Let theta equals 11 times pi over 12 periodPart A: Determine tan θ using the sum formula. Show all necessary work in the calculation.Part B: Determine cos θ using the difference formula. Show all necessary work in the calculation.
Answers
The fisrt part is the divide your angle into two angles, could be 6/12π and 5/12π
[tex]\begin{gathered} A=\frac{4\pi}{12}=\frac{\pi}{3} \\ B=\frac{7\pi}{12} \end{gathered}[/tex]For the sum formula:
[tex]\begin{gathered} \tan (\theta)=\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B} \\ \tan (A+B)=\frac{1.73-3.73}{1-1.73\cdot(-3.73)} \\ \tan (A+B)=\frac{-2}{7.45}=-0.27 \end{gathered}[/tex]For the difference formula:
[tex]\begin{gathered} A=\frac{1\pi}{12} \\ B=\pi \end{gathered}[/tex][tex]\begin{gathered} \tan (B-A)=\frac{\tan B-\tan A}{1+\tan A\cdot\tan B} \\ \tan (B-A)=\frac{0-0.268}{1+0\cdot0.267} \\ \tan (B-A)=-0.268 \end{gathered}[/tex]Both methods work and result in the same answeer
Related Questions
Questiona + 4 = 10. If a must be equal to one of the values below, what is the value of a?Select the correct answer below:4679
Answers
1) In this question, we can solve it in two different ways. Either algebraically, or by mental Math.
2) Algebraically we have:
[tex]\begin{gathered} a+4=10 \\ a+4-4=10-4 \\ a=6 \end{gathered}[/tex]By mental math, we just need to ask ourselves how much can I add to 4 and get 10,? The answer will be six.
3) Thus, the answer is 6
If 2x - 2 < 8 + x, then x <
A) 2
B) 4
C) 9
D) 10
Answers
Answer:
D) 10
Step-by-step explanation:
2x - 2 < 8 + x
add 2 to both sides:
2x - 2 + 2 < 8 + x + 2
2x < 10 + x
subtract x from both sides:
2x - x < 10 + x - x
x < 10
Consider the following system of equations 4x + 6=24 and 2x + 3y=8 How many solutions does this system have? Justify your answer. Part B If we triple each side of the first equation 4x+6y=24, we have 12x+18y=72. Explain why the new system 12x+18y=72 and 2x+3y=8 has the same number of solutions as the original system.
Answers
For the given system of equations 4x + 6y=24 and 2x + 3y=8, there is no solution exists.
What is defined as the system of equations?When two or more equations are solved together in algebra, the solution should satisfy all of the equations with in system. The amount of equations must equal the amount of unknowns for a system to produce a unique solution. Even so, no solution is guaranteed. If there is a solution, the system has been consistent; otherwise, it is inconsistent.For the given system of equation,
4x + 6y =24 ......eq 1
and 2x + 3y = 8 ..... eq2
use elimination method.
Multiply eq 2 with 2 and subtract from eq 1.
0 = 16
But 0 ≠ 16, the system of equation becomes untrue.
As, the values o f the variables x and y are getting cancelled. So, the there is no solution existed for the given system.
Also,the ratio of 4x/2x = 2 and 6y/3y = 2 is same thus, no solution is possible for the system.
Now, when the we triple each side of the first equation 4x+6y=24, we have 12x+18y=72.
The new system 12x+18y=72 and 2x+3y=8
Then, also 12x/2x = 6 and 18y/3y = 6 is also same. Then, also the system of equation does not have any solution of the system.
Thus, the system of equation does not have any solution.
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What is the correct answer
Answers
∠GJI ≅ ∠LKF is proved below.
What is congruent?If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical. If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.
Given Data
EF║GH
AB║CD
In given figure,
AB║CD,
While line segment GH is the transversal line.
So,
∠GJI ≅ ∠JLK (because it is corresponding angle) ..(1)
Also,
EF ║GH
Line segment DL is the transversal line.
So,
∠JLK ≅ ∠LKF (because it is interior alternate angle)..(2)
From (1) and (2)
∠GJI ≅ ∠LKF
Hence, proved.
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(2580+2920+x)/3=3000
Answers
Answer:
x = 3500
Step-by-step explanation:
2580 + 2920 + x
------------------------ = 3000
3
5500 + x
------------------------ = 3000(3)
3(3)
5500 + x = 9000
-5500 -5500
------------------------------
x = 3500
I hope this helps!
Simplify these below with explainations please. Thank you
Answers
Answer:
3x^5y^8
Step-by-step explanation:
so the cube root of 27 is 3
to find the cube root of x^15 divide the exponent by 3 which gets you x^5
do the same thing for y^24 and that gets you y^8
mhm and i think thats right
what is this pleaseeee
Answers
The correct option C: y = (x + 2)(x -3)²(x - 1)² is function which correctly represents the given graph.
What is defined as the graphing?A diagram that depicts the relationship between quantities, particularly one in which lines, bars, as well as proportional areas portray how a quantity depends on it or changes with the other. A curve or line depicting a mathematical function or eq, usually drawn in Cartesian coordinates.In mathematics, a graph is characterized as a pictorial representation or diagram that organizes data or values.The graph's points frequently depict the connection between two or more variables.For the given graph;
Select one coordinate of the curve from the graph.
Point (0, 18); in which y is 18 for x = 0.
Now, go by option and put the value of x = 0 and find the correct value of y.
Option C: y = (x + 2)(x -3)²(x - 1)²
Put x = 0
y = (0 + 2)(0 -3)²(0 - 1)²
y = (2)(-3)²(- 1)²
y = 18
We, get the correct coordinates (0, 18).
Thus, the correct option is C, which satisfies the given graph.
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Here are the approximate populations of three cities in the United States, expressedin scientific notation: San Jose: 1.1 x 10^6; Washington: 7 x 10^5 ; Atlanta: 4.8 x 10^5.a. Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. Doyou agree with her? Explain your reasoning.Your answer
Answers
Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. To find if she is right you substract the population of Atlanta from the population in San Jose:
Substraction of numbers in scientific notation:
1. Turn the numbers to get the same power of base 10.
You move to the left the decimal to increase the power of base 10 and move to the right to g
[tex]undefined[/tex]Solve the following polynomial equation by grouping and factoring. 36y^3−49y=0
Answers
Given:
[tex]36y^3-49y=0[/tex]solve for y:
[tex]\begin{gathered} 36y^3-49y=0 \\ y(36y^2-49)=0 \\ y=0;36y^2-49=0 \end{gathered}[/tex]Value of y is zero and
[tex]\begin{gathered} 36y^2-49=0 \\ 36y^2=49 \\ y^2=\frac{49}{36} \\ y=\pm\sqrt[]{\frac{49}{36}} \\ y=\pm\sqrt[]{1.361111} \\ y=\pm1.166 \\ y=1.166,y=-1.166 \end{gathered}[/tex]consider a quadrilateral and its diagonals.wich conjecture below would best describe a quadrilateral whose diagonals divide into four isosceles triangles
Answers
Isosceles triangle have 2 equal lengths
Square or Rectangle have 4 equal teiangles
Isosceles trapezoid also divides
Then answer is
Isosceles trapezoid. Option A)
PLEASE HURRY IM GIVING POINTS!!!!!!!!!
Part A: Given the function
g(x) = |x - 5| describe the graph of the function, including the vertex, domain, and range.
Part B: If the parent function
f(x) = |x| is transformed to
h(x) = Ix| + 3, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answers
Part A: The vertex, domain, and range of the function g(x) = |x-5| is
( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).
Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y - coordinate of the vertex is shifted by 3 units.
In Part A:
The given function is;
g(x) = | x - 5 |.
Now, The x - coordinate of the vertex will be:
x - 5 = 0
x = 5
Therefore, the y- coordinate of the vertex will be:
y = g(x) = | x - 5 |
y = g(7) = | 5 - 5|
y = 0
So, The vertex of the absolute function is ( 5, 0 ).
Since, All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this case, the phrase is defined even if there is no real number.
Hence, In Interval Notation the domain is;
⇒ ( - ∞ , ∞ )
And, The set of all legitimate y values is the range.
Hence, In Interval Notation the range is:
⇒ [0, ∞ )
Now, In Part B:
Function h(x) = |x| + 3 is the transformed version of the parent function
f(x) = |x|.
For the parent function f(x) = |x|, the vertex is ( 0, 0).
Since, The range of an absolute function in the form c( | ax + b | ) + k is
f(x) ≥ k.
Therefore, The range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).
For the transformed function h(x) = |x| + 3.
The vertex of the function is ( 0, 3 ).
The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).
Hence, the y coordinate of the vertex is transformed by 3 from f (x) to h(x).
So, Part A: The vertex, domain, and range of the function g(x) = |x-7| is
( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).
Part B: The function f(x) = |x| is vertically shifted by 2 units to get the function h(x) = |x| + 3. The y coordinate of the vertex is shifted by 3 units.
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Altred is saving up money for a down payment on a house. He currently has $4739, but knows he can get a loan at a lower interest rate if he can put down $5336. If heinvests the $4739 in an account that earns 5.1 % annually, compounded monthly, how long will it take Alfred to accumulate the $5336? Round your answer to two decimal places, if necessary.
Answers
Given the word problem, we can deduce the following information:
Principal amount = $4739
Future amount = $5336
Interest = 5.1 % =0.051
To determine the time to accumulate the $5336, we use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A=Future amount=$5336
P=Present amount=$4739
r=interest rate = 0.051
n=number of compounding periods =12
t=time in years
We also note that the number of compounding periods must be 12 since the investment is compounded monthly.
We plug in what we know:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 5336=4739(1+\frac{0.051}{12})^{12t} \\ Simplify\text{ and rearrange} \\ 5336=4739(\frac{12.051}{12})^{12t} \\ 12t=\frac{\ln\frac{5336}{4739}}{\ln\frac{12.051}{12}} \\ t=\frac{\operatorname{\ln}\frac{5,336}{4,739}}{12\operatorname{\ln}\frac{12.051}{12}} \\ Calculate \\ t=2.33 \end{gathered}[/tex]Therefore, the answer is 2.33 years.
The cost of attending an amusement park is $15 for children and $35 for adults. On a particular day, the attendance at the amusement park is 25,000 attendees, and the total money earned by the park is $600,000. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
Answers
The number of children's tickets sold is 13750.
Let the number of children be x and the number of adults be y.
The total number of attendance at the amusement park is 25,000.
So we have an equation
x + y = 25000 ......(i)
The cost for children is $15 and the cost for adults is $35, and the total money earned by the park is $600,000.
So we have another equation,
15x + 35y = 600,000
3x + 7y = 120,000 ......(ii)
Multiplying equation (i) with 3 we get
3x + 3y = 75000
3x + 7y = 120,000
Now subtract both the equation we have,
4y = 45000
y = 11250
Now put the value of y in equation (i) we get
x + 11250 = 25000
x = 13750
Where x is the number of children's tickets sold.
Therefore the number of children's tickets sold is 13750.
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the equation of three lines are given below line 1:y=5/3x-6line 2:10x-6y=8line 3: 3y=5x+7for each pair of lines determine whether they are parallel perpendicular or neither line1 and line 2: parallel perpendicular or neither Line 1 and line 3:parallel perpendicular or neither line 2 to a line 3:parallel perpendicular or neither
Answers
line 1 = y = 5/3 x - 6
Find the slope of the line by comaring it with y = mx+ b
m= 5/3
Line 2
Write the equation in the form y =mx +b and find the slope m
10x - 6y = 8
6y = 10x - 8
Divide through by 6
y = 10/6 x - 8/6
y = 5/3 x - 4/3
m= 5/3
Line 3
3y = 5x + 7
Also write in the form y =mx + b and find the slope m
y = 5/3 x + 7/3
m = 5/3
Line 1 and line 2 are parallel since they have the same slope
Line 1 and 3 are parallel (they have the same slope)
Line 2 and 3 are parallel, they have the same slope
What is the slope of the line on the graph?
Enter your answer in the box.
PLEAZ HELP
Answers
Answer:
-2, 6 or -2/6 is what im seeing i could be wrong though
Step-by-step explanation:
sub to imaginefn
12345678912345678912456789
Answers
Answer:
3 is missing in there numbers,the last pair
HELP FAST. Please explain how to find the answer for the equation step by step.
Answers
The equation for the given summation is:
[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]
How to find the equation?Here we have a summation of unknown terms of the form:
uₙ
That summation goes between n = 1 and n = 4, this means that we will have a sum of 4 terms, such that:
[tex]\sum_{n=1}^4 u_n[/tex]
Means that we need to sum the terms u₁, u₂, u₃, and u₄, then we can write the equation:
[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]
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Write a unit rate for the situation
$45.00 for 9 pounds
$24 for 3 pound
$390 for 6 pounds
$42 for 21 pounds
$180 for 10 pounds
$864 for 8
Answers
The unit rate for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound
What is unit rate and how to compute it?
Unit rate is the rate for 1 unit and to compute the unit rate we divide the total price by the total number of elements
We are given certain price we have to find there unit rate
a) $45 for 9 pound
Divide both sides by 9 to find the unit rate
we get $5 for 1 pound
a) $24 for 3 pound
Divide both sides by 3 to find the unit rate
we get $8 for 1 pound
a) $390 for 6 pound
Divide both sides by 6 to find the unit rate
we get $65 for 1 pound
a) $42 for 21 pound
Divide both sides by 21 to find the unit rate
we get $2 for 1 pound
a) $180 for 10 pound
Divide both sides by 10 to find the unit rate
we get $18 for 1 pound
a) $864 for 8 pound
Divide both sides by 8 to find the unit rate
we get $108 for 1 pound
Hence the unit rates are for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound
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Jeffrey has been visiting family in Arizona and is about
511 miles away from home.
If Jeffrey drives an average speed of 60 mph, how
many hours will it take for him to get home? (Round
your answer as seems appropriate.)
Define your variable:
Label for Solution
Change My Variable
Equation (use x)
Answers
We can conclude that Jeffry will reach his home in the time of 9 hours.
What is time?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.So, the time taken by Jeffrey to get home:
The distance is 511 miles.The speed is 60 mph.The time formula: T = d/sWhere d is distance and s is speed.Now calculate time as follows:
T = d/sT = 511/60T = 8.51Rounding off: 9 hours
Therefore, we can conclude that Jeffry will reach his home in the time of 9 hours.
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which statement is true of this function f x equals 1/5 - 2
Answers
Its a decreasing function, and the y-intercept is NOT on (0, -2).
The correct option is A
(A) As the value of x increases, the value of f(x) moves towards a constant
21/24 simplified plsssssssssssssssssssssssss
Answers
(Divide both 21 and 24 by the greatest common factor, 3)
Answer:
7/8
Step-by-step explanation:
WILL GIVE BRAININESS HELP PLEASE Which function is increasing at the highest rate?
Answers
The first equation is increasing at highest rate.
Which function has highest increasing rate?
We can know which function has the highest rate of increase by looking at its slope. The function with the highest slope will have the highest rate.
In equation first m = 2 and is highest among every slope.
12x - 6y = -24
-6y = -12x -24
y = 2x +4
m = 2 (increasing)
In second equation m = 1
m = (-4 + 5)/(2-1) = 1
for a straight line function , the slope is given by
m = ( y₂ -y₁)/(x₂-x₁)
m = ( -3 -3)/(2- (-1)) = -6 /3 = -2
Therefore the function is decreasing
8,0) (0,-4)
m = (-4 -0) /(0-8) = 4/8 = 1/2
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Please show steps 1/2 divided by 1/2
Answers
To divide by a fraction is the same as multiplying by the reciprocal, which is (2/1), or just 2.
(1/2) x (2/1) = (2/2) = 1
multiply across and simplify
the table shows the population of California during the 20th century. which type of function best models this data?
Answers
Given data:
The given table is shown.
Draw the points on the graph paper as shown below.
Please help me i’m begging so much
Answers
The test statistic for an ANOVA hypothesis test is an F-statistic. Is the P-value the area to the right or left the F-statistic?
Answers
The test statistic for the anova is an F test and it is said to be positively skewed which would be to the right of the F test statistic.
What is the ANOVA?This is the term that is used to refer to the short form of the term that says analysis of variance.
The ANOVA is used to show the variation that would be in existence of a group of observations.
The F test is known to be positively skewed at all times. So we would have it that the P value would have to be to the right and not to the left in the ANOVA hypothesis.
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Find the altitude of rhombus whose area is 208 cm² and perimeter is 64 cm.
Answers
Given the area of a rhombus is 208 cm square and the perimeter of rhombus is 64 cm.
Recall that all the sides of the rhombus are equal.
Hence,
[tex]\begin{gathered} \text{perimeter}=4\times sides \\ 64=4\times\text{side} \\ 16cm=\text{side} \end{gathered}[/tex]Area of rhombus is :
[tex]\begin{gathered} area=base\times height \\ 208=16\times h \\ h=\frac{208}{16} \\ h=13\operatorname{cm} \end{gathered}[/tex]Hence the altitude of the Rhombus is 13 cm.
USChoose the definition for the function.1(-x + 2 x < 1 --x+ 2 x > 1C. Y = { x + 1x S1a.y=x+1--x+ 2 x51 d. y = { x+1b. y = x + 1-x + 2 x 2 16*x > 1Enter
Answers
Given data:
The given graph.
The equation of the line when x is less than or equal to 1 is,
x+1
he equation of the linne when x is greater than 1 is,
-x+2.
Thus, the correct option is (c).
I’m needing guidance solving this equation 9x-9=3x+7
Answers
GROUP THE LIKE TERMS FIRST.
[tex]9x - 3x = 7 + 9[/tex]
WHEN TERMS CROSS THE EQUAL SIGN THEY CHANGE SIGN.
[tex]6x = 16 \\ \frac{6x}{6} = \frac{16}{6} \\ x = \frac{16}{6} [/tex]
x can be simplified further
[tex]x = \frac{8}{3} [/tex]
HOPE THIS HELPS.
Answer:
The answer should be x=2.6
Step-by-step explanation:
9x-9=3x+7
-first you should move the numbers so you can get all your x values on one side and all your regular numbers on the other like this
9x-3x=7+9
-What i basically did was i passed the 3x from the right side to the left side of the equation, since in adding the 3x originaly, when i pass it to the left side itll be subtracting. then i passed my -9 to the right side of my equation, since i was subtracting originaly ill have to now switch it to adding
-after you do this you are going to want to want to combine like terms
6x=16
-then you are going to want to devide on both sides so you can get x alone
x=2.6
find the absolute value of each number -1/3, 6 & -0.2
Answers
The absolute number of an integer is the distance that separates the number from position zero "0" so, if it is a distance it cannot be a negative value.
Then the absolute value of these numbers is: