Answers
In degrees: -270°, 90°, 450°.
In radians: -3π/2, π/2, 5π/2.
Step-by-step explanation:The cosine is always zero where the sine is 1. The sine is 1 at an angle of 90°, and every integer number of 360° added (or subtracted) to that. The corresponding point on the unit circle is (0, 1), labeled A in the diagram.
The angle from the x-axis to the positive y-axis can be called any of ...
... 90°
... -270°
... 450°
... 810°
... π/2 radians
... -3π/2 radians
... 5π/2 radians
... 9π/2 radians
You are asked to pick three of these (or some others you may choose) so that you have 3 different names for the angle to this point.
_____
Comment on the second figure
The graphing calculator easily shows places where function values are zero. To show where sin(x) = 1, we rewrite it as sin(x) -1 = 0. Then, the zeros are highlighted. In degrees, the ones shown are -270°, 90°, 450°, 810°. You can see that cos(x) is zero at those same angles.
Related Questions
find the missing value of the sides.
Answers
Answer:
The values for both of the missing sides is 8.
Step-by-step explanation:
The hypotenuse of a right triangle = a(square root of 2)
Therefore the other two missing sides equal a.
Therefore, the other two sides equal 8.
now, recalling the pythagorean theorem a little.
the hypotenuse here is 8√2, and then we have the other two sides, BUT, the opposite angle for each is actually the same 45°, if each opposite angle is the same, the length of the side on the other end is also the same.
so we have say side "b" and side "a", but because each has an opposite angle of 45°, that means "b" and "a" are actually twins.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies (8\sqrt{2})^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{8\sqrt{2}}\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \stackrel{\textit{since we know that \underline{a = b}}}{[8^2(\sqrt{2})^2]=a^2+a^2}\implies 64(2)=2a^2\implies \cfrac{64(2)}{2}=a^2\implies 64=a^2 \\\\\\ \sqrt{64}=a\implies 8=a=b[/tex]
Kevin buys a skateboard that is on sale for 20% off the original price. The original price is $35 more than the sale price. What is the original price of the skateboard?
Answers
Explanation
20%×35= original price
At the city museum, child admission is $5.20 and adult admission is $8.80 . On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1090.80 . How many child tickets were sold that day?
Answers
Answer:
27 total child tickets sold
Step-by-step explanation:
Price of child ticket = $5.20
Price of adult admission = $8.80
Now according to given condition of the day of Monday
Let no of child tickets sold are = x
then
total no of adult tickets sold are =4 x
Total sales = $ 1090.80
Now according to given
we know that
sales of child tickets + sales of adults tickets = total sales
Putting in the values
x * (5.20) + (4x)*(8.80) = 1090.80
5.20 x + 35.2 x = 1090.80
40.4 x = 1090.80
Dividing both sides by 40.4
[tex]\frac{40.4x}{40.4}=\frac{1090.80}{40.4}[/tex]
x= 27
So total no of child tickets sold are 27
At the movie theatre, child admission is $6.60 and adult admission is $9.80 . On Thursday, 182 tickets were sold for a total sales of $1508.40 . How many adult tickets were sold that day?
Answers
Answer:
96
Step-by-step explanation:
Let x represent the number of adult tickets sold. Then (182-x) is the number of child tickets sold. The total sales is then ...
... 6.60·(182 -x) +9.80·x = 1508.40
... 3.20x = 1508.40 -1201.20 . . . . . simplify, subtract 1201.20
... 307.20/3.20 = x = 96 . . . . . . . . divide by the coefficient of x
96 adult tickets were sold that day.
Final answer:
By setting up and solving a system of equations, it is determined that 96 adult tickets were sold at the movie theatre.
Explanation:
To solve the problem of how many adult tickets were sold at the movie theatre, we need to set up a system of equations based on the given information: child admission is $6.60, adult admission is $9.80, 182 tickets were sold in total, and the sales amounted to $1508.40.
Let's denote the number of child tickets sold as c and the number of adult tickets sold as a. We can then create the following two equations:
c + a = 182 (since the total number of tickets sold was 182)
6.60c + 9.80a = 1508.40 (representing the total sales from the tickets)
We can solve these equations using substitution or elimination methods. Here's the step-by-step solution using the elimination method:
First, we multiply the first equation by -6.60 to set up for elimination:
-6.60c - 6.60a = -1201.20
Now we add this to the second equation:
6.60c + 9.80a = 1508.40
3.20a = 307.20
Dividing both sides by 3.20 gives us a = 96.
Therefore, 96 adult tickets were sold that day.
Sully is driving a race car in a race. The table gives the speeds recorded by the speedometer on Sully's car with respect to time.
x
(seconds)
y
(mph)
x y
2 60
8 120
16 170
What type of function is the function representing Sully's speed?
It is a constant function.
It is a linear function.
It is a nonlinear function.
It is a decreasing function.
Answers
It is a nonlinear function.
Step-by-step explanation:When the points are graphed, they do not all lie on the same line. The lines connecting the points have positive slope, so the function is neither constant nor decreasing.
Answer: It is a nonlinear function.
Step-by-step explanation:
A function is said to be linear if the rate of change of dependent varaible (y) with respect to independent variable (x) is constant.
Rate of change in function [tex]=\dfrac{\text{Change in y}}{\text{Change in x}}[/tex]
The table gives the speeds recorded by the speedometer on Sully's car with respect to time. :
x y
(seconds) (mph)
2 60
8 120
16 170
For x= 2 and x= 8 , the rate of change in function will be
[tex]\dfrac{\text{Change in y}}{\text{Change in x}}\\\\=\dfrac{120-60}{8-2}=\dfrac{60}{6}=10[/tex]
For x= 8 and x= 16 , the rate of change in function will be
[tex]=\dfrac{170-120}{16-8}=\dfrac{50}{8}=6.25[/tex]
But 10 ≠ 6.25.
⇒ Rate of change is not constant.
It means the function non- linear.
Also , it is not a constant function because values of y is not constant w.r.t to x.
It is not a decreasing function because values of y increase with increase in x.
Find the domain of the inverse function, q−1(x). Express your answer as an inequality.
Answers
Hello from MrBillDoesMath!
Answer:
x >=4
Discussion:
The inverse of q is
-1 +\- (x-4)^(1/4) (the fourth root of x-4)
(Inverse found by solving x= (y+1)^4 +4 for y)
The domain of the inverse is therefore x such that x -4 >=0 , i.e. x >=4
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
what is the best estimate of mean for this data set PLZ HLP
(1)has 0 dots
(2)has 3 dots'
(3)has 1 dot
(4)has 4 dots
(5)has 0 dots
(6)has 2 dots
(7)has 3 dots
(8) has 1 dot
(9) has 1 dot
(10) has 0 dots
(dot plot)
Answers
Answer:
Sample Response: The math club has 8 members. The youngest member is 9. The oldest member is 13. Therer is a cluster between 11 and 13, with a peak at 13. There is a gap at 10.
Ryan completed 1/8 of his test in 2/5 hour. If Ryan’s rate stayed the same, how much of his test was finished in one hour
Answers
Answer:
5/16
Step-by-step explanation:
In 5/2 the time, we expect that 5/2 × 1/8 = 5/16 of the test will be complete.
_____
5/2 × (2/5 h) = 1 h
Answer:5/16
Step-by-step explanation: In 5/2the time, we expect that 5/2 *1/8= 5:16
The distance between city A and B is 600 km. The first train left A and headed towards B at the speed of 60 km/hour. The second train left B heading towards A three hours after the first train left A, and it traveled with a speed of v km/hour. The trains met t hours after the time at which the first train left A. Express v in terms of t. Find the speed v if t=7; t=6.
Answers
Answer:
v(t) = 420/(t-3) -60v(7) = 45 km/hv(6) = 80 km/hStep-by-step explanation:
When the second train leaves, the remaining distance between the trains is ...
... 600 km - (3 h)×(60 km/h) = 420 km
That distance will be covered at the speed of (60 +v) so the time it takes for the second train to cover that distance is ...
... 420/(60 +v)
The variable t represents the time since the first train left, so is 3 hours more than this time value. Hence ...
... t = 3 +420/(60 +v)
Solving for v, we have ...
... t -3 = 420/(60 +v) . . . . subtract 3
... 60 +v = 420/(t -3) . . . . multiply by (60+v)/(t -3)
... v = 420/(t -3) -60 . . . . subtract 60
For t = 7 ...
... v = 420/(7 -3) -60 = 105 -60 = 45
For t = 6 ...
... v = 420/(6 -3) -60 = 140 -60 = 80
Solve the system of linear equations. −x+2y=4 and −2x−2y=14
Answers
Answer:
x=-6, y=-1
Step-by-step explanation:
−x+2y=4 and −2x−2y=14
I will solve by elimination. We can eliminate the y variable by adding these together.
−x+2y=4
−2x−2y=14
-----------------
-3x = 18
Divide each side by -3
-3x/-3 = 18/-3
x = -6
But we still need to solve for y
-x + 2y =y
Substitute x in
- -6 +2y =4
6 +2y = 4
Subtract 6 from each side
6-6 + 2y = 4-6
2y = -2
2y/2 = -2/2
y= -1
To solve the system, we added the two equations, resulting in -3x = 18. Solving for x, we found x = -6 and then substituted this value into one of the original equations to solve for y, yielding y = -1. The final solution is (x, y) = (-6, -1).
To solve the system of linear equations -u+2y=4 and -2x-2y=14, we can utilize the elimination method. This involves adding the two equations together in order to eliminate one of the variables, resulting in an equation with a single variable which can be easily solved.
We begin by adding the two equations:
-(-x+2y)+(-2x-2y)=4+14
x - 2y - 2x - 2y = 18
-3x = 18
Divide both sides by -3 to find the value of x:
x = -6
With the value of x known, we substitute it back into one of the original equations to solve for y. Let's use the first equation:
-(-6) + 2y = 4
6 + 2y = 4
2y = -2
Divide both sides by 2 to find the value of y:
y = -1
The solution to the system of equations is (x, y) = (-6, -1).
Plz help What is sum of 5.3x10^5 and 3.8x10^4 in scientific notation
A. 4.33x10^4
B. 5.68x10^5
C. 9.1x10^9
D. 9.1x10^5
Answers
Answer:
I would say your answer is B.
Step-by-step explanation:
5.3 times 10^5 + 3.8 times 10^4
Tirn them into their regular form and add them together you will get the answer
Mr. Gonzales has only $42.50 to spend at a clothing store. He want to buy a shirt that costs $29, including tax and some bracelets that cost $4.50 each, including tax. Write an equation to determine x, the maximum number of bracelets Mr. Gonzales could but.
1) Equation ________________________
2) Solve the equation to determine the number of bracelets Mr. Gonzales could buy.
Show your work
Answer _____ bracelets
Answers
1) 29 + 4.50x = 42.50
2)4.50x=42.50-29
x=13.50/4.50=3 bracelets
Answer:
Equation: 29+ 4.50x= 42.50
Answer: 3
Step-by-step explanation:
simplify the polynomials:5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3
Answers
Simplify each term: 5x^4y + 7x^4y - 5x^5 - 5x^3z + 3x^3z
Combine like terms: -5x^5 + 12x^4y -2x^3z
That is the most simplified form.
If necessary, factor:
x^3(-5x^2+12xy-2z)
For 14a through 14d, tell which expressions require you to rename mixed numbers before you can subtract. Find each difference. Write each expression and the difference as an equation in the correct box PLEASE ANSWER
Answers
PLEASE HELP!!!
Find all possible values of m and the corresponding a, b, and c’s for each one. Show your work.
m • a = 196
m • b = 441
m • c = 210
Answers
(m, a, b, c) ∈ {(1, 196, 441, 210), (7, 28, 63, 30)}
Step-by-step explanation:m is a common factor of 196, 210, 441
The prime factors of those numbers are
... 196 = 2²×7²
... 210 = 2×3×5×7
... 441 = 3²×7²
7 is the only prime factor common to all the numbers. Hence the possible values of m are 1 and 7.
For m = 1, (a, b, c) = (196, 441, 210).
For m = 7, (a, b, c) = (196, 441, 210)/7 = (28, 63, 30).
Find the measure of the acute angle x. Round your answer to the nearest tenth, if necessary.
29.1
0.01
60.9
0.03
Answers
Answer:
29.1°
Step-by-step explanation:
You can use your good sense to select the correct answer.
You know it is not near zero (so, not 0.01 or 0.03—neither of which is rounded to the nearest tenth). Since the adjacent side is longer than the opposite side, you know the angle is less than 45°. (Of the two complementary angles X and T, X is the smaller.) That only leaves one answer choice.
If you really need to figure it out, use SOH CAH TOA to remind you ...
... Tan(X) = Opposite/Adjacent = (5 in)/(9 in)
... X = arctan(5/9) ≈ 29.1° . . . . . make sure your calculator is in degrees mode
In this trigonometric problem, intuitive reasoning and basic principles were used to deduce the angle X as approximately 29.1 degrees, before employing the tangent function for precise calculation.
When faced with a problem involving trigonometry, sometimes you can intuitively deduce the correct answer using logic and a basic understanding of trigonometric principles. Let's break down how to approach the problem step by step:
Eliminate Options: In this case, you are provided with multiple answer choices. You can start by ruling out certain options based on your intuition. You can eliminate answers that are "near zero," such as 0.01 and 0.03, which are not rounded to the nearest tenth.
Analyze the Triangle: By examining the given information, you can infer that the angle you are looking for (angle X) is less than 45°. This deduction is based on the fact that the adjacent side is longer than the opposite side in a right triangle, and X is the smaller of the two complementary angles.
Use SOH CAH TOA: If you want to calculate the angle more precisely, you can apply trigonometric ratios. In this case, you use the tangent function: Tan(X) = Opposite/Adjacent = 5 in / 9 in. Then, you can find the angle using the arctan function, which yields X ≈ 29.1°.
In summary, while you can employ trigonometric functions for precise calculations, sometimes a logical approach and a good understanding of the problem can lead you to the correct answer more efficiently. In this scenario, the angle X is approximately 29.1 degrees, provided your calculator is in degrees mode.
For more such information on: tangent function
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who's better Messi or Ronaldo when messi has scored 700 goals in his carrer and ronaldo has scored 600 what is the ratio please for a bunch of points
Answers
Answer:
The ratio of Messi : Ronaldo
7:6
Step-by-step explanation:
The ratio of Messi : Ronaldo
700 :600
Divide each side by 100
7:6
You cannot tell who is better because we do not know how many shots they took.
Express 4 as a fraction. A) 1 1 B) 1 4 C) 4 1 D) 4 4
Answers
Answer:
C) 4/1
Step-by-step explanation:
Any integer can be expressed as a fraction by using a denominator of 1.
By how much does the dependent variable change in response to a change of 1 unit of the independent variable?
Independent 2 4 6 8
Dependent 15 25 35 45
Select one or more:
A. 1
B. 2
C. 5
D. 10
Answers
Answer: C) 5
--------------
x = independent variable, y = dependent variable
Assuming this is a linear function, each increase of x by 2 leads to y going up by 10. So 10/2 = 5 is the unit increase each time x bumps up by 1.
-------------------
An alternative is to use the slope formula to get
m = (y2 - y1)/(x2 - x1)
m = (25 - 15)/(4 - 2)
m = 10/2 <--- this expression shows up again
m = 5 <---- leading to the same answer as before
So we see that the slope formula is a more drawn out method to finding the answer.
Answer:
c) 5
Step-by-step explanation:
A manufacturing company builds construction machinery. It sells 10 machines for $18,100 and 20 machines for $26,600. Which equation models the revenue, R(x), as a linear function of the number of machines built, x ?
Select one:
A. R(x)=750x−10100
B. R(x)=450x+7200
C. R(x)=1200x−4500
D. R(x)=850x+9600
Answers
m = (y2 - y1)/(x2 - x1)
y = (26,600 - 18100)/(20 - 10)x + b
y = 850x + b
18100 = 850(10) + b
b = 9600
R(x) = 850x + 9600
Answer:
R(x) = 850x + 9600
Step-by-step explanation:
Kelly reads x hours a week. Tim reads two times more than Kelly and Jim reads five hours more than Tim. Which expression represents the amount of time Jim reads? A) 2(5x) B) 2x - 5 C) 2x + 5 D) 2(x - 5)
Answers
Tim reads 2 more times than Kelly(2x) and then you add 5 because Jim reads 5 more hours than Tim.
What is the solution set to the following system x+y=5
x^2+y^2=25
A (0, -5) (-5,0)
B (0,5) (-5,0)
C (0,-5) (5, 0)
D (0, 5) (5,0)
Answers
D (0, 5), (5, 0)
Step-by-step explanation:Anything with -5 and 0 will not satisfy x+y=5. This eliminates the first three choices.
___
It is easiest to check the offered answers. You can also solve this graphically, or by solving the simultaneous equations.
You can, for example, square the first equation and subtract the second:
... (x+y)² -(x²+y²) = 5² -25
... 2xy = 0
This will be true for x=0 or for y=0, so (0, 5) and (5, 0) are solutions to the pair of equations.
To find the solution set to the given system, substitute the value of x into the second equation, factor, and solve for y. The solution set is (5,0).
Explanation:To find the solution set to the given system of equations, we can solve them simultaneously. From the first equation, we have x = 5 - y. Substituting this value of x into the second equation, we get (5 - y)^2 + y^2 = 25. Expanding and simplifying this equation gives us 2y^2 - 10y = 0. Factoring out y, we have y(2y - 10) = 0. So either y = 0 or 2y - 10 = 0. Solving the second equation for y, we get y = 5.
Therefore, the solution set to the system of equations is (5,0).
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Find the value of this^
Answers
Answer:
x=63
y=27
Step-by-step explanation:
As we can see from the graph x+ 117 form a straight line
x+ 117 = 180
Subtract 117 from each side
x+117-117 = 180 -117
x = 63
The graph indicates that x+y forms a right angles
x+y = 90
We know x = 63
63+y = 90
Subtract 63 from each side
63-63+y = 90-63
y = 27
Answer:
y=27 simple one
Step-by-step explanation:
ez
In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some point. Find the length of segments between this point and the vertices of the greater base.
Answers
The values of x and y are 5/7 and 11 respectively.
Similar triangles are triangles with equal corresponding angles and equal side ratios.
We use similarity theorem to solve for x and y
x/3+x = 11/18
18x = 33 + 11x
collect like terms
18x - 11x = 33
7x = 33
x = 33/7
x = 4 5/7
y/7+y = 11/18
18y = 77 + 11y
7y = 77
y = 11
Therefore, the values of x and y are 4 5/7 and 11 respectively.
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations). PLEASE HELP ME ASAP!!!
Answers
Answer:
The area of the entire yellow region is 48 cm^2.
Step-by-step explanation:
See the attached image :)
Charlie's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Charlie $4.85 per pound, and type B coffee costs $5.95 per pound. This month, Charlie made 150 pounds of the blend, for a total cost of $789.10 . How many pounds of type A coffee did he use?
Answers
Answer:
94 pounds
Step-by-step explanation:
Let "a" represent the weight of type A coffee Charlie used. Then 150-a is the weight of the type B coffee. The total cost of the blend is then ...
... 4.85a +5.95(150 -a) = 789.10
... -1.10a +892.50 = 789.10 . . . . . . simplify
... -1.10a = -103.40 . . . . . . . . . . . . . .subtract 892.50
... a = 94 . . . . . . . . . . . . . . . . . . . . . divide by -1.10
Charlie used 94 pounds of type A coffee.
Final answer:
Charlie used 94 pounds of type A coffee for the blend, which was found by setting up a system of equations based on the total weight and cost of the coffee blend and solving for the quantity of type A coffee.
Explanation:
To solve how many pounds of type A coffee Charlie used, we need to set up a system of equations based on the given information.
Let x be the amount of type A coffee and y be the amount of type B coffee. We have two types of coffee totaling 150 pounds, so x + y = 150.
The cost of the two types of coffee leads to the second equation: 4.85x + 5.95y = 789.10.
We solve this system of equations either by substitution or elimination. If we solve for y from the first equation (y = 150 - x) and substitute it into the second equation, it simplifies to 4.85x + 5.95(150 - x) = 789.10, which becomes 4.85x + 892.50 - 5.95x = 789.10. Simplifying further gives -1.10x = -103.40, which when solved for x gives x = 94.
Therefore, Charlie used 94 pounds of type A coffee for his blend.
Can anyone HELP with my HOMEWORK for GRADE‼️
Answers
Answer:
The coordinates of point C are (a,0).
Step-by-step explanation:
Given information: ABC is right isosceles triangle.
From the given figure it is noticed that the side BC is hypotenuse of the triangle ABC.
By pythagoras theorem,
[tex]hypotenuse^2=leg^2+leg^2[/tex]
[tex]hypotenuse^2=2leg^2[/tex]
[tex]hypotenuse=leg\sqrt{2}[/tex]
Therefore hypotenuse cannot be equal to leg. So, we can say that in triangle ABC,
[tex]AB=AC[/tex]
Length of AB is
[tex]AB=\sqrt{(a-0)^2+(0-0)^2}=a[/tex]
From the figure it is noticed that the point C lies on the x-axis, therefore the y-coordinates of C is 0.
Let the coordinates of C be (x,0) and length of AC must be a.
[tex]AC=\sqrt{(x-0)^2+(0-0)^2}[/tex]
[tex]a=x[/tex]
Therefore coordinates of point C are (a,0).
Cara has driven one-fifth of the total distance, d, to her destination. Which statement explains why both 1/5d and 0.2d can find the distance she has driven?
A Multiplying by 15 is the same as multiplying by 2%.
B The fraction 15 is the same as the decimal 0.8. Therefore, 1/5d can be written as 0.8d.
C Multiplying by 15 is the same as multiplying by 20%.
D
The expressions are not equivalent.
Answers
Answer:
The correct answer is option C, Multiplying by 1/5 is the same as multiplying by 20%.
Step-by-step explanation:
The equation 1/5 = 1 divided by 5 = 0.2
and 0.2 can be expressed as 20%
Thus both the factor 1/5 and 20 % are same
Answer:
c is the answer
Step-by-step explanation:
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Answers
Answer:
(25/54)x⁻⁶y⁻⁹
Step-by-step explanation:
[4(5x³y³)²]/(6x⁴y⁵)³ Do the outside exponents first
= [4(25x⁶y⁶)]/(216x¹²y¹⁵) Group like terms
= [(4×25)/216] × x⁶/x¹² × y⁶/y¹⁵ Reduce fractions to lowest terms
= 25/54 × x⁻⁶ × y⁻⁹ Recombine the terms
= (25/54)x⁻⁶y⁻⁹
What is the decimal value of cos X?
(Round the answer to the nearest thousandth if necessary.)
Answers
Answer:
0.153
Step-by-step explanation:
It has been a long time since I've done this, so I hope it is correct:
cos = adjacent side / hypotenuse
cos x = 13 / 85 = 0.153
The decimal value of cos X can be found using a calculator or trigonometric table. Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the hypotenuse of a right triangle.
Explanation:The decimal value of cos X can be found using a calculator or trigonometric table. Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the hypotenuse of a right triangle. For example, if cos X is equal to 0.6, this means that the adjacent side of the triangle is 0.6 times the length of the hypotenuse.
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