Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
which table represents an exponential function of the form y=bx when 0
The table that represents an exponential function of the form y = [tex]b^{x}[/tex] when 0 < b < 1 is Table - 2. See the attached tables.
What is an exponential function?
A function is exponential when its value is a constant that is raised to the power of the argument. This is so especially when the function of the constant is e.
What is the solution?Recall that the exponential function y = [tex]b^{x}[/tex] given that 0 < b < 1. Notice that the table number 2 see to the exponential function that has the following form:
y(x) = (1/3)ˣ
substituting the values of x into the equation, we have:
y(-3) = (1/3) ⁻³ = 27
x = -2; thus
y(-2) = (1/3) ⁻³ = 9
x = -1; thus
y(-1) = (1/3) ⁻³ = 3
x = 0; thus
y(0) = (1/3) ⁻⁰ = 1
x = 1; thus
y(1) = (1/3) ¹ = 1/3
x = 2; thus
y(2) = (1/3) ⁻² = 1/9
x = 3; thus
y(3) = (1/3) ⁻³ = 1/27
Therefore, according to the obtained values, one can summarize that the table that depicts the exponential function y = bˣ is table 2.
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Solve the equation sin 79.5° = cos 2x
Answer:
x=5.24-9+180n,174.75+180n
Step-by-step explanation:
Chris and Hillary are remodeling their family room. They are deciding on the flooring, sofa and TV. How many possible combinations are shown in the tree diagram?
A. 10
B. 11
C. 12
D. 13
Answer:
its C ^^ makes more sense :D
Step-by-step explanation:
hope this helps
Find the area with the radius of 27
Answer: The answer is 2289.06
Step-by-step explanation: I assume it’s a circle as it has a radius so simply multiply 3.14 by the radius 27^2
I need the answer please help!
I just need help with question one, but if you want to you can answer question 2 as well. I’ll give 100 points!
Explanation:
Given f(x) : (2, -3)
Translation's:f(x) + 2 then graph translates up by 2 units up = [tex]\boxed{\sf (2, -1)}[/tex]
f(x) - 3 then graph translates down 3 units down = [tex]\boxed{\sf (2, -6)}[/tex]
f(x + 5) then graph translates left 5 units = [tex]\boxed{\sf (-3, -3)}[/tex]
-f(x) then graph reflects over x axis = [tex]\sf \boxed{\sf (2, 3)}[/tex]
f(-x) then graph reflects over y axis = [tex]\sf \boxed{\sf (-2,-3)}[/tex]
f(2x) then graph has horizontal compression = (2/2, -3) = [tex]\boxed{\sf (1, -3)}[/tex]
2f(x) then graph has vertical compression = (2, (-3)2) = [tex]\boxed{\sf (2, -6)}[/tex]
-f(x - 4) then graph reflects over x axis, moves 4 units to right = [tex]\sf \boxed{\sf (6, 3)}[/tex]
Solution 2Parent function: y = x²
Graph function: f(x) = (x + 8)² - 4
After Identification:
D. The graph has a translation of 8 units left and 4 units down.
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Question 1Given: [tex]f(x)=(2,-3)[/tex]
[tex]f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)[/tex]
[tex]f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)[/tex]
[tex]f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)[/tex]
[tex]-f(x) \implies (x,-y)=(2,-(-3))=(2,3)[/tex]
[tex]f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)[/tex]
[tex]f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)[/tex]
[tex]2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)[/tex]
[tex]-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)[/tex]
[tex]\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}[/tex]
Question 2Parent function: [tex]y=x^2[/tex]
Given function: [tex]f(x)=(x+8)^2-4[/tex]
[tex]f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}[/tex]
[tex]f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}[/tex]
Therefore, a translation 8 units to the left and 4 units down.
The sales tax for an item was $15 and it cost $500 before tax. Find the sales tax rate. Write your answer as a percentage.
The estimated distribution (in millions) of the population by age in a certain country for the year 2015 is shown in the
pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the
sample standard deviation of the data set. Use 70 as the midpoint for "65 years and over."
The sample mean is x- (Round to two decimal places as needed.)
Under 4 years: 24.8
15-14 years: 422
15-19 years 194
20-24 years: 256
25-34 years 50.7
35-44 years: 35.7
45-64 years 75.2
65 years and over 54.3
The sample mean for the data is 21.38 and the sample standard deviation for the data is 56.19
The frequency distribution for the dataTo do this, we start by calculating the midpoint of each class using:
Midpoint= (Lower + Upper)/2
Using the above formula, we have:
Age (x) Frequency (f)
2 24.8
9.5 422
17 194
22 256
29.5 50.7
39.5 35.7
54.5 75.2
70 54.3
The sample mean for the dataThis is calculated using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{2*24.8 + 9.5*422 + 17*194 + 22*256 + 29.5*50.7 + 39.5*35.7 + 54.5*75.2+70*54.3}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3}[/tex]
Evaluate
[tex]\bar x = \frac{23793.8}{1112.7}[/tex]
[tex]\bar x = 21.38[/tex]
Hence, the sample mean for the data is 21.38
The sample standard deviation for the dataThis is calculated using:
[tex]\sigma_x = \sqrt{\frac{\sum f(x- \bar x)^2}{\sum f - 1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{2*(24.8-21.38)^2 + .............+70*(54.3-21.38)^2}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3 - 1}}[/tex]
Evaluate
[tex]\sigma_x = \sqrt{\frac{3509508.4556}{1111.7}}[/tex]
[tex]\sigma_x = \sqrt{3156.88446128}[/tex]
[tex]\sigma_x = 56.19[/tex]
Hence, the sample standard deviation for the data is 56.19
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Given the function f(x) = ³x – 1, evaluate f(-12).
Evaluation:
The answe for the function is -1.
Manuela has a piece of red ribbon 7 1/2 feet long. She cut the ribbon to have one piece 1 3/4 feet long.
How long is the piece of ribbon that is left?
Answer:
the leftover piece of ribbon is 5 3/4 feet long.
Step-by-step explanation:
if she has 7 1/2 feet of ribbon, and she removes (by cutting it off) 1 3/4 feet of ribbon.
So, if we set up this scenario like a math problem, we can write it as this:
7 1/2 feet of ribbon - 1 3/4 feet of ribbon = remaining ribbon
[ - = take away]
so, we are solving the equation:
7 1/2 - 1 3/4
To solve this, it is easiest to make the fractions have the same denominators
1 / 2 is equal to 2 / 4
However, 2/4 is less than 3/4, so we need to make this fraction a larger number.
To do this, we can take away 1 foot from the 7, and write it as if it were fourths
1 [foot] = 4/4 quarter foot
So, we can add 4/4 + 2/4 = 6/4
Now, we can re-write our situation.
6 6/4 - 1 3/4 = left over ribbon
6 6/4
- 1 3/4
__________
5 3/4
So, the leftover piece of ribbon is 5 3/4 feet long.
Hope this helps!
When -3v = -18 is solved, the result is:
Answer:
When -3v = -18 is solved, the result is:
21v
The result of this mathematical sentence is v=6
First degree equationFirst degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.
*Note: Equal signs, the result will be equated as positive.
-3v = -18
v = -18/-3
v = 6
Therefore, the correct value of this equation is v = 6.
A train leaves Little Rock, Arkansas, and travels north at 85 kilometers per hour. Another train leaves at the same time and travels south at 85 kilometers per hour.
How long will it take before they are 680 kilometers apart?
Answer:
4hours
Step-by-step explanation:
1hour =85+85
=170km/h
time= distance÷
speed=170km/h
680÷170=time
=4h
Given the graph of f(x), determine the range of f−1(x).
R
(2, infinity)
(-infinity, 2) U (2, infinity)
(-infinity, 3) U (3, infinity)
The range of a graph of a function is (-∞, 3) U (3, ∞) option (D) (-∞, 3) U (3, ∞) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The graph of a hyperbola function is given.
As we know the graph of an inverse of a function is reflections over the line y=x.
We get the same graph as given in the picture.
The range of a graph of a function:
Range: (-∞, 3) U (3, ∞)
Thus, the range of a graph of a function is (-∞, 3) U (3, ∞) option (D) (-∞, 3) U (3, ∞) is correct.
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If 2,6 kg of potatoes cost R13,20, what will the cost of 3,3 kg be?
Answer:
[tex]\huge\boxed{\sf R. 16.75}[/tex]
Step-by-step explanation:
*Assuming commas are used for decimals.
Given that:2.6 kg potatoes = R 13.20
Using unitary methodDivide 2.6 to both sides
1 kg potatoes = R 13.20/2.6
1 kg potatoes = R 5.1
Multiply 3.3 to both sides
3.3 kg potatoes = R 5.1 × 3.3
3.3 kg potatoes = R 16.75
[tex]\rule[225]{225}{2}[/tex]
Use the following math quiz scores to answer the questions. 85%, 65%, 87%, 68%, 90%, 73%, 65%, 85%, 95%, 85% 17) What is the mean of these scores? 18) What is the median score? The point on the scale that divides the distribution of scores in half 19) What is the mode of these scores? The value that occurs most frequently in a set. 20) What is the range of these scores? The difference between the lowest and highest values
Answer:
79.8
Step-by-step explanation:
2. The number of hours you study for an exam impacts your grade. What is a reasonable value of the range?
70
-8
1.75
1/6
Answer:
62.
Step-by-step explanation:
because I subtract 70 to 8 equal to 62
Answer:
I think
Step-by-step explanation:
I think 62 hope you have a good day
HELP!!!!!!!!!!!!!!!!!!!!
Answer:
D is the answer hope
Step-by-step explanation:
hope this helped
Finding the slope from points
Answer:
m = -3
Step-by-step explanation:
The formula to find the slope of the line is :
slope = m = [tex]\frac{y_1 - y_2}{x_1-x_2}[/tex]
Given that the two coordinates of the line are :
( -1 , - 7 ) ⇒ ( x₁ , y₁ )
( 1 , -13 ) ⇒ ( x₂ , y₂ )
Let us solve now.
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
m = ( -7 - ( -13)) ÷ ( -1 - 1 )
m = ( -7 + 13 ) ÷ ( -2 )
m = 6 ÷ -2
m = -3
Answer:
m = -3
Step-by-step explanation:
Given two points:
(-1,-7) & (1,-13)To Find:
The slopeSolution:
Using slope's formulae,
[m denotes slope][tex] \boxed{ \rm{m = \cfrac{y_2 -y_1 }{x_2 - x_1} }}[/tex]
According to the question, on the formula:
(y_2,y_1) = (-13,-7)(x_2,x_1) = (1,-1)Substitute them onto the formulae:
[tex] \rm \: m = \cfrac{ - 13 - ( - 7)}{1 - ( - 1)} [/tex]
Simplify using PEMDAS:
P = ParenthesesE = exponentsM = MultiplicationD = DivisionA = additionS = subtraction[tex] \rm \: m = \cfrac{ - 13 + 7}{1 \ + 1} [/tex]
[tex] \rm \: m = \cfrac{ - \cancel6}{ \cancel2} = \boxed{ - 3}[/tex]
Hence, the slope of the line that passes through the given points in it's simplest form is -3.
please help i will give brainliest
39°F = °C rounded to the nearest tenth of a degree
Answer:
3.9 degrees celsius
Step-by-step explanation:
(°F − 32) × 5/9 = °C
input 39
7 times 5/9 = c
35/9 = c
c = 3.9
Answer:
3.9 degrees Celsius.... it's 3.8888 when translated from Farenheit
You need to make party favors for a friend's birthday. 48 people were invited, but you'll only have to make favors for those who say they will attend. Some of the favors will be yellow and the rest will be xanadu. Make a graph using paper or technology that shows all of the possible combinations of yellow or xanadu party favors you might choose to make. Let a represent the xanadu favors and y represent the yellow favors. Your graph should be labeled with x-intercept, y-intercept, shaded region, linear boundary (solid or dashed). Also include an additional point with coordinates clearly labeled in the solution region that shows me how many of each favor you choose to make after all RSVP's are received
The update of the completed graph is given in the image attached as it shows the possible combinations of Yellow or Xanadu party favors that might choose will be ( 48, 0).
What is the graph about?For this graph, we shall make Xanadu party favors as X
and yellow favors as Y
Therefore note that: X + Y = 48
In the graph of X - Intercept
Y = 0, X = 48
In the graph of Y- intercept,
Y = 48 , X = 0
Therefore, the graphical representation of the combinations is given in the image attached.
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4.
Solve the system of inequalities graphically. Label the solution set with an S.
Help asap
Answer:
Solution = (2,1)
Step-by-step explanation:
Make them equal each other and solve for x.
2x - 3 = 1
2x = 4
x = 2
2 * 2 - 3 = 1
Solution = (2,1)
30 POINTS ANSWER ASAP PLS
Complete the square to justify that Julia’s graph is correct.
6x2 + 12x + 6y2 – 48 ≤ 0
Answer:
1) x + 1
2) y - 0
3) 9
Step-by-step explanation:
Answer:
the first answer is (x+1) the second box (y-0) and the last box is 9
Step-by-step explanation:
WILL GIVE BRILLIANT
Which of the following is not true of a trapezoid that has been reflected across the x-axis?
A
The x-coordinates of the new trapezoid are the same as the x-coordinates of the
original trapezoid.
B
The new trapezoid is the same size as the original trapezoid.
C
The new trapezoid is the same shape as the original trapezoid.
D
The new trapezoid is in the same orientation as the original trapezoid.
Answer:
D
Step-by-step:
The y-coordinates will change, not the x. Size and shape will also remain the same.
Triangle QRS is reflected across the x-axis. Then it is reflected across the y-axis. Finally, it is
translated according to the rule (x + 7, y + 3). What are the final coordinates of point R'?
Answer: (4,-4)
Step-by-step explanation:
Reflection across the x axis means [tex](x,y) \longrightarrow (x,-y)[/tex], so [tex](3,7) \longrightarrow (3,-7)[/tex].
Reflection across the y axis means [tex](x,y) \longrightarrow (-x,y)[/tex], so [tex](3,-7) \longrightarrow (-3,-7)[/tex].
Then, [tex](-3,-7) \longrightarrow R'\boxed{(4,-4)}[/tex]
Mr Stephen saved 350 rupees per month how much money will he save in 3 years
Answer:
the answer to that question is 12,600 rupees
what are the solution of the quadratic equation (x-8)3-13x(x-8)+3=0? use u substitution to solve.
[tex]3(x - 8) - 13x(x - 8) + 3 = 0 \\ 3x - 24 - 13 {x}^{2} + 104x + 3 = 0 \\ - 13 {x}^{2} + 107x - 21 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ a = - 13 \\ b = 107 \\ c = - 21 \\ x = \frac{ - 107 + - \sqrt{ {107}^{2} - 4(13)( - 21)} }{2( - 13)} \\ x1 = \frac{107 - \sqrt{10357} }{26} \\ x2 = \frac{107 + \sqrt{10357} }{26} [/tex]
Hope it helps
Please give brainliest
What is 20 divided by 1/2 inches
REPEATED SUBTRACTION TO DIVIDE
PLSSS TELL.
Answer:
40Step-by-step explanation:
What is 20 divided by 1/2 inches
20 : 1/2 =
20 * 2 =
40
Explain how the modern double-slit experiment showed different results than Young’s double-slit experiment.
Modern:
Where there are two open slits, the resulting pattern will simply be the sum of the two single-slit patterns (two vertical lines). But again and again, the experiment demonstrated that the coherent beams of light were interfering, creating a pattern of bright and dark bands on the screen.
Young's
In the end, the double slit experiment discovered that electrons, and all quantum particles, both exist as particles and probability waves. Quantum particles existing as probability waves means that we don't know for certain where these particles are, we can only know the probability of where they will be.
What is the answer?
I want the explanation step by step
Help me