The point P=(x,1/2 ) lies on the unit circle shown below. What is the value of x x in simplest form?
Answers
Answer:
The answer is below
Step-by-step explanation:
A unit circle is a circle on the coordinate plane with a radius of 1 unit. The unit circle center usually lies on the origin.
The equation of a circle is given as:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius of the circle.
As seen in the diagram attached, the center of the circle is at the origin (0, 0) and the circle is a unit circle with a radius of 1. Hence:
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = 1²
x² + y² = 1
Given the point P(x, 1/2) lies on the circle. To find x, substitute y = 1/2:
x² + (1/2)² = 1
x² + 1/4 = 1
x² = 1 - 1/4 = 3/4
x² = 3/4
x = √(3/4)
[tex]x=\pm\frac{\sqrt{3} }{2} \\\\Hence\ P=(\frac{\sqrt{3} }{2},\frac{1}{2} )\ or\ P=(-\frac{\sqrt{3} }{2},\frac{1}{2} )[/tex]
Related Questions
What number is equal to 58 × 5-6? 5 -2 5 2 5 48 5 -14
Answers
Step-by-step explanation:
please, write the problem statement properly. it is not clear what you are asking for.
for example, the way how you wrote it, the first expression would be
58 × 5 - 6
and that would be (remember, multiplication and division happen before any additions or subtractions)
58 × 5 - 6 = 290 - 6 = 284
nothing on the right side of numbers fits to that.
so, I am speculating. did you mean
58 × (5-6) ?
in that case we get
58 × (5-6) = 58 × (-1) = -58
and then I assume that the right side of all the numbers includes also operations (like +, -, ...), as I see no -58 in the list of numbers.
and then I just propose that the right side could look like
-2×5 - 48 (which would also be -58).
but again, this could be something completely different.
so, please, write your problem statement again. and carefully.
Find the solution to the system
of equations (look at picture)
answer both please
Answers
Answer:
(-1, 1)
Step-by-step explanation:
(-1, 1) is the solution to this system of equations because it is the point of intersection. If you would want to solve this algebraically, you would need to use the equations of each line.
Answer:
the answer is (-1,1)
i think we needed to calculate the coordinates
hope it helps
probability................................
Answers
Answer:
outcome 10
simple space10
A 5
B 5
C 5
Step-by-step explanation:
Hope this helps!!!
which of the following are equation for the line shown below.(-2,4) and 1,-5)
Answers
= -9/3
= -3
y = -3(x - 1) -5
y = -3x + 3 - 5
y + 3x = -2
A=1/2 h(x+y) make x the subject
Answers
Answer:
Step-by-step explanation:
A =1/2 *h (x+y)
A =hx+hy/2
A*2 =hx+hy
2A =hx+hy
2A - hy = hx
(2A -hy)/h = x
Answer:
x = [tex]\frac{2A-hy}{h}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] h(x + y) ← multiply both sides by 2 to clear the fraction
2A = h(x + y) ← distribute
2A = hx + hy ( subtract hy from both sides )
2A - hy = hx ( divide both sides by h )
[tex]\frac{2A-hy}{h}[/tex] = x
If f(x) = 5x² – 2x + 7 and g(x) = -2x2 +6x + 3
then f (x)-g(x) =
Answers
Answer:
7x² - 8x + 4
Step-by-step explanation:
f(x) - g(x)
= 5x² - 2x + 7 - (- 2x² + 6x + 3) ← distribute parenthesis by - 1
= 5x² - 2x + 7 + 2x² - 6x - 3 ← collect like terms
= 7x² - 8x + 4
Can someone help me? It's urgent and thank you!
Answers
Answer:
option A
Step-by-step explanation:
[tex]\frac{x+ 3}{12x} \ \cdot \ \frac{4x}{x^2 +x - 6}\\\\= \frac{x+ 3}{12x} \ \cdot\ \frac{4x}{x^2 +3x - 2x - 6}\\\\= \frac{x+ 3}{12x} \cdot \frac{4x}{x(x + 3) -2(x+3)}\\\\= \frac{x+ 3}{12x} \cdot \frac{4x}{(x + 3)(x -2)}\\\\= \frac{1}{12x} \ \cdot \ \frac{4x}{(x - 2)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\\\= \frac{1}{3} \ \cdot \ \frac{1}{(x - 2)}\\\\= \frac{1}{3(x - 2) }[/tex]
the slope of the line
Answers
Answer: -2
Explanation: On the image we can see it goes down 4 units and right 2. Giving us the slope [tex]\frac{-4}{2}[/tex]
Simplified that is -2 which is the slope of the line
Ayuda,help,ayuda,help
Answers
Answer:
14/3
Step-by-step explanation:
Set up two ratios and cross multiply. Solve for missing segment.
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{7}[/tex]
3x = 14
x = 14/3
The graph shows the absolute value parent function.
5
-5
5
-5
Which statement best describes the function?
O A. The function is increasing when x < 0.
Answers
Answer:
C, never negative
absolute value is like asking for "how much away from zero", so -5 is 5 away from zero.
The graph of the function is increasing when x>0.
What is graph?Graph a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
here, we have,
We know, cube root parent is:
The basic parent cube root function is of the form f (x) = ∛x. It increases on the interval (-∞, ∞). It increases on the interval [0, ∞). It is positive on (0, ∞) and negative on (-∞, 0). It is a non-negative function always (on [0, ∞)). Its absolute min is 0 but no absolute max. Its domain and range is the set of all real numbers.
Given,
The function f(x) = ∛x
Let x = 1, we get f(x) = 1,
x =2, f(x) = 8
if x =3, f(x) = 27.
As we know, with increase in the value of x, the value of f(x) is also increasing.
To know more about graph, visit:
brainly.com/question/19205767
#SPJ7
pls help pls show how you got the answer
Answers
Answer:
L ACB = 25 ( L at centre = 2× L at circumference)
prove
sum = 75
centre = 50
then L AOB +ACB = 75
50 + L ACB =75
L ACB = 75 - 50
then L ACB= 25
20 points!!! Tysmmm!! If you can help with other questions on my page to that would mean so much
Answers
Answer:
(2w+2)(w+8) ≤ 100
Step-by-step explanation:
Answer:
●(2w+2)(w+8)< 100 represents the inequality that combined the area of Garden and walk away.
Step-by-step explanation:
this is correct!!
Finish the congruence statement for the triangles in question #4 by filling in the blank:
BCD = ???
Answers
Answer:
ASA
Step-by-step explanation:
Given the lines, we know ED = CD
Given the right angles, we know angle DEF = angle BCD
Because angles BDC and FDE are on the same line, and are opposite of each other, those are congruent as well
Adwoa received a commission of 20% on bread she sold. In one week, Adwoa's commission was Gh¢540. How much bread did she sell during that week. And find her average daily commission.
Answers
Answer:
a). 2700
b). 385.7
Step-by-step explanation:
According to the Question,
Given that, Adwoa received a commission of 20% on the bread she sold. In one week, Adwoa's commission was 540.
let x be the total cost of bread she sells during the week.
a). Thus, 20% of x = 540
x = 540 × (100/20) ⇒ 2700 is the total cost of bread she sells during the week.
b). Now, her average daily commission is 2700/7 ⇒ 385.7
Select the two values of x that are roots of this equation.
x2 + 3x - 6 = 0
A. X =
-3+15
B.
-3-133
X=
C. x. -3+2/
-3-15
Answers
Answer:
b
Step-by-step explanation:
The roots of the quadratic equation x² + 3x - 6 = 0 are, x = [- 3 + √(33)]/2,
x = [- 3 - √(33)]/2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
We any to find any types of roots of a quadratic equation, real, complex or imaginary we use the formula,
[- b ± √(b² - 4ac)]/2a.
Therefore, The roots of the quadratic equation x² + 3x - 6 = 0 is,
x = [- 3 ± √(3² - 4×1×-6)]/2×1.
x = [- 3 ± √(9 + 24)]/2.
x = [- 3 ± √(33)]/2.
learn more about quadratic equations here :
https://brainly.com/question/30098550
#SPJ7
The library has 215 new books 155 of those books already have been put on shelves .the rest of the books are divide equally amount 5 boxes
Answers
Answer:
Ok to do this question we must first put it into a algebraic equation.
215=5x-155
This is are equation. lets first get rid of the 155 by adding it to the 215 which is 370.
370=5x
Ok now we will divide 370 by 5 which is 74.
x=74
Your Welcome
BIFFY OUT!!!
At what rate, in minutes per lap, does this swimmer swim?
Answers
Answer:
1.6
Step-by-step explanation:
all u gotta do is divide 6.4 by 4:)
hope that helps!<3
Could someone help me with this?
Answers
Answer:
1.16777216
2.279936
3.32768
4.49
[tex]\longrightarrow{\green{ a) \:16,777,216 }}[/tex]
[tex]\longrightarrow{\green{ b)\: 279,936 }}[/tex]
[tex]\longrightarrow{\green{ c) \: 32,768 }}[/tex]
[tex]\longrightarrow{\green{ d) \:49 }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
a)
[tex] {4}^{9} \times {4}^{3} \\ = {4}^{9 + 3} \\ = {4}^{12} \\ =\:16,777,216[/tex]
b)
[tex] {6}^{5} \times {6}^{2} \\ = {6}^{5 + 2} \\ = {6}^{7}\\=\: 279,936[/tex]
c)
[tex] {8}^{6} \div {8}^{1} \\ = {8}^{6 - 1} \\ = {8}^{5} \\=\:32,768[/tex]
d)
[tex] {7}^{8} \div {7}^{6} \\ = {7}^{8 - 6} \\ = {7}^{2}\\=49 [/tex]
Note:-[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} \\ {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
HELP ASAP
Jim went to the bank and made of a deposit of $525 into his checking account. He had both cash and a check. The check he deposited was written for $250. How much cash did he deposit? Construct an equation to represent the situation. Make sure to identify and label your variable. Solve for the variable and describe your answer. Show your work and prove your solution to be correct.
Answers
Amount of Cash deposited = $275
For this equation, you are looking to find the amount of cash specifically withdrawn. The ‘x’ variable represents this.
The ‘d’ variable represents the total deposit amount, which is $525.
And the ‘c’ variable represents the check amount that was deposited.
All you have to do to solve it is replace the variables with the numbers provided.
x = 525 - 250
x = 275
can someone pls help for brainlest
Answers
Answer:60
Step-by-step explanation:20x6=120 120/2=60
Answer:
200 cubic centimetres
Step-by-step explanation:
Length = [tex]20 \: cm[/tex]
Width = [tex]6 \: cm[/tex]
Height = [tex]5 \: cm[/tex]
Volume = [tex] \frac{1}{3} \times w \times l \times h[/tex]
[tex] = \frac{1}{3} \times 20 \times 6 \times 5[/tex]
[tex] = \frac{20}{3} \times 6 \times 5[/tex]
[tex] = \frac{20}{3} \times (3(2)) \times 5[/tex]
[tex] = 20 \times 2 \times 5[/tex]
[tex] = 40 \times 5[/tex]
[tex] = 200 \: {cm}^{2} [/tex]
Hope it is helpful...which inequality is shown in the graph
Answers
Answer:
Less than.
Step-by-step explanation:
Express 1800 ml as percentage of 2.1 L
Answers
Answer:
1400 ml is 66.67% of 2.1 L
To express one number as a percentage of another, form a fraction using these two numbers and multiply it by 100. Note that the number that is being expressed as a percentage is placed in the numerator of the fraction.
WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing
Answers
Answer:
A. [tex]2x^2y\sqrt[3]{7xy^2}[/tex]
Step-by-step explanation:
When given the following problem,
[tex]\sqrt[3]{56x^7y^5}[/tex]
The problem asks one to find the cube root of the value under the radical. The cube root of a number is essentially a value that must be multiplied by itself three times to get the result under the radical. An easy way to do this is to prime factorize the value under the radical sign. This will allow one to see the components of the number, thus making it easier to take value out of the radical;
[tex]=\sqrt[3]{7*2^3x^7y^5}[/tex]
Now divide each of the exponents by (3), write the whole result outside the radical, and the remainder under the radical,
[tex]=2x^2y\sqrt[3]{7xy^2}[/tex]
Find the roots of the quadratic equation (4p-1)² = 4p²
( Please show me how it works , Thankiuuu ༎ຶ‿༎ຶ )
Answers
Answer:
p = 1/2
Step-by-step explanation:
(4p - 1)^2 = 4p^2
(4p - 1)^2 =(2p)^2
4p - 1 =[tex]\sqrt{(2p)^2}[/tex]
4p - 1 =2p
4p - 2p =1
2p = 1
p =1/2
Find the perimeter of the composite figure
Answers
Answer: 172.3ft
Step-by-step explanation:
Help Please question in the picture
Answers
Answer:
Option (1)
Step-by-step explanation:
Given figure in the picture has two parallel sides and fulfilling the property of a trapezium.
Since, an isosceles trapezium contains two parallel sides and other pair of the sides are equal in length.
Therefore, the given trapezium can't be an isosceles trapezium.
Option (1) will be the correct option.
HELPP!
A: Line a
B: Line b
C: Line c
D: None of the lines fit the data well
Answers
Answer:
B: Line b is the correct answer
para realizar una minga en una escuela sehan reunido 750 personas .en la organizacion de las actividades se solicito a 1/15 de total para limpiar los patios y jardines a 2/25 del total arreglar bancas y al rwsto de las peronas se les pidio limpiar las pertas y ventanas de toda la institucion
¿cuantas personas limpiam los patios y jardines ?
¿cuantas personas pintan las paredes ?
¿cuantas personas arreglan las bancas ?
¿cuantas personas limpiam las puertas y ventanas ?
pliss ayuda espara manaña hasta las 5 am :")
Answers
help
dhgdfdfyfyfgfgfjfgfghfhgfdhgdfh
Answers
1=26
2=17
Answer:
5=26
14=17
n=1
31n=31*1=31
can someone answer B for me please and thank you sm
Answers
Answer:
a = 1/8
b = 8
Step-by-step explanation:
a (1/2) ^3 = (1/2) *(1/2) * (1/2) = 1/8
b( 1/2 ) ^ -3 The negative exponent means 1 / (1/2)^3 = 1/ (1/8) = 8
