The point p=(2/5,y) lies on the unit circle below what is the value of y in simplest form
Answers
Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
Related Questions
If f(x) = 4x + 5 and fog(x) = 8x + 13 then find g(x).
Answers
Answer:
given
f(x).4x+5
fog(x).8x+13
now
fog(x):8x+13
4x+5(g(x)):: 8x+13
g(x):: 8x+13/4x+5
Answer:
g(x) = 2x + 2
Step-by-step explanation:
One is given the following information:
f(x) = 4x + 5f o g (x) = 8x + 13One is asked to find the following:
g(x)Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:
f(g(x)) = 8x + 13
Substitute the given infromation into the equation:
4(g(x)) + 5 = 8x + 13
Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:
4(g(x)) + 5 = 8x + 13
Inverse operations,
4(g(x)) + 5 = 8x + 13
4(g(x)) = 8x + 8
g(x) = (8x + 8) ÷ 4
g(x) = 2x + 2
f (x) = x - 5. Find f'(x) and its domain.
Answers
Answer:
C
Step-by-step explanation:
f(x) = √x - 5
domain: [0. ∞)
range: [-5, ∞)
Let y = √x - 5
√x = y+5
x = (y+5)²
Switch x and y:
y = (x+5)²
f⁻¹(x) = (x+5)²
domain of f⁻¹(x) is the range of f(x): [-5,∞)
Find the value of x
9
7
X
9
Answers
Answer:
13.41
Step-by-step explanation:
You are so welcomed
The measure of each of the remaining angles in the right angle triangle is 45 degrees.
To find the measure of the remaining angles in the triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees. Since we know one angle is 90 degrees, we can find the measure of the other two angles by subtracting 90 from 180.
Let's call the remaining two angles A and B. Thus, we have:
Angle A + Angle B + 90 degrees = 180 degrees.
Rearranging the equation, we get:
Angle A + Angle B = 90 degrees.
Since the two sides of the triangle adjacent to the right angle are equal (given as 9 and 9), we can conclude that the remaining two angles are congruent (equal). Let's call the measure of each of these angles x.
Therefore, we have:
x + x = 90 degrees.
Simplifying, we get:
2x = 90 degrees.
Dividing both sides by 2, we find:
x = 45 degrees.
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Solve the following system of equations for x: xy = 6
3y = x - 3
Answers
Answer:
B
Step-by-step explanation:
rearrange 3y = x-3 as x=3y+3 sub in for x in xy=6
(3y+3)(y)=6
solve by factoring 3y^2+3y-6=0
3(y-1)(y+2) = 0
y= 1, -2
sub y back in to either equation but for ease xy=6
x(1)=6 = 6
x(-2)=6 = -3
Difference between 5429 and 5907 to the greatest place.
Answers
answer- u have to subtract the great no. from the smaller one
Given numbers are 5429 and 5907..
To find the difference we should subtract..
5907
- 5429
-------------
478
_______
#Answered by: Cutest Ghost87.5 into fraction pls help I need this Monday
Answers
Answer:
[tex]87.5 = \frac{175}{2} = 87 \frac{1}{2} [/tex]
Answer:
7/8 im not 100% sure i could be wrong tho
Simplify the expression. Express your answer as an improper fraction in simplest form.
Answers
Answer:
Step-by-step explanation:
3/40 is the correct answer
find the range of the function f (x) = 2x + 5 for the domain 2,5,7
Answers
Answer:
The range is {9,15,19}
Step-by-step explanation:
f (x) = 2x + 5
Let x = 2
f (2) = 2*2 + 5 = 4+5 = 9
Let x = 5
f (5) = 2*5 + 5 = 10+5 = 15
Let x = 7
f (7) = 2*7 + 5=14+5 = 19
The domain is {2,5,7}
The range is {9,15,19}
Answer:
i think what you wrote is that the domain is 2 to 5.7.
so you plug in these two numbers inside the equation cause domain means the distance in the x axis so this is how it goes.
2(2) + 5 = 9
2(5.7) +5= 16.4
so the range is 9 to 16.4
hope that answers your question...
Given a sphere with radius r, the formula 4 r2 gives
O A. the volume
O B. the surface area
O c. the radius
O D. the cross-sectional area
Answers
Answer: surface area
Step-by-step explanation:
If a ants can dig b tunnels in c hours, how many tunnels can b ants dig in a hours?
Answers
9514 1404 393
Answer:
b²/c tunnels
Step-by-step explanation:
The number of tunnels per ant-hour is ...
b/(ac)
Multiplying that by the new number of ant-hours, we have ...
(b/(ac))(ab) = b²/c . . . . tunnels
Solve for d.
d - 5
———- = -1
-3
Answers
Answer:
d = 8
Step-by-step explanation:
(d-5)/ -3 = -1
Multiply each side by -3
(d-5)/ -3 *-3 = -1*-3
d-5 = 3
Add 5 to each side
d-5+5 = 3+5
d = 8
How would x^3+8 be expressed in factored form
Answers
[tex]\it x^3+8=x^3+2^3=(x+2)(x^2-2x+4)\\ \\ \\ a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
In a closed box there are 7 blue balls and 5 red balls. Randomly pick one from the box one at a time until the ball is green, then stop. Find the probability that the person stops after the 4th time
Answers
Answer:
1/7 is the probabiltiy
Step-by-step explanation:
Can someone please help me? Please C: And thanks!
How much would you need to deposit in an account each month in order to have $50,000 in the account in 8 years? Assume the account earns 4% annual interest compounded monthly.
Answers
Answer:
$540.98
Step-by-step explanation:
future value= $ 50,000
number of deposits (n)= 8*12 = 96
rate (r) = 4% per month
= 4÷12 per annum
= 0.33% p.a
i = 0.33÷100
= 0.0033
We know,
Future value of annuity = P÷i [ (1 + i)^n - 1 ]
$50,000 = P÷ 0.0033 [ ( 1+0.0033)^96 - 1]
$50,000 * 0.0033=P [ (1.0033)^96 - 1 ]
$165 = P*0.305
P = $165÷0.305
P = $ 540.98
Rough::
let x= 1.0033)^96
log x = 96 * log (1.0033)
log x = 0.1156
x = Antilog (0.1156)
= 1.305
1.305 - 1 = 0.305
solve 8x=5x+3 pls pls pls
Answers
Answer:
x = 1
Step-by-step explanation:
8x = 5x + 3
Subtract 5x from both sides
8x - 5x = 5x - 5x + 3
Simplify
3x = 3
Divide both sides by 3
3x/3 = 3/3
Simplify
x = 1
Rabi Sahu fixed the marked price of his radio to make a profit of 30 %. Allowing 15 % discount on the marked price, the radio was sold. What percent profit did he make?
Answers
The percent profit that Rabi made will be 10.5%
Let's assume that the price of the house is $100.
Since he fixed the marked price of the good to make a profit of 30%, then the price will be:
= $100 + (30% × $100)
= $100 + $30
= $130
Now, there is a discount of 15%, then the selling price of the good will be:
= $130 - (15% × $130)
= $130 - (0.15 × $130)
= $130 - $19.50
= $110.50
Then, the percentage of profit made will be:
= [($110.50 - $100) / $100] × 100%
= $10.50/$100 × 100%
= 10.5%
In conclusion, the percent profit that he makes is 10.5%.
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Find theta to the nearest tenth of a degree, if theta is between 0 degrees and 360 degrees for sin theta = 0.4649 with theta in quadrant 2
Answers
9514 1404 393
Answer:
152.3°
Step-by-step explanation:
The arcsine function only gives angles in quadrants I and IV. Since this is a quadrant II angle, its value will be ...
θ = 180° -arcsin(0.4649) = 180° -27.7°
θ = 152.3°
Explain why this quadrilateral is not a parallelogram.
Answers
Answer:
because only two of it's sides are parallel
Answer:
In this quadrilateral, opposite sides are not parallel. So, this quadrilateral is not a parallelogram.
Step-by-step explanation:
In Parallelogram, opposite sides are parallel
Find the sum of the first 100 terms of the sequence below:
-19, -15, -11, -7, -3, ...
S100
Answers
Answer:
17900
Step-by-step explanation:
First term a = -19
common difference d = -15-(-19) = 4
number of terms, n = 100
sum of first 100 terms,
n/2(2a+(n-1)d)
= 100/2(2×(-19)+(100-1)4)
= 50×(-38+99×4)
= 50×358
= 17900
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answers
Answer:
B
Step-by-step explanation:
The inequality will be 35000-320m>0
A new screening test for West Nile Virus is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. 300 subjects are screened at a clinic during the first year the new test is implemented. (Assume the true prevalence of West Nile Virus among clinic attendees is 10%.), The predictive value of a positive test is:
Answers
The predictive value of a positive test is is 0.43.
------------------
This question is solved using the concepts of sensitivity and specificity.
Sensitivity: It is the true negative rate, that is, the proportion of people without the disease that test negative.Specificity: It is the true positive rate, that is, the proportion of people with the disease that test positive.------------------
Sensitivity of 60% means that of the 100 - 10 = 90% of people without the disease, 60% test negative and 100 - 60 = 40% test positive.Specificity of 70% means that of the 10% with the disease, 70% test positive.------------------
The predictive value of a positive test is:
Probability of a positive test, which is 40% of 90% plus 70% of 10%, so:
[tex]p = 0.4\times0.9 + 0.7\times0.1 = 0.43[/tex]
The predictive value of a positive test is is 0.43.
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What is the prime factorization of 75
Answers
Step-by-step explanation:
The prime fractorization of 75 is 3×5×5 or 3×52
The final price of the textbook for an English literature course is 13.5% more than the listed price when tax and shipping costs are included. If the listed price is $147, what is the final price of the textbook?
(Round to the nearest dollar.)
Answers
Answer:
The final price of the textbook rounded to the nearest dollar is $167
Step-by-step explanation:
To solve this problem, we need to find out what 13.5% of $147 equals.
13.5% = 0.135
0.135 x $147 = $19.845
$147 + 19.845 = 166.845
Round to the nearest dollar to get $167
name all sets of numbers to which each real number belongs
Answers
Answer:
1. Natural Number
2. Integer
3. Rational Number
4. Rational Number
5. Irrational Number
6. Rational Number
7. Rational Number
8. Natural Number
9. Irrational Number
10. Integer
11. Irrational Number
12. Natural Number
Maximum and minimum value
Answers
Answer:
Maximum: 1
Minimum: -1
Step-by-step explanation:
To solve this, we can find the derivative of the function and then solve for when the derivative is equal to 0, finding the local maximum and minimum values in this function. Then, we can compare those points to the endpoints of the interval to find the maximum and minimum.
Using the Quotient Rule, we can say that
(f/g) ' = (f'g - fg')/(g²)
[tex]\frac{2x}{x^2+1}dx = \frac{\frac{d}{dx}(2x) * (x^2+1) - \frac{d}{dx} (x^2+1) * (2x) }{(x^2+1)^2} \\= \frac{2 *(x^2+1) - (2x)*(2x)}{(x^2+1)^2} \\[/tex]
Since we just need to solve for 0, we can disregard for the bottom part, resulting in
2(x²+1)-(2x)(2x) = 0
2x²+2-4x² = 0
2-2x² = 0
add 2x² to both sides to isolate the x² and its coefficient
2x² = 2
divide both sides by 2
x²=1
x = ±1
Therefore, we have 4 possible values for the maximum and minimum over this interval:
-2, -1, 0, 1
Trying each of these numbers into f(x),
f(-2) = -4/5
f(-1) = -2/2 = -1
f(0) = 0/1 = 0
f(1) = 2/2 = 1
Therefore, the maximum and minimum values of the function over the given interval are 1 and -1 respectively
Which is an estimate of V75 to the
nearest whole number?
Answers
Answer:
9
Step-by-step explanation:
if that v is root symbol
choose a expression that represents three less than seven times a number
Answers
The seven times is 7x.
The three less than is the -3
Answer:
7x-3
Step-by-step explanation:
First write the 7 times a number
7x
Then subtract 3
7x-3
Trên tập hợp số thực cho quan hệ tương đương T như sau: m, n : mTn ⇔ m^3-n^3= m-n . Tìm lớp tương đương của 0 và lớp tương đương của 2021
Answers
Answer:
where are u from bro?
Step-by-step explanation:
I didn't understand your language.
Julio is paid 1.1 times his normal hourly rate for each hour he works over 28 hours in a
week. Last week he worked 43 hours and earned $631.90.
Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation
how you know that your answer is reasonable.
The earnings equation is $631.90 =
Julio's hourly l'ate is $
per hour.
This is reasonable because working 43 hours at a rate of $14 per hour is
43 · 14 = 43(10 + 4) = 430 + 172 =
and $
is close to $631.90.
Answers
Answer:
43-28= 15 extra hours
normal hourly rate = a
extra hourly rate = 1.1a
28a + 15(1.1a) = 631.90
28a + 16.5a = 631.90
Which expression is equivalent to 3t-5+8t+3
Answers
Answer:
11t-2
Step-by-step explanation:
Add like terms: 3t+8t=11t -5+3=-2 11t-2
Answer: 11t-2
Step-by-step explanation:
First combine like terms
=3t-5+8t+3
= (3t+8t)-5+3
= 11t - 2
Therefore answer is 11t - 2
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