The point P= (x,-1/7) lies on the unit circle shown below. What is the value of x in simplest form? ​

Answers

Answer 1

Answer:

[tex] x^2 + \frac{1}{49} =1 [/tex]

And solving for x we got:

[tex] x^2 = 1- \frac{1}{49}[/tex]

[tex] x^2 = \frac{48}{49}[/tex]

And taking square root we got:

[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]

Step-by-step explanation:

For this case we have the following point given [tex] P(x , -1/7)[/tex]

And we want to find the value of x, since P lies on the unitray circle if we find the distance from P to the center of the unitary circle (0,0) we need to get 1. Using the definition of Euclidean distance that means:

[tex] d = \sqrt{(x -0)^2 +(-1/7 -0)^2}=1[/tex]

And if we square both sides of the last equation we got:

[tex] x^2 + \frac{1}{49} =1 [/tex]

And solving for x we got:

[tex] x^2 = 1- \frac{1}{49}[/tex]

[tex] x^2 = \frac{48}{49}[/tex]

And taking square root we got:

[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]


Related Questions

The repairmen are fixing 9 cars 2 motorcycle and 6 trucks what is the ratio of cars to motorcycle?

Answers

Answer:

9:2

Step-by-step explanation:

Put in what we know

cars: motorcycles

9         2

.- Alicia tiene una finca de 1 km2 de superficie. Dedica 28 hm2 a cultivar trigo, 3.900 dam2 a plantar olivos y el resto lo ha plantado de girasoles.¿ Cuántos metros cuadrados ocupan los girasoles?

Answers

Answer:

330 000 m²

Step-by-step explanation:

1. Area of farm

[tex]A = \text{1 km}^{2} \times\left (\dfrac{\text{1000 m}}{\text{1 km}} \right )^{2}= \text{1 000 000 m}^{2}[/tex]

2. Area for wheat

[tex]A = \text{28 hm}^{2} \times \left (\dfrac{\text{100 m}}{\text{1 hm}}\right)^{2} = \text{280 000 m}^{2}[/tex]

3.Area for olive trees

[tex]A = {\text{3900 dam}^{2} \times \left (\dfrac{\text{10 m}}{\text{1 dam}}\right )^{2}}= \text{390 000 m}^{2}[/tex]

4. Area for sunflowers

Total area                  =                          1 000 000 m²

- Area for wheat        = 280 000 m²

- Area for olive trees = 390 000                                  

                                                                 670 000      

Area for sunflowers =                              330 000 m²

Sunflowers occupy 330 000 m².

if the population is growing by 17% you will use 1.17 as your rate in the equation true or false

Answers

Answer:

False. 0.17

Step-by-step explanation:

There are 125 sheep and 5 dogs in a flock how old is the shepherd?

Answers

Answer:

25 years old

hope this helps  

~savannah:))

If there are 125 sheep and 5 dogs in a flock  then the shepherd is 25 years old.

What is Division?

A division is a process of splitting a specific amount into equal parts.

Given,

The number of sheeps are 125

One hundred twenty five

The number of dogs are 5

Five.

We need to find how old is the shepherd

To find this we just need to divide one hundred twenty five by five

125/5

25

Hence, if there are 125 sheep and 5 dogs in a flock  then the shepherd is 25 years old.

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ5

Can you pleasee help me with the Screenshot Below its Overdue.

Answers

Answer:

what grade is this its and your answer is

Step-by-step explanation:

13/5 63/1 A = X

Deja is training for a race on Saturday. On Sunday, she runs 1/6 of a mile. On Monday she runs 1/5 of a mile. On Tuesday she runs 1/4 of a mile. On Wednesday she runs 1/3 of a mile. On Thursday she runs 1/2 of a mile. Finally, on Friday, the day before the race, she runs a whole mile. If the length of the race is the same as the total distance Deja ran in preparation, how many miles is the race?

Answers

Answer:

49/20 miles or 2.45 miles

Step-by-step explanation:

LCM(1,2,3,4,5,6,)=60

10/60+12/60+15/60+20/60+30/60+60/60=147/60=49/60 or 2.45

Correct Answers only!

Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Round your answer to the nearest cent.

Answers

Answer:

$12000

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 40000 × 15/100 × 2

I = $12000

4/x - 3/y = 1 ............(1)
6/x + 15/y = 8 ........(2)​

Answers

Answer:

1. No x-intercept/Zero

2. x = 3/4

Step-by-step explanation:

find the value of x in the following..... 3^x = 8​

Answers

Find logarithm of both sides

log (3^x) = log 8

xlog3 = log8

x = log8/log3

x = 1.893

Answer:

x ≈ 1.893 ( to 3 dec. places )

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] = n logx

Given

[tex]3^{x}[/tex] = 8 ( take the log of both sides )

log[tex]3^{x}[/tex] = log8, that is

xlog3 = log8 ( divide both sides by log3 )

x = [tex]\frac{log8}{log3}[/tex] ≈ 1.893

Gavin owes the bank $63,000. After 10 years, Gavin owes $93,255. Gavin knows the debt grows with an interest rate that compounds once every year. What is the rate of interest (as a percentage)?

Answers

Answer:

 1,616.60

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

substitute in the formula above  

Step-by-step explanation:

Simplify the expression:
5k + 7 + 10​

Answers

Answer:

5k+17

Step-by-step explanation:

Combine like terms. Like terms are terms such as 10 and 7. Some caome with variables, such as 5k and 6k. 10+7 is 17. Since you can't combine unlike terms, the expression becomes 5k+17.

I NEED HELP FAST, 20 POINTS
Which of the following fractions is not equivalent to 2?

1 4/4
10/5
3/6
2/1


Answers

Answer:

The 1st one  1 4/4 and the 3rd one 3/6

Step-by-step explanation:

10/5=2

2/1=2

Si al numerador de una fraccion se añade 5, el valor de la fraccion es 2, y si al numerador se resta 2, al valor de la fraccion es 1.Hallar la fraccion.

Answers

Answer:

Respuesta.- La fracción es 9/7

Step-by-step explanation:

1) Llamando X e Y a la fracción, tenemos: X/Y

Si al numerador se le añade 5, es decir X+5, el valor de la fracción es 2, luego:

(X+5)/Y = 2

Y si al numerador se le resta 2, es decir X-2, el valor de la fracción es 1, luego:

(X-2)/Y = 1

Juntando amabas ecuaciones:

(X+5)/Y= 2

(X-2)/Y = 1

Despejando Y en ambas:

Y = (X+5)/2

Y = (X-2)..........(1)

Igualandolas:

(X+5)/2= (X-2)

De donde:

X+5 = 2X-4

X = 9

Y finalmente, sustituyendo el valor de X = 9 en la ecuaión (1), tendremos:

Y = (X-2)

Y = (9-2)

Y = 7

Respuesta.- La fracción es 9/7

Phoebe built the sandbox below for her younger sister.
2 feet
4 feet
5 feet
What is the volume of the sandbox?

Answers

I think its 40ft i hope it helps

Answer: 40 feet

Step-by-step explanation:  Volume = length * width * height

then substitute Volume = 2 * 4 * 5

multiply Volume = 8 * 5

multiply again Volume = 40

hope this helps mark me brainliest if it did have a great day

Ben decided to invest his savings into a friends local business if he invests 1,750 at an annual interest rate of 6.4% how much interest will he earn in 4 years

Answers

Answer:

He will earn an interest of $448 in 4 years

Step-by-step explanation:

In this question, we are interested in calculating the interest earned on an investment for a period of 4 years.

To calculate this interest, we shall be using the formula for simple interest but with slight difference in terms definition

Mathematically;

I = PRT/100

Where ;

P is the amount invested which is $1,750 according to the question

R is the interest rate which is 6.4%

T is the time which is equal to 4 years

Plugging these figures, we have

I = (1,750 * 6.4 * 4)/100 = 44,800/100 = $448

What 2 numbers that multiply to make 7 and add to 6

Answers

Answer:1 and 6

Step-by-step explanation:1 x 6 = 6

1 + (6) = 7

Are you asking because you are trying to figure out how to factor the following quadratic equation?

x2 + 7x + 6 = 0

If so, the solution to factor the quadratic equation above is:

(X + 1 ) (X + 6)

To summarize, since 1 and 6 multiply to 6 and add up 7, you know that the following is true:

x2 + 7x + 6 = (X + 1 ) (X + 6)

Los alumnos de una clase han formado 4 equipos para hacer un mural en una pared del patio. Los equipos tienen 8,7, 10 y 5 componentes. Si la pared mide 12 m de largo, ¿cuántos metros de pared le corresponde a cada equipo para que sea proporcional al número de componentes?

Answers

Answer:

8 - 3.2m

10- 4m

7- 2.8m

5- 2m

Step-by-step explanation:

Aquí, podemos hacer los componentes en forma de relaciones para conocer la longitud equivalente de cada uno de los componentes a la longitud total de la pared.

Ahora usando los componentes en forma de proporciones, tenemos 8: 7: 10: 5. sumando todos los componentes juntos, tenemos; 8 + 7 + 10 + 5 = 30.

Para 8, tenemos 8/30 * 12 = 3.2 metros

para 7, tenemos 7/30 * 12 = 2.8 metros

Para 10, tenemos 10/30 * 12 = 4 metros

para 5, tenemos 5/30 * 12 = 2 metros

Mabel is the costume manager for a large theater company. She has 20 different hats,
including 4 pork pie hats.
What is the probability that a randomly chosen hat from Mabel's inventory will be a pork pie
hat?
Write your answer as a fraction or whole number.
P(pork pie hat) =
Submit​

Answers

Answer:

4/20 or 1/5 being simplified

Step-by-step explanation:

A daycare center charges $300 per month for preschool and $3.50 per hour every hour after preschool. The function c = 300 + 3.50h can be used to represent the total cost c of monthly preschool and childcare, where h is the number of hours spent in childcare after preschool. If the one month charges for one child totaly $637.75, what was the total number of hours the child spent in childcare after preschool? *

Answers

Answer:

The total number of hours the child spent in childcare after preschool was 96.5.

Step-by-step explanation:

The cost of the preschool, in function of the number of hours that the child spent there, is given by the following equation:

[tex]c(h) = 300 + 3.5h[/tex]

If the one month charges for one child totaly $637.75, what was the total number of hours the child spent in childcare after preschool?

This is h when c(h) = 637.75. So

[tex]c(h) = 300 + 3.5h[/tex]

[tex]637.75 = 300 + 3.5h[/tex]

[tex]3.5h = 337.75[/tex]

[tex]h = \frac{337.75}{3.5}[/tex]

[tex]h = 96.5[/tex]

The total number of hours the child spent in childcare after preschool was 96.5.

Which equation can be used to find the unknown length, a, in this triangle?

Answers

You need more information. Maybe a picture?

Answer:

To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides. This number divided by 2 is the width.

Step-by-step explanation:

I need help with question number 3

Answers

Hey there! I'd be delighted to help you out!

First, let's write down our expression!

[tex](x^2-x)+(8x-2x^2)[/tex]

When we look at this expression, we see that all of the numbers are terms, or numbers that are added. We have four terms in this equation, which are:

[tex]x^2, -x, 8x, -2x^2[/tex]

Now, to simplify, we want to combine like terms. Like terms are numbers that have the same variable (or no variable) and are raised to the same power. 1 and 5 are like terms because they both have no variable and they are both raised to the power of 1 (any number that is itself is raised to this power). 4x and 12x are like terms because they both have an x and a power of 1. 4y and 5x are not like terms because they have different variables. 4x³ and 2x² are not like terms because they are raised to different powers.

Now, we see that  with our numbers, x² and -2x² are like terms, and -x and 8x are also like terms. We can combine accordingly.

[tex]x^2-2x^2=-x^2\\\\-x+8x=7x[/tex]

Now we combine to get our simplified expression!

[tex]-x^2+7x[/tex]

I hope that this helps! Have a wonderful day!

Grade 7 . Pre-Assessment
4. David has a total of 72 game cards in his collection. A friend gave him 27 of the
cards. David purchased the rest of the cards in packages of 9 at the store.
How many packages of cards did David purchase?
A. 6
B. 5
C. 4
D. 3​

Answers

Answer: 5



Step by step:
Take 72-27=45
then 45/9=5
David purchased five packs
Use subtraction

Solve. - 5 3/4 - 3 1/2

Answers

Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form: −37/4

Step-by-step explanation:

The answer is -9.25 I hope I helped

Trace a pattern block. Divide it into two equal parts, and write a unit fraction to describe the area of each part. Explain your work.

Answers

Answer:

1/2

Step-by-step explanation:

The unit fraction for an area (or anything, for that matter) divided into 2 parts so the area of each one is equal to each other and be a haft of the original block. Please have a look at the attached photo.

Jessie installed 12 more axles than the number of engine blocks her friend Gus installed yesterday. Write an equation for g, the number of engine blocks Gus installed yesterday.

Answers

Answer:

g = j - 12

Step-by-step explanation:

We know that if g is Gus' number of engine quantity, then j is Jessie's number of engine quantity, from this statement we have that Jessie made 12 more than Gus, therefore:

j = g + 12

if we solve for g:

g = j - 12

which is the same as saying that Gus made 12 number of engine less than Jessie

Answer:

g = x - 12

where x is the number of axles installed by Jessie

Step-by-step explanation:

Using a simple analogy. If a man has 7 cars while his friend has 3 cars, The statement may be written as the man has 4 cars more than his friend. The 4 cars being the difference between the number of cars he has and the number his friend has.

As such, if the number of engine blocks installed by Gus is g and Jessie installed 12 more axles than the number of engine blocks Gus installed yesterday, where Jessie must have installed x axles,

x = g + 12

Such that

g = x - 12

Find the area of the shaded regions:

Answers

Answer:

You are gonna need to gimme that  shaded area

Step-by-step explanation:

I cant do it without them

Answer:

144

Step-by-step explanation:

72 the 72 it equals it and plus they are adjacent

Find the length of the third side to the nearest tenth.

Answers

Answer:

What’s the third length?..

Step-by-step explanation:

Consider rectangle ABCD with diagonals BD and AC

intersecting at

Which is true about the angle relationships in the

rectangle? Check all that apply.

BEA and 2 CED are vertical angles and equal

76

ZABE and 2 CBE are complementary angles,

BEC and CED are vertical angles,

-------

BEA and AED are supplementary angles

whose sum is 180°

O

BEC and

AED are adjacent angles,

Answers

Answer:

BEA and AED are supplementary angles  whose sum is 180°

Step-by-step explanation:

complete question is:

Consider rectangle ABCD with diagonals BD and AC  intersecting at E.

Which is true about the angle relationships in the  rectangle? Check all that apply.

BEA and 2×CED are vertical angles and equal  76 ABE and 2×CBE are complementary angles, BEC and CED are vertical angles,BEA and AED are supplementary angles  whose sum is 180° BEC and  AED are adjacent angles,

Answer:

it is abd

Step-by-step explanation:

The radius of a circle is 6mm. What is the area of the shaded portion of the circle.

Answers

The area of the shaded portion of the circle is [tex]\frac{29\pi}{3} \ mm^{2}[/tex]. The correct option is b) 29 π mm² got to station 3

Area of a sector

From the question, we are to determine the area of the shaded portion.

The shaded portion in the circle is the major sector.

The area of a sector is given by the formula,

[tex]A = \frac{\theta}{360 ^\circ} \times 2\pi r[/tex]

Where [tex]\theta[/tex] is the angle subtended by the sector

and r is the radius of the circle.

From the given information,

r = 6 mm

and [tex]\theta[/tex] is the angle subtended by the major sector

Therefore

[tex]\theta = 360^\circ - 70^\circ[/tex]

[tex]\theta = 290^\circ[/tex]

Putting the parameters into the formula, we get

[tex]A = \frac{290^\circ}{360 ^\circ} \times 2\pi \times 6[/tex]

Simplifying

[tex]A = \frac{29}{3} \tim\pi \ mm^{2}[/tex]

Hence, the area of the shaded portion of the circle is [tex]\frac{29\pi}{3} \ mm^{2}[/tex]. The correct option is b) 29 π mm² got to station 3

Lear more on area of a sector here: https://brainly.com/question/10090807

PLZ HELP ME I DON'T WANNA FAIL THIS

Answers

Answer

Step-by-step explanation:

sentence 3 does not use a correct verb.

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