Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point (6, -7) are Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

Answers

Answer 1

Answer: [tex](6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)[/tex] are the required points.

or  (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

[tex]\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}][/tex]

Taking square on both the sides , we get

[tex](x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0[/tex]

Using quadratic formula : [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}[/tex]

so, [tex](6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)[/tex] are the required points.

since [tex]\sqrt{3}=1.732[/tex]

so, [tex](6+7(1.732),0)\text{ and }(6-7(1.732),0)[/tex] are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.


Related Questions

Find the Cardinal number of the set of all solutions to x^2=100

Answers

Answer: 2

Step-by-step explanation:

this is the answer knewton alta said

The Cardinal number of the set of all solutions to x²=100 is 2.

What is Number system?

A number system is defined as a system of writing to express numbers.

Cardinal numbers are natural numbers or positive integers. The smallest cardinal number is 1.

We have to find the Cardinal number of the set of all solutions to  x²=100

To find the solution of the equation we have to take square root on both the sides' x=10, -10

The set of solutions will be {-10, 10}

It has two terms. Hence cardinal number is 2.

Hence, the Cardinal number of the set of all solutions to x²=100 is 2.

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-13.3°C=_________K °C is Celsius and K is Kelvin

Answers

Answer:

259.85 K

Formula:

-13.3°C + 273.15 = 259.85K

Step by step solution:

To convert, just add 273.15 to the Celcius value to get the Kelvin value.

Hope this helps!

The sum of a number and 5
Help

Answers

Hey there! I'm happy to help!

Let's call our number n.

The word sum means to add.

Therefore....

n+5

Have a wonderful day! :D

A crowd of people stood on both sides of the street to view a 4th of July Parade.
The length of the parade was 3 miles long and 15 feet deep on each side of the street.
If 5 people can fit into a 25 ft^2 area.
Estimate the size of the crowd.
(1mile = 5280ft)

Answers

Given :

Length of parade , [tex]L = 3\ miles=3\times 5280\ miles = 15840\ miles[/tex] .

Breadth of parade , [tex]B=2\times 15=30\ ft[/tex] .

5 people can fit into a [tex]25\ ft^2[/tex] area.

1 mile = 5280 ft .

To Find :

The size of the crowd.

Solution :

Area of parade ,

[tex]A=15840\times 30\ ft^2\\\\A=475200\ ft^2[/tex]

Also , 5 people can fit in [tex]25\ ft^2[/tex] area .

So , number of people fit in A is :

[tex]n = \dfrac{475200\times 5}{25}\\\\n=95040[/tex]

Therefore , 95040 can fit in the parade .

Hence , this the required solution .

A factory makes 300 sheets of construction paper per hour. How many sheets of construction paper will the factory make in 9 hours?

Answers

Answer:

2700

Step-by-step explanation:

One hour is 300 sheets. We need to find 9 hours,

so 300*9= 2700

Eddie Lange earns $11.50 per hour. He worked 40 hours, plus time and a half for 7 hours?​

Answers

Answer:

Total amount earned = $500.25

Step-by-step explanation:

Given:

Wage per hour = $11.50

Time worked = 40 hours

Extra time worked = 7 hour

Wage paid per extra hour = $11.50 / 2 = $5.75

Find:

Total amount earned

Computation:

Total amount earned = [Wage per hour][Time worked] + [Extra time worked][Wage paid per extra hour]

Total amount earned = [11.50][40] + [7][5.75]

Total amount earned = [460] + [40.25]

Total amount earned = $500.25

If y varies directly as x and y=5 when x=8 find y when x=4

Answers

Answer:

2.5

Step-by-step explanation:

x=8 x=4

y=5 y=2.5

is ratio problem

If y varies directly with x and y = 5 when x= 8 . then the value of y when x = 4 is 2.5

What is directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called constant of proportionality.

If y varies directly with x and y = 5 when x= 8 . then we need to find y when x = 4

Therefore, y = kx

k = y/x

k = 5/8

Then y = kx

y = (5/8)4

y = 5/2

y = 2.5

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(1 point) Find the antiderivative F of f(x)=4−3(1+x2)−1 that satisfies F(1)=−3.

Answers

Here is your answer I hope it’s helpful

The value of antiderivative F will be;

⇒ F = 4x - 3 arc tan x - 7 + 3π/4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = 4 - 3 (1 + x²)⁻¹

Now,

Since, The function is,

⇒ f (x) = 4 - 3 (1 + x²)⁻¹

Hence, The antiderivative F of f (x) is,

⇒ F = ∫ (4 - 3 (1 + x²)⁻¹ ) dx

⇒ F = ∫ 4 dx - 3 ∫ (1 + x²)⁻¹ dx

⇒ F = 4x - 3 arc tan x + c

Where, c is constant of integration.

Here, The antiderivative of f (x) is satisfy F(1) = - 3,

So, Substitute x = 1, F = - 3

⇒ F = 4x - 3 arc tan x + c

⇒ - 3 = 4×1 - 3 arctan (1) + c

⇒ - 3 = 4 - 3π/4 + c

⇒ - 3 - 4 + 3π/4 = c

⇒ c = - 7 + 3π/4

Thus, The antiderivative F of f (x) is,

⇒ F = 4x - 3 arc tan x - 7 + 3π/4

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3.99 4.29 and 2.89 range

Answers

Answer:

1.4

Step-by-step explanation:

Sample size: 3

Lowest value: 2.89

Highest value: 4.29

Range: 1.4

formula for calculating the range:

Range = maximum(x_i) - minimum(x_i)

where x_i represents the set of values.

Find square of -9.2​

Answers

Answer:

84.64.

Step-by-step explanation:

(-9.2)^2

= (9.2)^2

= 84.64.

PLEASE HELP ME


A map has a scale of
2 in. = 18 mi. If you measured the distance between two cities to
be 16 in. on the map, how many miles would it actually be?

Answers

Answer:

it would be 144 miles

Step-by-step explanation:

We start by a ratio of map to mile =      2:18

if we see that the map distance is 16,   16:?

We divide 16 by 2 to get 8, so we enlarge the 2, 8 times, and we get 16

the 18, also has to be enlarged, so 18x8 = 144

It will be 144 miles

5. A six sided number cube is tossed onto a table 25 times. The results are shown below.
Number on die
Number of times
rolled out of 25
1
.
OWN
III
MINI
11
What is the theoretical probability of a 5 or 6?
_Answer as a fraction. (5 pts)
What is the experimental probability 5 or 6?
Answer as a fraction. (5 pts)

Answers

Answers:

Theoretical probability of 5 or 6 is 1/3

Experimental probability of 5 or 6 is 9/25

======================================================

Explanation:

For the theoretical probability, we ignore the table of values. We assume the cube will land on any of the 6 sides with equal probability.

So landing on any given side has probability 1/6. Landing on 5 or 6 has probability 2*(1/6) = 2/6 = 1/3.

---------

For the experimental probability, we use the table. We see that '5' shows up twice, and '6' shows up seven times. In total, those values show up 2+7 = 9 times out of 25 total.

So that's how I got 9/25.

What is the square root of -16?
е в
-87
0 ООО
8

Answers

[tex]4i[/tex]

[tex]i=\sqrt{-1}[/tex]

[tex]\sqrt{-16}=\sqrt{-1}*4[/tex]

[tex]\sqrt{-16}=i*4[/tex]

[tex]4i[/tex]

Hope this helps.

頑張って!

Find the focus and directrix of the parabola y= 1/2 (x+2)^2 - 3 A. The focus is at (–2,–2) and the directrix is at y = –4. B. The focus is at (–2,–3) and the directrix is at y = –5. C.The focus is at (–2,–2 1/2) and the directrix is at y = –3 1/2. D. The focus is at (–2,–1 1/2) and the directrix is at y = –2 1/2.

Answers

Answer:

C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]

Step-by-step explanation:

First of all, let us learn about the formula to find Focus and Directrix from the standard equation of a parabola.

Standard form of a parabola is given as:

[tex](x - h)^2 = 4p (y - k)[/tex]

where the focus is [tex](h, k + p)[/tex] and

the directrix is [tex]y = k - p[/tex]

Now, we are given the equation of parabola as:

[tex]y= \dfrac{1}2 (x+2)^2 - 3[/tex]

Let us try to convert it to standard form:

[tex]\Rightarrow y+3= \dfrac{1}2 (x+2)^2 \\\Rightarrow 2(y+3)= (x+2)^2 \\\Rightarrow (x+2)^2 = 2(y+3)\\\Rightarrow (x+2)^2 = 4\times \frac{1}{2}(y+3)[/tex]

Comparing the above with standard equation of parabola [tex](x - h)^2 = 4p (y - k)[/tex]:

[tex]h = -2, p = \frac{1}{2}, k = -3[/tex]

So, Focus is at [tex](h, k + p)[/tex]

[tex]k + p = -3+\frac{1}{2} = -2\frac{1}{2}[/tex]

Focus is at [tex](-2, -1\frac{1}2)[/tex].

Equation of directrix:

[tex]y = k - p=-3-\frac{1}{2}\\\Rightarrow y = -3\frac{1}{2}[/tex]

Also, please refer to the attached image for the diagram of given parabola, focus and directrix.

So, the answer is:

C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]

how can simplify 5x-4=6​

Answers

5x -4 = 6 simplified would be x = 2 hope this helps ♡

PLS HELP simplify (2b^3)^2

Answers

Answer: 4b^6

Remember if theres a bracket you multiply the power instead of adding

For example if it was 2b^3 x 2b^2 then the answer would be 4b^5 instead according to indices law, read up on it if you havent yet itll help a bunch! :)

7x(15+4) = (7x ) + (7+4)

Answers

Add the numbers inside the parentheses
7x(15+4)=(7x)+(7+4)
and you get
7x*19= 7x+11

Calculate the product
133x=7x+11

Move variable to the left hand side & change its sign
133x-7x=11

Collect like terms
126x=11

Divide both sides by 126 & you get
x=11/126


Answer: x= 11/126

Hope this helps ʕ•ᴥ•ʔ

Simplify: 80÷4−2(2+1)2

Answers

Answer:

8

Step-by-step explanation:

Applying the PEDMAS rule, the expression 80÷4−2(2+1)² would be simplified as: 80÷4−2(2+1)² = 2.

What is the PEDMAS Rule?

The PEDMAS rule guides the order of operation when solving a math problem with several operations.

P - parenthesis, E - exponent, D - division, M - multiplication, A - addition, S - subtraction.

To simplify 80÷4−2(2+1)², apply PEDMAS rule:

Solve parenthesis

80÷4−2(3)²

Solve exponent

80÷4−2(9)

Divide

20 −2(9)

Multiply

20 − 18

Subtract

= 2

Therefore, 80÷4−2(2+1)² = 2

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145,973 write in sentence form

Answers

Answer:

one hundred forty-five thousand nine hundred seventy-three

hope this helps!

There are 7 books on the floor. The number of books on the shelf is 2 more than 3 times the number of books on the floor.

Answers

Ok so what you do is 7 multiplied by 3 that gives you 21 then you do 21+2 and get your answer which is 23

Please please please help me with this please and i will give you a brainlist and 10 points

Answers

Im pretty sure it’s the third one :)
The answer is the third one because it is the only isometric figure of X. Reflections don’t change dimensions, only coordinates.

Solve for w . p=w/t

Answers

Answer:

w = pt

Step-by-step explanation:

[tex]p=\frac{w}{t}\\\\p*t=\frac{w}{t}*t\\\\pt=w\\\\\boxed{w=pt;t\neq 0}[/tex]

Hope this helps.

A driver education course
costs $45 but saves those
under 25 years old 10% of their annual insurance premiums until they are 25. Dan has just
turned 18, and his insurance is $100 per month.

1. When will the amount saved from insurance equal the price of the course?
2. Including the cost of the course, when Dan turns 25, how much will he have saved?

Answers

Answer:

after 4.5 months (or 5)$795

Step-by-step explanation:

10% of $100 per month is $10 per month.

1. By saving $10 per month on insurance cost, Dan's savings after 4.5 months will be equal to the $45 cost of his course. (If billing is monthly, he won't experience any net gain from the course until the 5th insurance payment--after 5 months.)

__

2. In 7 years, the savings on insurance costs will total ...

  (7 years)×(12 months/year)×($10 /month) = $840

His cost for the course is $45, so his net saving is ...

  $840 -45 = $795 . . . net saving by age 25

please help asap, and if you can explain why after the answer, please and thank you❤️

Answers

DF=14. Because DE is half the line and EF is the other half the line you add up both the lengths to get the length of whole line.
DE=EF. DE and EF both equal 7 so they are equal.

the sum of 6 and the product of 8 and x" into mathematical expression

Answers

Answer:

6=8x

Step-by-step explanation:

Answer:

6+8x

Step-by-step explanation

We are going to make sure we can do this as best as possible. We need to make sure that the words that you are reading are making sense.

Sum can be taken out because its just 6. We do not know what adds to 6, it could be 1 +5,  2+4, 3+3, -3 and 9, WE DO NOT KNOW. So don't put extra information into the expression, when it is not given.

The and would be an addition to something, because when we are speaking and say the word AND, we want to add to that sentence. So, and is the plus sign.

6+

Then product is multiplication. So 8 times x.

Put it all together and you get the expression:

6+8x

I really hoped that helped you!

7x-6y=11 solve for y​

Answers

Answer:

7x+11 =  6y

(7x+11)/6 = y

7x/6= y-11

There are multiple answers for this

Step-by-step explanation:

missing angle for triangle

Answers

Answer:

86

Step-by-step explanation:

33+61=94

180-94=86

150 students in 3 classes

Answers

Answer:

50 if you're asking for dividing

Step-by-step explanation:

if you're dividing then it's 50 hopefully this is the answer your asking

What is the simplified form of the following expression

Answers

The second option is the answer

idk what this is


pls help​

Answers

Answer:

Coplanar points

Step-by-step explanation:

Coplanar points are three or more points that lie in the same plane.

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