what are the coordinates of a point on the unit circle if the angle formed by the positive x- axis and the radius is 45°??
Answers
sin(angle( = y-coordinate / radius = y-coordinate / 1 = y-coordinate = y
cos(angle) = x-coordinate / radius = x-coordinate / 1 = x
Then:
y = sin(angle) = sin(45°) = √2 / 2
x = cos (angle) = cos (45°) = √2 / 2
=> Answer: (√2 / 2 , √2 / 2), which is the option A)
Related Questions
Which inequality is correctly represented by this graph
A) 3x-y>3
B) x-3y>=2
C) 3x-y<=3
D)x-3y>2
Answers
You should first solve each equation for y.
Eliminate answer choices with wrong slopes or y intercepts.
Then, because it is a dotted line, the answer will only be < or >.
And because the area is shaded to the right, it would mean that x > y.
So the answer is A) 3x - y > 3
Answer:
The correct option is A.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is
[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0)[/tex]
[tex]y+3=3x[/tex]
The (0,0) is not in the solution set. So check the equation be (0,0).
[tex]0+3=3(0)[/tex]
[tex]3=0[/tex]
This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.
The required inequality is
[tex]y+3<3x[/tex]
[tex]3<3x-y[/tex]
It is also written as
[tex]3x-y>3[/tex]
Therefore the correct option is A.
Suppose $x$,$y$, and $z$ form a geometric sequence. if you know that $x+y+z=18$ and $x^2+y^2+z^2=612$, find the value of $y$.
Answers
r = y/x = z/y
That is,
y² = xz (1)
We are given:
x + y + z = 18
Therefore
x + z = 18 - y (2)
Also,
x² + y² + z² = 612
Therefore, from (1), obtain
x² + z² + xz = 612
(x + z)² - xz = 612
From (1) and (2), obtain
(18 - y)² - y² = 612
324 - 36y + y² - y² = 612
-36y = 288
y = -8
Answer: y = -8
We use the information that $x$, $y$, and $z$ forms a geometric sequence, and that $x + y + z = 18$ and $x^2 + y^2 + z^2 = 612$ to set up two equations in terms of $y$. These can be solved simultaneously to get the value of $y$.
Explanation:The problem involves a geometric sequence and two simultaneous equations in mathematics. Given $x$, $y$, and $z$ are in a geometric sequence, then they can be represented as $x=y/r$, $y=y$, $z=yr$, where $r$ is the common ratio. This sequence gives us the first equation, $ x + y + z = 18 $.
We have another given equation which is $ x^2 + y^2 + z^2 = 612 $. Substituting $x$, $y$ and $z$ with the terms of the geometric sequence in the second equation, we have $y^2(1/r^2+1+r^2)=612$. Now we have two equations: $ y(1/r+1+r)=18 $ and $ y^2(1/r^2+1+r^2)=612 $, which we can solve simultaneously to find the value of $ y $.
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What is the slope of y-9=-2(x-8)
Answers
Let's write the problem: [tex]y-9=-2\left(x-8\right)[/tex]
We have to isolate for y.
[tex]y-9=-2\left(x-8\right)[/tex]
Apply the distributive property.
[tex]y-9=-2x+16[/tex]
Add 9 to both sides.
[tex]y-9+9=-2x+16+9[/tex]
[tex]y=-2x+25[/tex]
A line equation is on the form of [tex]y=mx+b[/tex]. The [tex]m[/tex] represents the slope. So, our answer would be:
[tex]m=-2[/tex]
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
To find the slope, we must first simplify this equation, then turn it into the slope-intercept form :)
So, simplify.
y - 9 = -2x + 16
Remember : Slope-intercept form ~ y = mx+b
Where m = slope, and b = y-intercept
So, now we must add 9 to both sides.
y = -2x + 16 + 9
Simplify.
y = -2x + 25
Since (-2) is in the (m) spot, and m = slope, then -2 is our slope.
Slope = -2
~Hope I helped!~
PLEASE HELP!!!!!
Which function has the following domain and range?
Domain: {−7,−3,0,4,12}
Range: {−5,1,2}
Select one:
a. {(−7,12),(−5,2)}
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
c. {(4,1),(−3,−5),(12,2),(0,−5),(−7,1)}
d. {(−5,4),(2,12),(1,−3),(−5,−7),(1,0)}
Answers
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
fgh is a right triangle
Answers
Answer:
there is no picture
Step-by-step explanation:
Find the number of ways to listen to 4 different cds from a selection of 15 cds.
Answers
Thus, for this type of problem, the appropriate solution would be combination. The equation would be n!/r!(n-r)!. The factorial (!) is solved as follows: for example, 15! would be 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1. Applying this process, we could now determine the answer.
15!/4!(15-4)! = 1,365 ways
Answer:
The First person who answered it was wrong! Its 32,760 I took the test lol!
Step-by-step explanation:
nPr = n!/(n-r)! <-- The equation used for this.
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth? 99.8° 73.6° 68.2° 52.9°
Answers
If a price is 70$ and the price is now 56$ what is the percent decrease
Answers
70-56 = 14
14/70 = 0.2
0.2 = 20%
The sum of three numbers is 132 . the third number is 7 less than the first. the second number is 3 times the third. what are the numbers?
Answers
x = 7+z
y = 3z
(7+z)+3z+z = 132
5z = 132-7
z = 125/5
z = 25 <=====
x = 7+z
x = 7 + 25
x = 39 <=====
y = 3z
y = 3 × 25
y = 75 <=====
hope it helps :)
The given problem can be solved by setting up and solving a system of linear equations. By assigning variables x, y, and z to represent the three unknown numbers and translating the relationships given in the problem into equations, we can then solve for the unknowns.
Explanation:The subject of this question is algebra and it involves a system of linear equations. Let's denote the three numbers as x, y, and z. We have the following equations based on the problem:
The sum of the three numbers is 132, which gives us the equation: x + y + z = 132. The third number (z) is 7 less than the first (x), which gives us the equation: z = x - 7. The second number (y) is 3 times the third (z), which give us the equation: y = 3z.
Now, let's substitute the second and the third equations into the first to solve for the variables:
Substituting z = x - 7 into y = 3z gives y = 3(x - 7). Substituting z = x - 7 and y = 3(x - 7) into x + y + z = 132 gives x + 3(x - 7) + (x - 7) = 132.
Solving this equation will give the values for x, y, and z that represent the three numbers.
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A carpenter is building a bookcase. The perimeter of the top is 108 in. If the width is 8 in., what is the length of the shelf?
Answers
Perimeter = 2 x length + 2 x width.
Width = 16 (2x 8)
Subtract that from the perimeter (108) to get 92.
92 = 2 x length
Divide 92 by 2 to get 46 = length.
Quadrilateral $abcd$ is a parallelogram. if the measure of angle $a$ is 62 degrees and the measure of angle $adb$ is 75 degrees, what is the measure of angle $adc$, in degrees?
Answers
In the given parallelogram ABCD, angle $a$ is 62 degrees and angle $adb$ is 75 degrees. Angle $bd$ is calculated to be 105 degrees making angle $adc$ the supplementary to $bd$, and therefore also 75 degrees.
Explanation:In a parallelogram, opposite angles are equal and consecutive angles are supplementary (adding up to 180 degrees). In your given quadrilateral $abcd$, the measure of angle $a$ is 62 degrees and $a$ and $adb$ are consecutive angles. Therefore, knowing that angle $adb$ is 75 degrees, angle $bd$ should be the supplementary to $adb$, which is 180 - 75 = 105 degrees. Finally, since $adc$ is a straight line and $bd$ and $dc$ are parts of it, therefore angle $dc$ = 180 - angle $bd$ = 180 - 105 = 75 degrees. So, the measure of angle $adc$ is 75 degrees.
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Segment TR is a mid-segment of triangle ABC. What is the length of segment RC?
A) 5 inches
B) 6 inches
C) 8 inches
D) 10 inches
Answers
answer
A) 5 inches
Write a compound inequality that represents the situation:
all real numbers at least -6 and at most 3
A) -6 < x ≤ 3
B) -6 ≤ x ≤ 3
C) -6 ≥ x ≥ 3
D) -6 < x < 3
Answers
The keywords at least and at most mean that it has to be less than or equal to/more than or equal to.
There is no value for x that can satisfy the conditions for C
-6 ≤ x ≤ 3
Letter B
help me please help me
Answers
The human eye blinks about 6.25x10 to the 6th power times each year. A seal blinks about 1.01x10 to the 3rd power times per year. How many times do a human and a seal blink in one year?
Answers
A seal blinks 1,010 times a year.
The human eye blinks about [tex]\( 6.25 \times 10^6 \)[/tex] times each year, and a seal blinks about [tex]\( 1.01 \times 10^3 \)[/tex] times per year.
To find out how many times a human and a seal blink in one year, we simply take the given values for each. The question provides us with the number of times a human eye blinks in one year as [tex]\( 6.25 \times 10^6 \)[/tex]times. Similarly, it gives us the number of times a seal blinks in one year as [tex]\( 1.01 \times 10^3 \)[/tex] times.
Therefore, without the need for any additional calculations, we can state that in one year:
- A human blinks [tex]\( 6.25 \times 10^6 \)[/tex] times.
- A seal blinks [tex]\( 1.01 \times 10^3 \)[/tex] times.
These values are already given in the question and represent the total number of blinks for each species in a year. No further calculations are required to answer the question as it is asking for the number of blinks in one year, which is directly provided.
The table below represents the displacement of a horse from its barn as a function of time:
Time(hours) x.
0
1
2
3
4
Displacement from barn (feet) y
8
58
108
158
208
part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?
PLEASE HELP!! WILL RATE BRAINLIEST!!
Answers
A. The y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the given table,
y - intercept = 8
Since at time zero the displacement is 8 ft, this means that the horse was already outside the barn initially.
B. The average rate of change of the function represents the slope of the linear equation (m). This can be calculated using the formula:
average rate of change = m = (y2 – y1) / (x2 – x1)
m = (158 – 58) / (3 – 1)
m = 50
C. Since we have determine the y-intercept and the slope, we can formulate the linear equation:
y = m x + b
y = 50 x + 8
The domain is the value of x. When y = 508, x is equivalent to
508 = 50 x + 8
x = 10 hrs
A basket contains six apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and then mix the fruit. All three times, the fruit is an apple. Find the probability of this occuring.
Answers
Now as the 3 events are independent we multiply the probs:-
P( apple picked 3 times) = 6/11 * 6/11 * 6/11 = 216/1331 or about 16.2%
Answer:
16.22%
Step-by-step explanation:
A basket contains six apples and five peaches.
Total fruits in the basket = 6 + 5 = 11
The probability of selecting a piece of fruit is an apple [tex]P_{1}=\frac{6}{11}[/tex]
Now return it to the basket and select a fruit. so all events are independent.
Therefore, the probability of each time selecting an apple is same.
Probability=[tex]P_{1}\times P_{2}\times P_{3}[/tex]
P =[tex]\frac{6}{11}[/tex]× [tex]\frac{6}{11}[/tex]×[tex]\frac{6}{11}[/tex]
=[tex]\frac{216}{1331}[/tex] = 16.22%
The probability of all three times the fruit is an apple is 16.22%
What are the coordinates of the center of the circle whose equation is x^2+y^2-16x+6y+53=0?
Answers
note :
an equation of the circle Center at the w(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : x²+y²-16x+6y+53=0
(x²-16x) +( y²+6y ) +53 = 0
(x² -2(8)x +8² - 8²) +(y² +2(3)x -3²+3² ) +53=0
(x² -2(8)x +8²) - 8² +(y² +2(3)x +3²)-3² +53=0
(x-8)² +( y+3)² = 20
the center is : w(8,-3) and ridus : r = √20
Alive the equation 2 k+2= k+1
Answers
2k + 2 = k + 1
Subtract 1k from both sides.
k + 2 = 1
Subtract 2 from both sides.
k = -1
I hope this helps!
The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
I chose C, but can someone check for me? Thanks :)
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial wildflowers in the first year = 1200
Every year, the number of wildflower is one fourth of the previous year.
So, it form a geometric series:
1200,300,75............
so, using sigma notation we can express the infinite growth of the wildflowers:
[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]
As we know that sum of infinite terms in case of geometric series is given by
[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]
Therefore, there are 1600 wildflowers.
Hence, Third option is correct.
What is the factored form of 2x2 − 7x − 15? (2x + 3)(x − 5) (2x + 5)(x − 3) (2x − 7)(x + 8) (2x + 8)(x − 7)
Answers
(2x + 3)(x - 5) <==
is a factor of (2x+3)(x-5)
A class of 24 students is planning a field trip to a science museum. A nonrefundable deposit of $50 is required for the day-long program, plus a charge of $4.50 per student. Determine a linear function that models the cost, c, and the number of students, s. Which statements about the linear function and its graph are correct? Check all that apply.
A. The linear model is f(s) = 4.5s + 50.
B The linear model is f(c) = 54.5c + 24.
C.The domain is {x| 0 ≤ x ≤ 24}.
D.The range is {y| 50 ≤ y ≤ 158}.
E.The graph is continuous.
Answers
have a nice day:)
Please help!!! (-x/2)+(1/2x)=(-4/x)
Answers
you can't solve that for x because when you multiply both sides by x, 0*x = 0 and [tex]0 \neq 4[/tex]
I think you made a mistake in your typing or something...unless the answer was no solution!
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6
Answers
(x+5)/[(9-x+4)/(x+6)]
=(x+5)/[(-x+5)/(x+6)]
=(x+5)*(x+6)/(-x+5)
=[(x+5)(x+6)]/[-x+5]
=(x^2+11x+30)/(-x+5)
the answer is:
(x^2+11x+30)/(-x+5)
What value of x is the solution of the equation 1/7+2x/3 = 15x-3/21?
A. 6
B. 0
C. 4/13
D. 6/29
Answers
3+14x=15x-3 subtract 3 from both sides
14x=15x-6 subtract 15x from both sides
-x=-6 divide both sides by -1
x=6
*Notice the use of parentheses in this format to make it clear what the numerators and denominators are...
Answer:A=6
Step-by-step explanation:
What type of equation would best model this data
Answers
Find all complex solutions of x^2-3x+4=0.
(If there is more than one solution, separate them with commas.)
Answers
X= {1, 2}
Final answer:
Complex solutions of a quadratic equation are found using the quadratic formula. The solutions to x²-3x+4=0 are complex numbers.
Explanation:
The solutions to the equation x²-3x+4=0 are complex numbers.
To find the complex solutions, we can use the quadratic formula where a=1, b=-3, and c=4. Plugging these values into the formula, we get:
x = (3 ± √(-7))/2
Therefore, the complex solutions are x = (3 ± i√7)/2.
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3x.
h(x) = 0
h(x) = -32x
h(x) = 2(32x)
h(x) = 3x(2 - 3x)
Answers
Answer: h(x) = 3x(2 - 3x)
Step-by-step explanation:
Here the given functions are,
[tex]f(x) = x(2-x)[/tex]
[tex]g(x) = 3x[/tex]
[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]
[tex]= f( 3x )[/tex]
[tex]= (3x)[2-(3x)][/tex]
[tex]= 3x(2-3x)[/tex]
Hence,
[tex]h(x) = 3x(2-3x)[/tex]
⇒ Fourth option is correct.
Find the length of the missing side. The triangle is not drawn to scale.
A. 36
B. 6
C. 4
D. 13
Answers
64 + x^2 = 100
x^2 = 36
x = 6
10^2=y^2+8^2
y^2=100-64
y^2=36
y=√36
y=6
What is -4x - 5x <18 need help
Answers
Divide by both sides of the equations by [tex]-9 [/tex] like ↓
[tex] \frac{-9}{-9} \leq \frac{18}{-2} \\ \\ x \leq -2 \\ \\ Answer: x \leq -2 [/tex]
Good luck on your assignment and enjoy your day!
~MeIsKaitlyn :)