

Answer:

[tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Property

Algebra i

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle x^2 = y^2 + z^2[/tex]

Step 2: Solve for x

[Equality Property] Square root both sides:                                                    [tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]

18 cards are numbered from 11 to 29 if one card is chosen at random, what is the probability that if contains the digit ​

Answers

What digit? 2?
If it’s two:

“There are 29–10 = 19 cards in total. There are 11 cards that has at least one 2 on it (12, 20–29). The probability of choosing a card with a 2 on it is 11/19.”

For the triangle shown, what are the values of x and y?
60°
30°
6
Select the correct answer.
O x = 2V3, y = 473
O x= 3V3, y = 6/3
O x = 6/3, y = 12
O x = 6V3, y = 1273

Answers

Answer:

x = 6/√3 = 2√3

y = 2×2√3 = 4√3

So, 1st option is correct

1. Which of the following is an algebraic expression?
a. X+5= 7
b. 5-2x = 3
C. 5x +4- 2x
d. -2 = 3x + 1

Answers

1.

C. 5x + 4 - 2x is an algebraic expression

NEED EXPLANATION TOO! THANKS BESTIES


There are 3 different trains running to London. One train
leaves every 10 minutes, another leaves every 35 minutes,
and the last one leaves every 40 minutes. They first leave at
5:30am. What Time do they all leave again at the same time?

Answers

Answer:

2:50pm

Step-by-step explanation:

You have to find the least common multiple (LCM) between the 3 times. If you don't know what is the LCM, just say it and I'll try to explain for you in the comments.

10, 35, 40 have as LCM the number 560

So it means they'll leave together 560 minutes after 5:30am

One hour is 60 minutes, so we can divide 560 by 60 to find the time in hours:

560/60 = 9 hours and 20 minutes (the rest of the division will be the minutes)

So, they'll leave together at 2:50pm

the product of 7 and the quotient of 40 divided by 5 is​

Answers

The quotient of 40 and 5

40÷5=8

=> Product of that number with 7 and 8

So number to find is : 7x8=56

The product of 7 and the quotient of 40 divided by 5 is 56.

What is the quotient?

The quotient is the result which is derived by the division of two numbers.

For example, the quotient of 30 divided by 3 is 10.

What is the product of two numbers?

The product is the multiplication of two numbers which is written as a*b.

For example, the product of 8 and 9 is 72.

Here given we have to calculate the product of 7 and the quotient of 40 divided by 5.

The quotient of 40 divided by 5 is 40/5= 8

The product of 7 and The quotient of 40 divided by 5= 7*8= 56

Therefore the product of 7 and the quotient of 40 divided by 5 is 56.

Learn more about quotient

here: https://brainly.com/question/673545

#SPJ2

For the Parabolay = (x + 7)2 – 3. the equation for the Line Of Symmetry is

Answers

Answer:

Hello

Step-by-step explanation:

Axis of symmetry is vertical:

x=-7 (since (-7,-3) is the vertex)

Answer:

x = -7

Step-by-step explanation:

y = (x+7)^2 -3

This is in vertex form

y =a(x-h)^2+k  where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h

y = (x- -7)^2 -3

x = -7

Helpppppppppppppppppppppppp im not smart pls don't just say some bull i need help ill just get it deleted

Answers

Answer:

a. 6m

b. m-2

c. 5(m-2)

d. 6m +5m -10= 56

E. 11m=66

divide by 6: m=6

Maple Granola= 6$

Apple Granola= 4$

Please help simple alebgra! Write an equation representing the translation of f(x) = 7x + 3 down 4 units.

Will mark brainliest!

Answers

9514 1404 393

Answer:

  g(x) = 7x -1

Step-by-step explanation:

The y-coordinate of a function tells how many units the function value lies above the x-axis. Translating that value down 4 units is the same as subtracting 4 from the function value.

  g(x) = f(x) -4

  g(x) = 7x +3 -4

  g(x) = 7x -1

[tex]x - \frac{3\\}{8} = \frac{13}{2}[/tex]

Answers

X - 3/8 = 13/2

Add 3/8 to both sides:

X = 13/2 + 3/8

Rewrite 13/2 to have 8 as the denominator:

13/2 x 4 = 52/8

X = 52/8 + 3/8

X = 55/8

Answer:

55/8

Step-by-step explanation:

Add 3/8 to both sides

X - 3/8 = 13/2

X = 13/2 + 3/8

make sure the denominators are equal so we can add. so multiply 4/4 by 13/2 and that equals 52/8

X = 52/8+3/8

X= 55/8

Solve for the measure of angle QSR, given b=136.

Answers

The calculated measure of the angle QSR is 68 degrees

How to solve for the measure of angle QSR

From the question, we have the following parameters that can be used in our computation:

Angle b = 136 degrees

The measure of angle QSR can be calculated using

QSR = 1/2 * Angle b

substitute the known values in the above equation, so, we have the following representation

QSR = 1/2 * 136 degrees

Evaluate

QSR = 68 degrees

Hence, the measure of angle QSR is 68 degrees

Read more about angles at

https://brainly.com/question/31898235

#SPJ1

A person can run 3 miles per minute. (Convert to miles per hour to decide.)
O True
O False

Answers

it depends upon a persons pace a average pace is 9-10 mins

Can anyone plz solve this question step by step ASAP!

Answers

Answer:

40√3 cm²

Step-by-step explanation:

Step 1

Find the height:

h² = 8² - (12 - 8)²h² = 64 - 16 = 48h = √48 = 4√3

Step 2

Find the area:

A = 1/2(a + b)hA = 1/2(12 + 8)(4√3) = 40√3 cm²

the answer is 72cm…i think but i’m sure it’s right

Write an equation in standard form of the line that passes through the given point and has the given slope (-8,0); m= -4 PLEASE HELP NEED DONE ASAP WILL GIVE BRAINLIEST

Answers

Answer:

4x+y=-32

Step-by-step explanation:

given,

slope (m) = -4

point: (-8,0)

as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]

so,

b = 0-(-4)×(-8) = -32

y=mx+b

or, y=-4x-32

or, 4x+y=-32

(this is the standard form of the line)

Using the equation y - y1 = m(x - x1)

y - 0 = -4(x - (-8))

y = -4(x + 8)

y = -4x - 32

3. If triangle ABC has the following measurements, find the measure of angle A.
a = 17
b = 21
C = 25

Answers

9514 1404 393

Answer:

  (a)  42.3°

Step-by-step explanation:

Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.

  a² = b² +c² -2bc·cos(A)

  cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050

  A = arccos(777/1050) ≈ 42.3°

The measure of angle A is about 42.3°.

_____

Additional comment

The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.

Answer:

 (a)  42.3°

Step-by-step explanation:

Convert 75 mg into gram

Answers

75 mg into grams is 0.075

Answer:

[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]

y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?

Answers

Answer:

To find the leading coefficient, first expand the function:

[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]

The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².

To find the vertex: see image below

Vertex = (-3, -5)

I'LL GIVE BRAINLIEST !!! FASTERR !​

Answers

Answer:

Option A, 86°

Step-by-step explanation:

each diagonals of a rhombus divides the angles at half, so a+b+c+d = 360°/2 = 180°

now, a+b+c+d-94° = 180°-94° = 86°

Answer:

D 266°

Step-by-step explanation:

a+b+c+d-94°

90°+ 90°+ 90°+ 90° -94°

360°-94°

266°

find the derivative of y=x²+3x​

Answers

Answer:

[tex]\frac{dy}{dx}[/tex] = 2x + 3

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

y = x² + 3x

[tex]\frac{dy}{dx}[/tex] = 2[tex]x^{(2-1)}[/tex] + 3[tex]x^{(1-1)}[/tex]

   =  2x + 3[tex]x^{0}[/tex]

   = 2x + 3

Other Questions
Can bacteria break down plastics?Give reason what damage does the caranbola According to the agency that Jake and Summer work for, what will be stolen within four days?a cata work of arta mapa backpack f (x) = sqrt(x)+ 2, g(x)=x^2+ 1find f(g(x))and g(f(x)) Please show detailed work if possible-that will help me to better understand the questionsstart with this expression:f(x) = 2x2 x 101st- What are the x-intercepts of the graph of f(x)? Show work on how to get this 2nd- Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Show work on how to get thisPart C: What are the steps you would use to graph f(x)? show how you can use the answers obtained in Part A and Part B to draw a graph Determine if the words listed are a fragment or sentence.Adam and Drew in the pool.The words are a: White Leaf Disease is a devastating disease thataffects sugar cane crops in Thailand and has become amajor issue for farmers. The disease starts with a whiteline forming in the center of the sugar cane's leaves,which can change in size and shape as it develops.The sugar cane's new leaves will become increasingly whiter, often having stunted growth, and resulting in the sugar cane being less productive than the non-infected plants, Scientists are trying to determinewhat organelle must be damaged to produce theobserved results, I need 20 words/sentences in French with English translation asapTHANKS Cual era la grave cuestin que preocupaba a nuestros personajes briant, gordon y doniphan? what is tissue A called? Que es seguridad ciudadana Point C is on the midpoint of a section of highway, represented by AB. If AB = 32 miles,AC = 4x miles, and CB = 12 + x miles, explain three different waysthatyoucouldsolve for x. s bit ca pic 16f887 Select the correct answer.In which region of the world are hominids believed to have originated?O A.North AmericaB.EuropeC.AsiaD.AfricaEAustralia As director of a positive youth development program working with teens who have been expelled from school for violent behavior, what would be the main focus of your staff's activities look at the image below A fusion reaction releases energy because the binding energy of the resulting nucleus:______.a. is released in the process. b. is equal to the binding energy of the original nuclei. c. is absorbed in the process. d. is less than the binding energy of the original nuclei. e. is greater than the binding energy of the original nuclei. Choose the system of inequalities that best matches the graph below. A. B. C. D. Which of the following is not true about Triton, the large moon of Neptune? It is more reflective than Earth's Moon. It is larger than Earth's Moon. It is in a retrograde orbit. It has a thin atmosphere. It has nitrogen geysers. According to the graph, is f even, odd, or neither?Choose 1 answer:a. Evenb. Oddc. Neither