Answers
Here the angle is
[tex]\frac{4 \pi}{3}[/tex]
And radius is 1 units .
And
[tex]x = r cos \theta, y = r sin \theta[/tex]
Substituting the values of theta and r, we will get
[tex]x = 1 cos(\frac{4 \pi}{3} ) = -1/2 \\ y=1 sin( \frac{4 \pi}{3} ) =\sqrt3 /2[/tex]
So we will get
[tex]x = \frac{-1}{2} , y = -\frac{ \sqrt 3}{2}[/tex]
The coordinate of the point (x,y) shown on the unit circle is therefore: (-1/2, -√3/2)
The circle given is a unit circle.
In essence, the radius as indicated by the blue line is 1.
The angle subtended by the line is; 4π/3.
Therefore, from trigonometry of right-angled triangles; we have;
x = r Cos(4π/3)y = r Sin(4π/3)where, r = 1
Therefore,
x = -1/2y = -√3/2Read more:
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Related Questions
A bowl contains 24 marbles consisting of 6 white marbles, 8 blue marbles, 7 black marbles, 3 red marbles. What is the probability of drawing a red marble?
a. 6/24B.5/25C.1/8D.7/8
Answers
f(x)=3 cos (2x-pi) -1
HELP PLS!!
Answers
I sadly do not know what they mean by " smallest rate of change.
A painter is placing a ladder to reach the third story window, which is 12 feet above the ground and makes an angle of 80 degrees.how far out from the building does the base of the ladder need to be positioned
Answers
tan ∅=opposite side angle ∅/adjacent side angle ∅
adjacent side angle ∅=opposite side angle/tan ∅
in this problem
see the attached figure to better understand the problem
angle ∅=80°
opposite side angle ∅=12 ft (AB)
adjacent side angle ∅=? (AC)
adjacent side angle ∅=12/tan 80°------> 2.12 ft
the answer is
2.12 ft
The scale of a map is 0.5 inch : 20 miles. on the map, the distance between two cities is 1.5 inches. what is that actual distance between the two cities? select one:
a. 30 miles
b. 150 miles
c. 60 miles
d. 110 miles
Answers
A. 3
B. 26
C. 36
D. 51
Answers
The arcs in both angles A and D mean they are equal to each other
5y + 11 = 12y - 10
Now you solve it algebraically
Add 10 to both sides
5y + 21 = 12y
Subtract 5y from both sides
21 = 7y
Divide both sides by 7
3 = y
Put this into the equation for angle A
angle A = 5(3) + 11
Multiply
angle A = 15 + 11
Add
angle A = 26
The answer is 26°
Hope this helps!
Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)
Answers
in a right triangle
if sin A= cos B
then
angle A and angle B are complementary angles
so A+B=90
therefore
(2x-8)+(6x-6)=90-------> 8x-14=90----> 8x=104--------> x=13°
(2x-8)-----> 2*13-8----> 18°
(6x-6)-----> 6*13-6----> 72°
if α < β
then
α =18°
β=72°
A pet store has 12 puppies, including 3 poodles, 5 terriers, and 4 retrievers. if rebecka and aaron, in that order, each select one puppy at random without replacement, find the probability that aaron selects a retriever, given that rebecka selects a poodle.
Answers
The probability that Aaron will select a retriever given that Rebecka has selected a poodle is 4/11.
To calculate the probability that Aaron selects a retriever given that Rebecka selects a poodle, we will use the concept of conditional probability. The total number of puppies is 12, and the number of poodle puppies is 3.
When Rebecka selects a poodle, one puppy is removed from the total, leaving 11 puppies, including the same 4 retrievers (since she did not pick a retriever).
The probability that Aaron picks a retriever given Rebecka has picked a poodle is:
P(Aaron picks a retriever | Rebecka picks a poodle) = P(Rebecka picks a poodle and Aaron picks a retriever) / P(Rebecka picks a poodle)
Since Rebecka has already picked a poodle, we focus only on the event where Aaron picks a retriever. So the probability becomes:
P(Aaron picks a retriever | Rebecka picks a poodle) = Number of retrievers left / Total number of puppies left
= 4 retrievers / 11 total puppies
= 4/11
∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 28°, minor arc AB = 112°, and minor arc DE = 112°, what is the measure of ∠ACE? A) 14° B) 28° C) 40° D) 54°
Answers
BD+AB+DE+2ACE" on the circumference twice on the center"=360
28+112+112+2ACE=360
2ACE=108
∠ACE=54
Answer:
its 40 degrees
Step-by-step explanation:
rata ta taaa
If Tom, George and Mario work together, they can paint a 600 ft2 room in 4 hours. When only George and Mario work together, it takes 8 hours to paint the room. Tom and George, working together, take 6 hours to paint the room. How long would it take Tom to paint the room alone? Hint: Write the system of equations shown below in augmented form, then solve the system for T (Tom's painting rate). Next, use the equation Painted Area = Painting Rate× Time and solve for Time to determine how long it would take Tom to paint the room alone.
4(T+G+M)=600
8(0+G+M)=600
6T+G+0)=600
Answers
T = Tom's paiting rate [tex]( \frac{ ft^{2} }{h} )[/tex]
G = George's paiting rate [tex]( \frac{ ft^{2} }{h} )[/tex]
M = Mario's paiting rate [tex]( \frac{ ft^{2} }{h} )[/tex]
As the first statement says that they can work together, then:
T + G + M = Painting rate working together, that is the surface area they paint per hour.
Since the problem says that they last four hours painting a [tex] 600ft^{2} [/tex] room, then we need to multiply the amount of hours times the painting rate that is equal the surface area of the room, so:
4(T + G + M) = 600
Applying a similar reasoning, the George and Mario's painting rate is:
0 + G + M
Note that 0 implies that Tom didn't work in this case.
As they last eight hours painting the room, then:
8(0 + G + M) = 600
The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:
6(T + G + 0) = 600
We have a system of linear equations in three variables T, G, M:
4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600
Solving:
(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100
Substitute (3) in (1):
100 + M = 150 ∴ M = 50
Replace M in (2):
G + 50 = 75 ∴ G = 25
Substitute G in (3)
T + 25 = 100 ∴ T = 75
Then, the painting rates are:
Tom = 75 [tex]( \frac{ ft^{2} }{h} )[/tex]
George = 25 [tex]( \frac{ ft^{2} }{h} )[/tex]
Mario = 50 [tex]( \frac{ ft^{2} }{h} )[/tex]
Solving for Time to determine how long it would take Tom to paint the room alone:
Painted Area = Painting Rate×Time, so:
[tex]Time Tom = \frac{Painted Area}{Painting Rate (T)} [/tex]
[tex]Time Tom = \frac{600}{75} = 8 hours [/tex]
Answer:
A. 8 hours
Step-by-step explanation:
what crime is illigal but you cant get arrested for
Answers
What is the axis of symmetry for f(x)=2x2+8x+8
Answers
= 2(x^2 + 4x) + 8
= 2 [ (x + 2)^2 - 4) + 8
axis of symmetry is x = -2 ( because of the (x + 2)^2 )
Answer: The axis of symmetry for the function f(x) is x = -2.
Step-by-step explanation: We are given to find the axis of symmetry for the following function :
[tex]f(x)=2x^2+8x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
for a function g(x) with the form [tex]g(x)=a(x-h)^2+k,[/tex] the axis of symmetry is given by the following equation :
[tex]x-h=0~~~~\Rightarrow x=h.[/tex]
Now, from equation (i), we have
[tex]f(x)=2x^2+8x+8\\\\\Rightarrow f(x)=2(x^2+4x+4)\\\\\Rightarrow f(x)=2(x+2)^2+0.[/tex]
Therefore, the required axis of symmetry is given by
[tex]x+2=0\\\\\Rightarrow x=-2.[/tex]
Thus, the axis of symmetry for the function f(x) is x = -2.
50 Points and will mark Brainiest.
Draw four different triangles with the following two side lengths (you decide the length of side c). Be sure to label the sides and their lengths.
Side a = 2 cm
Side b = 5 cm
Look at the triangles you created. What do you notice about the different lengths of line c?
Write an inequality that shows the possible lengths for line c (the triangle inequality theorem will help you):
Answers
If the assumed length of c is less than 7, a triangle will not be formed.
Answer:
As we can observe from the drawing that with increasing length of side C the angle C also increases.
The scatterplot shows the depth of water in swimming pools, y, based on the days after filling, x. graph What can you conclude from the graph? Check all that apply. The depth of the water in the swimming pool decreases over time. The data are clustered. There are no outliers in the data. In general, increased time does not affect the depth of the water in the swimming pool.
Answers
1) The data is clustered
2) Increased time does not affect the depth of the water.
A scatterplot is a kind of graph in which each point on the graph represents an observation and values for two variables are shown using Cartesian coordinates. Generally, the dependent variable is represented by the y-axis, and the independent variable by the x-axis. Relationships, trends, patterns, and outliers between the variables can be found using scatterplots.
They can demonstrate, for instance, if a correlation is positive, negative, or absent. One can draw conclusions about the potential relationship between the two variables by looking at the point distribution.
Answer:
1) The depth of the water in the swimming pool decreases over time.
2)The data are clustered.
3)There are no outliers in the data.
Step-by-step explanation:
(Financial Algebra workbook 10-3)
Under his "Household expenses" Budget category, Mark has allocated $60 per month for pet food. He can purchase "wet food" for $1.50 per can or "dry food" for $3 per bag.
D.) Name a combination of bags and cabs that will allow him to meet his budget exactly.
Answers
We can find answers by creating this equation.
$1.50c + $3.00b = $60
where c and b represent the number of "wet food" cans and "dry food" bags, respectively. We can easily substitute numbers and solve for the other quantity that will satisfy the condition of total cost adding up to $60.
Final answer:
The question asked for a combination of wet and dry pet food that meets a monthly budget of $60. One such combination would be buying 10 bags of dry food and 20 cans of wet food, as 3(10) + 1.5(20) equals $60, which fits the budget exactly. There are also other combinations that can fulfill the budget constraint.
Explanation:
The student asked for a combination of bags and cans of pet food that would allow Mark to meet his monthly budget of $60 exactly. With wet food costing $1.50 per can and dry food costing $3.00 per bag, we can create a simple algebraic equation to find multiple combinations. Let's let x represent the number of bags and y represent the number of cans. The equation can be written as 3x + 1.5y = 60.
To find a combination that fits exactly into Mark's budget, consider the following example:
If Mark buys 10 bags of dry food, that would cost 10 × $3 = $30. He would then have $30 left of his budget. At $1.50 per can, he could buy 20 cans of wet food (because 20 × $1.50 = $30). Thus, one possible combination would be 10 bags and 20 cans. The equation for this would be 3(10) + 1.5(20) = 30 + 30 = 60, which satisfies Mark's budget constraint.
It's important to note that there are other combinations that would also meet Mark's budget exactly. The student could experiment with different numbers of bags (x) and cans (y) to find additional combinations. The key is that the total cost must not exceed $60.
Tom ordered a jacket at $70, a shirt at $30, and slacks at $38. If sales tax is 6% and the shipping and handling is $10.75, what is the total amount of his order?
Question options:
$157.03
$146.28
$87.03
$55.95
Randy ordered 3 T-shirts for $25.67 each and one skirt for $23.55 and an 8% tax. What is the total cost of the order?
Question options:
$108.60
$77.01
$66.03
$100.56
Answers
For question 2, We need to calculate the total and then find the tax. So, we do this: 25.67*3=77.01. Then we add the skirt to the total (77.01+23.55=100.56). Finally, we calculate the tax cost (100.56*0.08=8.0448). So our total is (100.56+8.0448=108.6048) So the answer is A.
The total amount of his order is $157.03.
The total amount of the order is the sum of the items bought, the tax paid an the cost of shipping and handling .
Total cost of the order = cost of the items bought + tax paid + shipping and handling
Total cost of the items bought = cost of jacket + slacks + shirt
$70 + $30 + $38 = $138
Tax paid = 6% x $138 = $8.28
Shipping and handling = $10.75
Total cost = $138 + $8.28 + $10.75 = $157.03
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Simplify the expression, leave your answer in exponential form :
Can you show the steps!??
Answers
[tex]\bf \left( \cfrac{x^{\frac{1}{2}}}{16z^{-8}} \right)^{\frac{3}{4}}\implies \left( \cfrac{x^{\frac{1}{2}\cdot \frac{3}{4}}}{16^{\frac{3}{4}}z^{-8\cdot \frac{3}{4}}} \right)\implies \left( \cfrac{x^{\frac{3}{8}}}{(2^4)^{\frac{3}{4}}z^{-6}} \right) \\\\\\ \left( \cfrac{x^{\frac{3}{8}}}{2^{4\cdot \frac{3}{4}}z^{-6}} \right)\implies \left( \cfrac{x^{\frac{3}{8}}}{2^3z^{-6}} \right)\implies \cfrac{x^{\frac{3}{8}}z^6}{8}[/tex]
Suppose a triangle has 3,4, and 5 sides.Which of the following must be true
Answers
Answer:
A. The triangle in question is a right triangle
Step-by-step explanation:
The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?
Answers
x^2 + 24x - 3456 = 0 is the equation you require
(x - 48(x + 72) = 0
x = 48
Dimensions are width 48 and length 72 in
HELPP ILL GIVE MAD POINT PLEASE
Answers
at S3, replace n with 3 , 2, and 1 , solve the equation and add all of answers together
when s = 3 the equation becomes 5(1/3)^3-1
5(1/3)^2 = 5/9
when s = 2 the equation becomes 5(1/3)^2-1
5(1/3)^1 = 5/3
when s = 1 the equation becomes 5(1/3)^1-1
5(1/3)^0 = 5
5/9 + 5/3 + 5 = 65/9
the answer is the 3rd choice
Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Check all that apply.
-
A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
Answers
A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
the cross sections that are parallel and perpendicular will have the same measurements as the non-intersected sides. the last one will be a diagonal so the intersected edge is 6 and it creates a right triangle so it must be larger than 15 inches.
Answer:
A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
the cross sections that are parallel and perpendicular will have the same measurements as the non-intersected sides. the last one will be a diagonal so the intersected edge is 6 and it creates a right triangle so it must be larger than 15 inches.
Step-by-step explanation:
The product of a number (n) and 12 is 64. Which equation shows this relationship
12+n=64
64n=12
12n=64
64-n=12
Answers
The equation that shows the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64, the correct option is C.
In this equation, the variable n represents the number we are trying to find. The equation states that when we multiply 12 and n together, the result is 64.
To solve this equation and find the value of n, we divide both sides of the equation by 12:
(12n)/12 = 64/12
n = 64/12
Which can be further simplified to:
n = 16/3
Therefore, the equation that represents the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64.
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amanda is shipping a package, which is in the shape of a cube. To determine the cost of shipping, she must determine the side length of the packages She knows that the volume of the package is V cubic inches
Which of the follow functions would best model this situation above?
Cube root
Polynomial
Piecewise
Absolute Value
Answers
V = L ^ 3
Where,
L: length of the sides
Clearing L we have:
L = 3 ^ root (V)
Answer:
A function that would best model this situation above is:
Cube root
What is the range of the function y= cot(x)?
A. all real numbers
B. all real numbers except pi/2 + n(pi), where n is any integer
C. all real numbers except n(pi)/2, where n is any integer
D. all real numbers except n(pi), where n is any integer
Answers
Answer:
all real numbers
Step-by-step explanation:
Given : y = cot(x)
To Find: Range.
Solution:
Refer the attached graph.
The domain of the function [tex]y=cot(x)=\frac{cos(x)}{sin(x)}[/tex] is all real numbers except the values where sin(x) is equal to 0 , that is, the values πn for all integers n .
The range of the function is all real numbers.
Referring the graph we can say that the range of the given function y = cot(x) is all real numbers .
Hence Option A is correct.
Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line
y = 1/4x + 5
Answers
Find the slope:
y = 1/4 x + 5
Slope = 1/4
Slope of perpendicular line = -4
Substitute m = -4 into the equation:
⇒ y = -4x + b
Find y-intercept:
At point (0, 2) ⇒ y-intercept = 2
Substitute b = 2 into the equation
y = -4x + 2
Answer: y = 4x + 2
Answer:
y=-4x+2
Step-by-step explanation:
The line passes through (0,2), so chuck these numbers in and you get a value of 2 for c. If you're sharp, you might spot that this point is the y-intercept of the line since the x- coordinate is 0, this point is on the Y-axis, and you don't even have to throw numbers in.
Therefore the equation of the line is:
y = -4x + 2
Hope that was clear!
What is the answer? Please help.
Answers
_______________________________________________
Explanation:
_______________________________________________
Given:
_______________________________________________
(x − 2) = √(2x + 1) ;
→ "Square" each side of the equation; that is, raised EACH SIDE of the equation to the power of "2" ; to get rid of the "radical" ; as follows:
_______________________________________________
[(x - 2)]² = [ √(2x + 1) ] ² ;
to get:
→ (x - 2)² = (2x - 1) ;
Expand the " (x - 2)² " ;
→ (x - 2)(x -2) = ?
NOTE: (a + b)(c + d) = ac + ad + bd .
→ = (x * x) + (x * -2) + (-2 * x) + (-2 * -2) ;
= (x²) + (-2x) + (-2x) + (4) ;
= x² − 2x − 2x + 4 ;
= x² − 4x + 4 ;
______________________________________________
Now, rewrite the entire question:
→ (x − 2)² = (2x − 1) ;
→ as follows:
______________________________________________
→ " x² − 4x + 4 = 2x − 1 " ;
Now, subtract "2x" from each side of the equation;
& add "1" to each side of the equation:
→ " x² − 4x + 4 − 2x + 1 = 2x − 1 − 2x + 1 " ;
to get:
→ " x² − 6x + 5 = 0 " ; Solve for "x" ;
Let us if : " x² − 6x + 5 " can be factors:
_____________________________________
What factors of "positive 5" ; add up to "-6" ;
-5 ,-1 ; → -5 + (-1) = - 6; YES.
5, 1 ; → 5 + 1 = 6 ; NO.
_____________________________________
So, we have: " (x − 5) (x − 1) = 0 " .
x = 5, and -1 .
_________________________________________
The population of a city is 578,992. The land area of the city is 67.2 mi². What is the population density of the city? Enter your answer in the box. Round your answer to the nearest whole number.
Answers
Population Density = Number of People / Land Area.
then
Number of People=578,992
Land Area=67.2 mi²
so
Population Density =578,992/67.2-----> 8615.95 people/mi²
the answer is
8616 people/mi²
Just took the K12 test and the correct answer is 8616 people/mi²
(please give the other person brainliest-thanks!!!)
I NEED HELP CAN SOMEONE HELP ME GET THIS?? ILL GIVE POINTS!!
Answers
this = (a^24 b^-3) / ( a^15 b^-9)
= a^9 b^6 Answer
Answer:
[tex]a^{9}b^{6}[/tex]
Step-by-step explanation:
solve for A
R=x(A+B)
Answers
R=Ax+Bx
Ax=R - Bx
A =(R - Bx)/x
The answer is A =(R - Bx)/x
To solve the equation R=x(A+B) for A, divide both sides by x to get R/x = A+B. Then, subtract B from both sides to isolate A. The final equation is A = R/x - B.
Explanation:The goal is to solve for A in the equation R=x(A+B). It's a simple problem of algebraic manipulation. Here's how to do it step by step:
First, divide both sides of the equation by x to isolate the term (A+B). This gives R/x = A+B.Next, subtract B from both sides of the newly formed equation to isolate A on one side. This gives us A = R/x - B.And there you have it! The value of A in terms of R, x, and B is A = R/x - B.
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Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.
A) reflect triangle 1 across the y-axis
B) reflect triangle 2 across the y-axis
C) rotate triangle 2 counter-clockwise 90° about the origin
D) reflect triangle 2 across the y axis and rotate 90° about the origin at
Answers
C) rotate triangle 2 counter-clockwise 90° about the origin
Answer:
The correct option is C.
Step-by-step explanation:
From the given graph it is noticed that the vertices of triangle 1 are P'(-2,2), Q'(-4,4) and R'(-2,4). The vertices of triangle 2 are P(2,2), Q(4,4) and R(4,2).
If a figure rotated counter-clockwise 90° about the origin, then
[tex](x,y)\rightarrow (-y,x)[/tex]
If we rotate triangle 2 counter-clockwise 90° about the origin, then[
[tex]P(2,2)\rightarrow P'(-2,2)[/tex]
[tex]Q(4,4)\rightarrow Q'(-4,4)[/tex]
[tex]R(4,2)\rightarrow R'(-2,4)[/tex]
If we rotate triangle 2 counterclockwise, then we get the triangle 1.
Therefore the correct option is C.
Which applies the power of a product rule to simplify (5t)^3?
Answers
Answer:
[tex]125t^{3}[/tex]
Step-by-step explanation:
The power product is given by the following formula:
[tex](ab)^{x} = a^{x}*b^{x}[/tex]
In this case, this gives us:
[tex](5t)^{3} = (5)^{3} * t^{3}[/tex]
= [tex]125*t^{3}[/tex]
= [tex]125t^{3}[/tex]