use the triangle to answer the question.
Which equation shows a correct relationship of trigonometric functions?
sin x/cos y=0
sin x/ cos x =0
sin x/ cos x =1
sin x/ cos y =1
Answers
---------------------------------------------
---------------------------------------------
Label the sides as shown in the image attachment.
P = horizontal leg (opposite of angle x; adajcent to angle y)
Q = vertical leg (opposite of angle y; adajcent to angle x)
R = hypotenuse (longest side; always opposite the 90 degree angle)
Use the definitions of sine and cosine to say...
sin(Angle) = opposite/hypotenuse
sin(x) = P/R
and
cos(angle) = adjacent/hypotenuse
cos(y) = P/R
Notice how sin(x) = cos(y). This is true any time x+y = 90 which is the case here (x and y are complementary angles). A more specific example is sin(30) = cos(60) which are both equal to 1/2 or 0.5
Since sin(x) = cos(y), this means sin(x)/cos(y) = 1 as any expression divided by itself is equal to 1. Keep in mind that cos(y) cannot equal zero.
This is why choice D is the final answer.
side note: something like cos(x)/sin(y) or sin(y)/cos(x) or similar are all equal to 1 as long as x+y = 90
Related Questions
a ride at an amusement park rises 8 feet every horizontal change of 2 feet. how could you determine the slope of the ride?
Answers
based off of the graph which of the following statements are true. select all that apply
Answers
The correct options are A, D, and G.
Correct statements about the graph are:
A. It has a minimum.
D. Vertex at (-1, -9).
G. Y-intercept at (0, -8).
To determine the truth of the statements given about the graph, we will analyze the graph step by step:
1. **Identify the Vertex**: The vertex of a parabola is the highest or lowest point of the graph, depending on whether it opens upwards or downwards. This graph opens upwards, so the vertex will be the minimum point.
2. **Find the Vertex**: We need to locate the vertex on the graph by looking for the point where the graph changes direction.
3. **Check for Maximum or Minimum**: Since this parabola opens upwards, it will have a minimum point but not a maximum.
4. **Determine the Zeros**: Zeros are the points where the graph crosses the x-axis. These are also known as the roots or solutions of the quadratic function when set to zero.
5. **Locate the Y-Intercept**: The y-intercept is the point where the graph crosses the y-axis.
6. **Examine the Solutions**: The solutions of the quadratic function are the x-coordinates of the zeros of the function.
7. **Assess the Y-Intercept**: We will find the y-coordinate of the point where the graph intersects the y-axis.
Now, let's examine the graph based on these steps:
A. **The graph has a minimum** - True. The parabola opens upwards, which means it has a minimum point where the vertex is located.
B. **The graph has a maximum** - False. Since the graph opens upwards, it does not have a maximum point; the vertex represents a minimum.
C. **The graph has zeros of -4 and 2** - False. The zeros of the graph (where it crosses the x-axis) appear to be different from -4 and 2, as the graph does not touch the x-axis at these points.
D. **The vertex is located at (-1,-9)** - True. By looking at the graph, it appears that the vertex, which is the minimum point, is indeed at the point (-1,-9).
E. **The graph has y-intercepts at (-4,0) and (2,0)** - False. A graph can only have one y-intercept, which is where it crosses the y-axis. The points given are actually x-intercepts or zeros of the function.
F. **The solution of the quadratic function represented by the graph is (-1,-9)** - False. The solution to a quadratic function is typically the x-values where the function crosses the x-axis (the zeros). The vertex is not the solution to the function; it is simply the minimum or maximum point.
G. **The y-intercept of the graph is (0,-8)** - True. The y-intercept is where the graph crosses the y-axis, which appears to be at (0,-8) according to the graph.
Hence, the correct statements are A, D, and G. The graph has a minimum at the vertex (-1, -9) and a y-intercept at (0, -8). It does not have a maximum, and the zeros are not at -4 and 2 as stated in option C. The solutions to the quadratic function would be the x-values of the zeros, not the vertex coordinates.
The complete question is here:
Which of the following statements are true about the graph? Check all that apply.
(GRAPH IS GIVEN BELOW)
A. The graph has a minimum.
B. The graph has a maximum.
C. The graph has zeros of -4 and 2 .
D. The vertex is located at (-1,-9).
E. The graph has y-intercepts at (-4,0) and (2,0).
F. The solution of the quadratic function represented by the graph is (-1,-9).
G. They-intercept of the graph is (0,-8).
The statements that are true from the graph are:
A. The graph has a minimum. D. The vertex is located at (-1,-9). G. The y-intercept of the graph is (0,-8).Why are the statements true ?
There is a vertex on the graph, which implies that there is either a minimum or maximum point. In this case, since the vertex is shown, it indicates a minimum point on the graph.
The vertex of a quadratic function in the form y = ax ² + bx + c is given by the coordinates (-b / 2a, f(-b/2a)), where a, b, and c are coefficients of the quadratic equation.
The y-intercept is the point where the graph crosses the y-axis, and it occurs when x = 0. This is shown to be the point ( 0, - 8 ).
The full question is:
Based off of the graph which of the following statements are true. select all that apply
A. The graph has a minimum.
B. The graph has a maximum.
C. The graph has zeros of -4 and 2 .
D. The vertex is located at (-1,-9).
E. The graph has y-intercepts at (-4,0) and (2,0).
F. The solution of the quadratic function represented by the graph is (-1,-9).
G. They-intercept of the graph is (0,-8).
Solve the following system of equations.
x − 2y = 5
−3x + 2y = 7
A. x = 3, y = −1
B. x = 11, y = 11/2
C. x = 3, y = 1
D. x = −6, y = -11/2
Answers
Let me help you out real quick.
x - 2y = 5
-3x + 2y = 7
We need to solve x - 2y =5 for x
x - 2y = 5
x = 5 + 2y
Now substitute 2y + 5 for x in -3x + 2y = 7
-3x + 2y = 7
-3(2y + 5) + 2y = 7
-6y - 15 + 2y = 7
-4y - 15 = 7
-4y = 7 + 15
-4y = 22
y = 22/-4
y = -11/2
Now we need to substitute -11/2 for y in x= 2y + 5
x = 2y + 5
x = 2(-11/2) + 5
x = -22/2 + 5
x = -6
Thus,
The answer is x = -6 and y = -11/2
The correct answer is option D
Good luck with your studies :)
You got it!
during the 2009-2010 basketball season, the number of points scored in each game by the boston celtics was approximately normally distributed with a mean of 99.2 points and a standard deviation of 10.5 pthe mean number of points scored by los angeles lakers was 101.7. in what proportion of their games did the celtics score more than the lakers' mean score?
Answers
To solve this problem, we use the z statistic. The z formula is:
z = (x – u) / s
where x is lakers score = 101.7, u is Celtics score = 99.2, s is standard dev = 10.5
z = (101.7 – 99.2) / 10.5 = 0.24
using the normal distribution table at z = 0.24, the P value is:
P (z = 0.24) = 0.5984 = 59.84%
Please help!!!
System of Equations Applications
Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.
Answers
Bill sold 9 for w and 2 for b for a total of 200. So 9w + 2b = 200
Cody sold 2 for w and 13 for b for a total of 283. So 2w + 13b = 283
Lets solve by elimination.
[tex]\begin{bmatrix}9w+2b=200\\ 2w+13b=283\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}9w+2b=200\mathrm{\:by\:}2:\quad 18w+4b=400[/tex]
[tex]\mathrm{Multiply\:}2w+13b=283\mathrm{\:by\:}9:\quad 18w+117b=2547[/tex]
[tex]\begin{bmatrix}18w+4b=400\\ 18w+117b=2547\end{bmatrix}[/tex]
18w + 117b = 2547
-
18w + 4b = 400
/
113b = 2147
[tex]\begin{bmatrix}18w+4b=400\\ 113b=2147\end{bmatrix}[/tex]
[tex]113b=2147 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}113 \ \textgreater \ \frac{113b}{113}=\frac{2147}{113} \ \textgreater \ b=19[/tex]
[tex]\mathrm{For\:}18w+4b=400\mathrm{\:plug\:in\:}\ \:b=19[/tex]
[tex]18w+4\cdot \:19=400 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:4\cdot \:19=76 [/tex]
[tex]18w+76=400 \ \textgreater \ \mathrm{Subtract\:}76\mathrm{\:from\:both\:sides} [/tex]
[tex]18w+76-76=400-76 \ \textgreater \ 18w=324 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}18[/tex]
[tex]\frac{18w}{18}=\frac{324}{18} \ \textgreater \ w=18[/tex]
Therefore the cost of the white chocolate chip cookies is $18 and the double choco is $19
Cody:. 2w+13d= $283
2(9w+2d=$200)
-9(2w+13d=$283)
18w+4d=$400
-18w-117d=-$2547
-113d= -2147
d= $19
9w+2(19)=200
9w+38=200
9w= 162
w= $18
double chocolate chip cookie dough:$19
white chocolate chip cookie dough: $18
The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
A. g(x) = (x – 3)2 – 4(x – 3) + 4
B. g(x) = (x2 – 4x + 4) – 3
C. g(x) = (x2 – 4x + 4) + 3
D. g(x) = (x + 3)2 – 4(x + 3) + 4
Answers
Answer:
answer is A for APEX..
Step-by-step explanation:
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
What is shifting of a function?A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.
Given
f(x) = [tex]x^{2} -4x+4[/tex]
The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
If the function is shifted to the left it is going to plus(+).
If the function is shifted to the right it is going to minus(-).
So, x = x - 3
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex]
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
Option A is correct.
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|3x-2|+2y if x=-4,y=7,and z=-9
Answers
The expression below represents the number of bacteria in a petri dish after t hours.
Interpret the meaning of the expression.
A. The initial number of bacteria is 57, and the growth rate is 3.1% per hour.
B. The initial number of bacteria is 57, and the growth rate is 31% per hour.
C. The initial number of bacteria is 131, and the growth rate is 5.7% per hour.
D. The initial number of bacteria is 131, and the growth rate is 57% per hour.
Answers
Solving this problem requires the supplement of the actual expression. However I believe you forgot to include it with the question.
However I believe that the expression is in the form of:
y = A e^(-k t)
where,
y is the number of bacteria after time t
A is a constant and represents the initial number of bacteria
k is the growth rate in decimal form
t is time
So whatever is located in A is the initial number of bacteria, while k times 100% is the growth rate.
Answer:
A
Step-by-step explanation:
what is the domain function of this table?
X Y
3 4
4 4
5 2
6 5
A) {2,4,5}
B) (3,4)
C) {3,4,5,6}
D) (3,4)(4,4)(5,2)(6,5)
Answers
The domain will always be your X value, while the range will always be the Y value.
Hope this helps!
The domain function of this table is C) {3,4,5,6}. Option c is the correct answer.
The domain of a function is the set of all possible input values. In this case, the input values are the X-values in the table.
The X-values in the table are 3, 4, 5, and 6. Therefore, the domain of the function is {3, 4, 5, 6}.
So the answer is (C).
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Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?
Answers
Final answer:
Randy is 10 years old.
Explanation:
The question is about solving a simple algebraic equation involving ages.
We are told Randy is twice as old as his sister Jane, and the sum of their ages is 15 years.
If we let Jane's age be represented by 'j', then Randy's age would be '2j' as he is twice as old as Jane.
The equation to represent the sum of their ages is:
j + 2j = 15
To find Jane's age, we combine the like terms:
3j = 15
Now, we divide both sides of the equation by 3 to isolate 'j':
j = 15 / 3
j = 5
Therefore, Jane is 5 years old. To find Randy's age, we multiply Jane's age by 2:
Randy's age = 2 * Jane's age
Randy's age = 2 * 5
Randy's age = 10
So, Randy is 10 years old.
Jenna saved $100. She wants to buy 6 games that cost $20 each. Dose Jenna have enough money? Explain.
Answers
hope this helps, God bless!
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The total amount Jenna have is only $100.
But the cost of 6 games is $120.
No, Jenna doesn't have enough money to buy 6 games.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount saved = $100
Cost of each game = $20
The cost of 6 games that cost $20:
= 20 x 6
= $120
The total amount Jenna have is only $100.
But the cost of 6 games is $120.
This means,
Jenna doesn't have enough money to buy 6 games.
Thus,
The total amount Jenna have is only $100.
But the cost of 6 games is $120.
No, Jenna doesn't have enough money to buy 6 games.
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what is the value of f (x) = 1/2 x + 5 when x=4
Answers
f(4)=1/2(4)+5
f(4)=4/2+5
f(4)=2+5
f(4)=7
Hope I helped :)
2 + 5
7
f(x) = 7
What is the slope is the x the top ordered pairs or the bottom !??? HELLPPP
Answers
Find the y-intercept of the line whose equation is 2x - 3y = -6.
Answers
to find y intercept, make x = 0 then solve equation:
2x-3y=-6
2(0) - 3y=-6
-3y =-6
y = -6 / -3
y=2
so y intercept is (0,2)
Amy has 1/2 hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore.
Answers
<-----------(5/2)----------->
Note: 5/2 is determined by multiplying (1/2)(5).
Translate this equation into a real life situation. 4m = -8
Answers
8. Evaluate the following expression for the given value.
-3x^2-4x+4 for x=-2
A) 0
B) 4
C) 12
D) 20
Answers
-3(-2)^2-4(-2)+4=0
What is 9,333,625 rounded to the nearest hundred thousand?
Answers
Suppose that 4 fair dice are rolled.let m be the minimum of 4 numbers rolled.what are the possible values of m
Answers
In this case, the total value of 4 is the minimum so that means them possibilities should be 100%
If the question asks about the possible way of all dice show at least 4 number, then the answer is: 3^4−2^4= 81 * 16= 1296
Lisa can run a mile in 7 minutes. at that rate of speed how long would it take her to run 2 kilometers
Answers
It would take Lisa approximately 8.669 minutes to run 2 kilometers at her rate of speed.
Explanation:To find out how long it would take Lisa to run 2 kilometers, we need to convert the distance she can run in a mile to kilometers. Since there are 1.60934 kilometers in a mile, we multiply the time it takes her to run a mile (7 minutes) by the conversion factor (1.60934 kilometers/mile). This gives us the time it would take her to run 1.60934 kilometers. To find the time it would take her to run 2 kilometers, we can set up a proportion:
Calculating this gives us x ≈ 8.669 minutes. Therefore, it would take Lisa approximately 8.669 minutes to run 2 kilometers at her rate of speed.
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Suppose you have a $8-off coupon at a fabric store. You buy fabric that costs $7.50 per yard. Write an equation that models the total amount of money y you pay if you buy x yards of fabric. What is the graph of the equation?
Answers
The graph would be an increasing straight line.
For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}
Answers
common ratio/r=-1/4
ar^(n-1), where a is the first term
substitute all the numbers in it
-80(-1/4)^(n-1)
Answer:
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
Step-by-step explanation:
{-80, 20, -5, ...}
General recusive formula for geometric sequence is
[tex]a_n = r \cdot a_{n-1}[/tex]
Where 'r' is the common ratio
To find common ratio 'r' we divide second term by first term
[tex]r=\frac{20}{-80} =-\frac{1}{4}[/tex]
Replace 'r' with -1/4
First term is -80
Recursive formula becomes
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
The Great Foods Warehouse contains 9435 pounds of watermelons. There are 6555.569 pounds of watermelons in the Tasty Food Warehouse. How many more pounds does the Tasty Food Warehouse need to have the same amount of watermelons as the Great Food Warehouse?
Answers
Answer: 2879.431 pounds
Step-by-step explanation:
Given : The Great Foods Warehouse contains 9435 pounds of watermelons.
There are 6555.569 pounds of watermelons in the Tasty Food Warehouse.
Clearly , 9435 > 6555.569.
By using Subtraction operation, The amount of watermelon needed by Tasty Food Warehouse to have to get the same amount of watermelons as the Great Food Warehouse will be :-
9435-6555.569=2879.431 pounds
Hence, the Tasty Food Warehouse needs to have 2879.431 pounds to gwt the same amount of watermelons as the Great Food Warehouse.
Graph the relation shown in the table. Is the relation a function? Why or why not?
{(–3, –2), (–1, 0), (1, 0), (5, –2)}
No; the relation passes the vertical-line test.
Yes; only one range value exists for each domain value.
Yes; two domain values exist for range value –2.
No; two domain values exist for range value –2.
Answers
---------------------------------
---------------------------------
Explanation:
The inputs are x = -3, x = -1, x = 1, x = 5. They are the first coordinate listed of each point. We don't have any x values repeating so this means we have a function. Each input leads to exactly one output which is what choice B is stating. The domain is the set of allowed inputs, or x values. The range is the set of possible y outputs.
If we had something like (1,2) and (1,5) then the input x = 1 leads to more than one output (y = 2 and y = 5). This example means we don't have a function
If you graph the points (-3, -2), (-1,0), (1,0) and (5,-2) as shown in the attached image, then you'll notice that it is impossible to pass a single line through more than one point. Therefore this graph passes the vertical line test visually proving we have a function.
Going back to the example with (1,2) and (1,5), plotting these two points leads to the vertical line test failing implying we don't have a function.
If 6 chocolate cost $0.93 how much do 22 cost
Answers
One die is rolled 3 times, what is the chance of getting all 4's?
Answers
The chances of getting 4 when a die is rolled three times will be 216.
What is the combination?A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given that a die is rolled 3 times. The chances of getting 4's will be calculated as:-
In a die, there are 6 numbers from 1 to 6. At one time only one number will come. the combination will be
Combination = 6 x 6 x 6
Combination = 216
Therefore, the chances of getting 4 when a die is rolled three times will be 216.
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Jordan makes 100 3-point shots per basketball practice. She makes 44 of these shots. What decimal represents the number of the shots she made?
Answers
0.44 is the answer
this is because she took 100 shots and made 44 of them in. the three doesn't matter because they never asked for the amount of points.
I only just started learning Algebra, and my teacher just threw all these worksheets at us without explaining much. Can someone please explain the concept of Algebra? Staring with this question, please:
Answers
2x - 3x = 3 + 5
-x = 8
x = -8
Answer:
x = -8
Step-by-step explanation:
Hello!
Algebra is based on the concept of unknown values called variables, the value of each variable must remain the same in each problem.
Here are steps to solve your problem!
1. Pull out like terms:
-x - 8 = -1 • (x + 8)
2. Solve -x-8 = 0
Add 8 to both sides of the equation:
-x = 8
Multiply both sides of the equation by (-1)
x = -8
Therefore, x = -8
Hope this Helps!
Karl runs a car wash. On the Monday, he recorded a loss of $80 and recorded it as -$80. On Tuesday he earned a profit of $120. What is Karl's balance at the end of Tuesday?
Answers
Karl's balance at the end of Tuesday is a net profit of $40, after combining his loss of $80 from Monday with his profit of $120 from Tuesday.
To find Karl's balance at the end of Tuesday, we need to combine his loss from Monday with his profit from Tuesday. Karl recorded a loss of -$80 on Monday. On Tuesday, he made a profit of $120. Add the two amounts together to find Karl's total balance after these two days.
Monday: -$80
Tuesday: +$120
Combining them, -$80 (loss) + $120 (profit) equals to a net profit of $40.
Therefore, Karl's balance at the end of Tuesday is $40.
Solve the below system of equations using the best method. Please describe the method used [substitution, graphing, elimination, etc], and give your answer in the form (x,y).
y = 2x + 3
y = -x - 5
Answers
y = 2x + 3
y = -x - 5
2x + 3 = -x - 5
3x + 3 = -5
3x = -8
x = -8/3
Now substitute -8/3 in for x in the original first equation, and solve for y.
y = 2x + 3
y = 2(-8/3) + 3
y = -16/3 + 9/3
y = -7/3
Solution: (-8/3, -7/3)