Answers
Answer:
[tex]sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}[/tex]
Step-by-step explanation:
[tex]\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\[/tex]
[tex]sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}[/tex]
Related Questions
Find the area of the triangle. Choices- Question 8 options: a) 70 units2 b) 35 units2 c) 28 units2 d) 14 units2
Answers
Answer:
35 (b)
Step-by-step explanation:
Area of a triangle = (height times base)/2
Height = 5
Base = 14
14 times 5 = 70
70/2 = 35
Answer:
it was b ) 35 units
Step-by-step explanation:
cuz 5*14 you got 70
then when is a triangle you have to do 70 divide by half
so you will got you answer which is b)35 units
hope it helps
please please help
25 POINTSS
Answers
Answer:
P ( not win) = (m-l) / m
Step-by-step explanation:
If there are m tickets and l are winners
m-l are not winners
P( not winning) = non winners/ total
(m-l) / m
Answer:
Step-by-step explanation:
P ( not win) = (m-l) / m
Find the distance of the line segment joining the two points: (sqrt 2,1) and (0, -sqrt 2)
Answers
Answer:
2.8
Step-by-step explanation:
√(-√2-1)²+(0-√2)²
Question 24 on this pictured math sheet please. Have a great day!
Answers
Answer:
[tex]y=-6[/tex].
Step-by-step explanation:
If a horizontal line passing through a point (a,b), then the equation of horizontal line is [tex]y=b[/tex] .
In the given question, it is clear that the horizontal line passing through the point (4,-6).
Here, [tex]a = 4[/tex] and [tex]b = -6[/tex].
Since, the equation of horizontal line is [tex]y=b[/tex] , therefore the required equation is
[tex]y=-6[/tex]
Hence, the equation of horizontal line is [tex]y=-6[/tex].
Find the area of the polygon XYZ that has its vertices at X(–3, 6), Y(–3, 1), and Z(5,1). Question 8 options: A) 26 square units B) 20 square units C) 40 square units D) 6.5 square units
Answers
Answer:
Area ≈ 20 square units
Step-by-step explanation:
Using Distance Formula to Find the lengths
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
Length XY:
=> [tex]\sqrt{(-3+3)^2+(1-6)^2}[/tex]
=> [tex]\sqrt{25}[/tex]
=> 5 units
Length YZ:
=> [tex]\sqrt{(5+3)^2+(1-1)^2}[/tex]
=> [tex]\sqrt{64}[/tex]
=> 8 units
Length ZX:
=> [tex]\sqrt{(-3-5)^2+(6-1)^2}[/tex]
=> [tex]\sqrt{89}[/tex]
=> 9.4
Perimeter:
=> 5+8+9.4
=> 22.4
Semi-Perimeter:
=> 11.2
Using Heron's Formula to find the area:
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where s is semi perimeter and a,b and c are side lengths
=> Area = [tex]\sqrt{11.2(11.2-5)(11.2-8)(11.2-9.4)}[/tex]
=> Area = [tex]\sqrt{(11.2)(6.2)(3.2)(1.8)}[/tex]
=> Area = [tex]\sqrt{399.9}[/tex]
=> Area = 19.99
=> Area ≈ 20 square units
the probability of spinning an odd number on a spinner is 62 percent . What is the probability of not spinning an odd number?
Answers
Subtract the percent of getting odd from 100 percent.
100 - 62 = 38%
Use the equation tool to complete the table.
y = 120 + 18(x)
Enter the correct answer.
Tara has made 120 cookies for the sale
and has one more day to bake. Tara's pan
allows her to bake 18 cookies per batch.
Tara can use the equation of the function to predict the total number of cookies: y=120+18(x). However, she prefers to use a table. (image)
Answers
Answer: ? = 264
Step-by-step explanation:
Hi, to answer this question we simply have to substitute x= 8 (number of batches) in the equation given:
y = 120 + 18(x)
Replacing and solving for y (number of cookies)
y = 120 + 18(8)
y = 120+144 = 264 cookies
The missing value in the table is⇒ ? = 264
Feel free to ask for more if needed or if you did not understand something.
Answer:
answer is 264
Step-by-step explanation:
(07.08 MC) The graph below shows the price, y, in dollars, of different amounts of peanuts, x, in pounds: Which equation best represents the relationship between x and y? (5 points) Select one: a. y = x + 6 b. y = 3x c. y = 6x d. y = x + 3
Answers
Answer:
B. y = 3x
Step-by-step explanation:
Since the y-axis is going up by 6's and the x-axis is going up by 2's, we can see that we would need to multiply the x-axis values by 3 to get our y-values. Therefore, our linear equation for this graph is y = 3x.
Write the expression in exponential form. logb M = y
Answers
Answer:
[tex]b^y=M[/tex]
Step-by-step explanation:
By definition of logarithms:
[tex]b^y=M[/tex]
Answer:
[tex]b^y=M[/tex]
Step-by-step explanation:
Recall the definition of logarithms: [tex]log_{b}M=y[/tex], where [tex]b^y=M[/tex].
The answer would be [tex]b^y=M[/tex].
For some examples, consider:
[tex]log_{2}8=y[/tex]. In other words: (b=2 and M=8), [tex]2^y=8[/tex]. Thus, [tex]y=3[/tex]. So:
[tex]log_{2}8=3[/tex]; [tex]2^3=8[/tex]
Jada sells her artwork at a trade show. She made $40 on the first day by selling one photograph, one painting, and one necklace. She made $110 on the second day by selling two photographs, three paintings, and three necklaces. She made $50 on the last day by selling one photograph, one painting, and two necklaces. Which system of equations matches Jada's sales at the trade show?
Answers
Answer:
x + y + z = 40
2x + 3y + 3z = 110
x + y + 2z = 50
Step-by-step explanation:
let
x = photograph
y = painting
z = neckless
the first part reads that jada sells 1 photograph, 1 painting, and 1 neckless. this written in a mathematical formula will be x + y + z = 40
the second part reads that jada sold 2 photographs, 3 paintings, 3 necklaces. This written as a mathematical formula will be 2x + 3y + 3z = 110
the third part reads that jada sold 1 photograph, 1 painting, and 2 necklaces. this written in a mathematical formulawill be x + y + 2z = 50
Complete the following item. Consult the table above to find the cosine number. Find A to the nearest degree. A ≈ a0degrees.
Answers
Answer: Angle A to the nearest degree = 50°
Step-by-step explanation:
Given the triangle ABC:
Since triangle ABC is a right angle triangle, Pythagoras rule can be used to obtain the value of it's angles.
cosine of A
Using Pythagoras rule :
Cos A = Adjacent / Hypotenuse
Cos A = 267 / 391
Cos A = 0.6828644
Taking the cos inverse of angle A
A = Cos^-1 (0.6828644)
A = 46.932111°
A = 50°
Answer:
47°
Step-by-step explanation:
Simplify.
3sqrt -64m^15n^3
-8m^5
-8m^5n
-4m^5n
-4m^5
Answers
Answer:
[tex]-4m^5n[/tex]
Step-by-step explanation:
∛-64 = -4
[tex]\sqrt[3]{m^{15}} =m^5[/tex]
∛n³ = n
Answer:
-4m⁵n
Step-by-step explanation:
(see attached)
If f(x) = 3x and g(x)=1/x
what is the domain of (gºf)(x)?
O x>0
O all real numbers except x=
= 0
X<0
all real numbers
Answers
Answer:
Here it is given that f(x)=3x and g(x)=1/x
We have to find the domain of (g o f)(x)
Now it is given that f(x) = 3x
and it is also given that g(x) = 1/x
so (g o f)(x) = g( f(x) ) = g( 3x )
which comes out to be 1 / 3x
The domain of the expression is all the real numbers except where the expression is undefined so the domain of the given expression is all real numbers except 0.
The domain of a function is the set of input values the function can take.
The domain of the function is (b).all real numbers except x = 0
The functions are given as:
[tex]\mathbf{f(x) = 3x}[/tex]
[tex]\mathbf{g(x) = \frac 1x}[/tex]
Calculate (gºf)(x) as follows:
[tex]\mathbf{(g\ o\ f)(x) = g(f(x))}[/tex]
So, we have:
[tex]\mathbf{(g\ o\ f)(x) = \frac{1}{f(x)}}[/tex]
Substitute 3x for f(x)
[tex]\mathbf{(g\ o\ f)(x) = \frac{1}{3x}}[/tex]
For the above function to have a real value, the value of x must not be 0.
Hence, the domain of the function is (b).
Read more about domains at:
https://brainly.com/question/14494061
Convert 5pi/4 radians time degree measure
Answers
Answer:225
Step-by-step explanation:
Question 6 (5 points)
Solve for the variable x in the equation x + 15 = 62.
Answers
Answer: x = 47
Step-by-step explanation: When you're asked to solve for x in an equation, what you're really being asked to do is get x by itself on one side of the equation.
In this problem since 15 is being added to x, in order to get x by itself,
we must subtract 15 from the left side of the equation.
If we subtract 15 from the left side, we must also subtract 15 from
the right side of the equation to keep the equation balanced.
So we have x = 47.
14. Solve 10 + 6(-9 – 4x) = 10(x - 12) + 8.
O A. X = 17
OB. X = 2
O C. X = -18
O D. X = -6
Answers
Answer:
B
Step-by-step explanation:
[tex]10+6(-9-4x)=10(x-12)+8[/tex]
[tex]10-54-24x=10x-120+8[/tex]
[tex]-44-24x=10x-112[/tex]
[tex]-44=34x-122[/tex]
[tex]78=34x[/tex]
[tex]x=2[/tex]
Find the equation of the exponential function represented by the table above
Answers
Answer: Y = 3 × 2^x
Step-by-step explanation:
Let assume that the equation of the exponential function represented by the table is
Y = 3(2)^x
When x = 0
Substitute x for 0. Then,
Y = 3 × 2^0
Anything raised to power of zero is equal to one.
Y = 3 × 1 = 3
When x = 1
Repeat the process
Y = 3(2)^1
Y = 3 × 2 = 6
When x = 2
Y = 3(2)^2
Y = 3 × 4 = 12
And finally, when x = 3
Y = 3(2)^x
Substitute x for 3
Y = 3 × 2^3
Y = 3 × 8
Y = 24.
We can therefore conclude that the equation of the exponential function represented by the table above is
Y = 3 × 2^x
which is a quadratic function
f(x)=2x+x+3
f(x)=0x2-4x+7
f(x)=5x2-4x+5
f(x)3x3+2x+2
Answers
Answer:
f(x)=5x^2-4x+5
Step-by-step explanation:
A quadratic function always has a squared symbol (represented by ^2). The first answer is a linear function, the second answer is a linear function (squaring 0 results in 0, therefore it is canceled out), the third answer has ^2 (this is correct), and the fourth answer has a ^3 (this is a cube function; not quadratic)
Answer:
It is indeed C. f(x) = 5x2 – 4x + 5
Step-by-step explanation:
If this Question is on Edg, then it is C!
Solve the equation :
[tex] \cos(x) - \sin(x) = \sqrt{2 } \: cos(3x)[/tex]
Answers
Answer:
General solution is
[tex]x = n \pi + \frac{\pi }{8}[/tex]
Step-by-step explanation:
Step(i):-
Given cos x - sin x = √2 cos (3 x)
Dividing '√2' on both sides , we get
[tex]\frac{1}{\sqrt{2} } cos (x) - \frac{1}{\sqrt{2} } sin (x) = \frac{\sqrt{2} cos (3 x)}{\sqrt{2} }[/tex]
we will use trigonometry formulas
a) Cos ( A + B) = Cos A Cos B - sin A sin B
b) [tex]cos \frac{\pi }{4} = \frac{1}{\sqrt{2} }[/tex]
Step(ii):-
[tex]\frac{1}{\sqrt{2} } cos (x) - \frac{1}{\sqrt{2} } sin (x) = \frac{\sqrt{2} cos (3 x)}{\sqrt{2} }[/tex]
[tex]cos (\frac{\pi }{4} ) cos x - sin(\frac{\pi }{4} ) sin x = cos 3x[/tex]
[tex]cos (\frac{\pi }{4}+x ) = cos 3 x[/tex]
Step(iii):-
General solution of cos x = cos ∝ is x = 2 nπ+∝
we have [tex]cos (\frac{\pi }{4}+x ) = cos 3 x[/tex]
The general solution of [tex]cos (\frac{\pi }{4}+x ) = cos 3 x[/tex] is
⇒ [tex]3 x = 2 n \pi + (\frac{\pi }{4}+x )[/tex]
⇒ [tex]3 x- x = 2 n \pi + \frac{\pi }{4}[/tex]
[tex]2x = 2 n \pi + \frac{\pi }{4}[/tex]
final answer:-
General solution is
[tex]x = n \pi + \frac{\pi }{8}[/tex]
Type the expression that results from the following series of steps: Start with z , subtract 5, then times by 3.
Answers
Answer:
(z - 5)3
Step-by-step explanation:
Since we are following the directions strictly, we must subtract 5 from z first.
z - 5
Then we multiply the ENTIRE thing by 3
3(z - 5)
Answer:
(z-5)3 or (z-5)*3
Step-by-step explanation:
Use Pedmas. I am sorry I am not good a explaining but that is the answer.
Please i need help with this ASAP....many thanks
Answers
Answer:
Yes, he has enough money.
Step-by-step explanation:
I found the heaviest healthy weight for the man which is at 84kg. This means he has to lose 14 kg to be healthy.
Take 14kg divided by 0.75 kg/week to find how many weeks of the diet he needs.
13/0.75 = 18.67 = 18 weeks
Take the number of weeks times the number of calories per week
18 x 600 = 10800
Take this number divided by 200 calories per hour to find the total number of hours.
10800/200 = 54 hours
Take this number times the amount of money per hour.
54 x 6 = 324 This number is less than 360
WILL AWARD BRAINLIEST
Note: This is the same question as #3, but the third row of the proof is different!
Statements
Reasons
0
DE || AB
Given
E
B
CDE
Given: DE || AB
Prove: AABC-
ZCE
AABCN
Answers
Answer:
ΔABC is similar to ΔCDE
Step-by-step explanation:
Statement Reason
DE ║AB Given
∠CDE ≅ ∠CAB Corresponding Angles Theorem
∠C ≅ ∠C Reflexive property of congruence
ΔABC is similar to ΔCDE AA postulate
The Corresponding Angles Theorem states: If two parallel lines (DE and AB) are cut by a transversal (CA), then the pairs of corresponding angles are congruent (∠CDE and ∠CAB).
Reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself (∠C is congruent to itself).
Angle Angle (AA) postulate states that two triangles are similar if they have two corresponding angles congruent (∠CDE ≅ ∠CAB and ∠C ≅ ∠C)
In one year, a satellite orbiting the Earth travels 9.6 x 10^10 m (meters). Which
of the following is the best way to rewrite this quantity, using more
appropriate units?
A. 9.6 x 10^10 m
O B. 9.6 x 10^7 km
O C. 9.6 x 10^12 cm
D. 9.6 x 10^13 mm
Answers
Answer: B: 9.6 x 10 7 km
Step-by-step explanation:
Ahmed is working at a burger joint. His boss pays him $6.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages, in dollars, starting with his current wage?
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
a basket holds 26 cards, and each card has a letter of the alphabet on it. each time a card is drawn, it is returned to the basket before the next card is drawn. what is the probability of selecting a constant on the first draw, a vowel (a,e, i,o or u) on the second draw, and then another constant on the third (and last) draw? a 7/52 b 525/4394 c 2205/17576 c 147/1040
Answers
Answer:
2205/17576
Step-by-step explanation:
26 cards
5 vowels , 21 consonants
P( consonant) = consonant / total =21/26
Return the card
26 cards
5 vowels , 21 consonants
P ( vowel) = vowel/total= 5/26
Return the card
26 cards
5 vowels , 21 consonants
P( consonant) = consonant / total =21/26
P( consonant, return, vowel, return, consonant) = 21/26 * 5/26* 21/26
2205/17576
6j + 7 =21 -j pls show work
Answers
Answer:
Step-by-step explanation:
6j + 7 = 21 - j
Add 'j' to both sides
6j + 7 + j = 21 - j +j
7j + 7 = 21
Subtract 7 form both sides
7j + 7 - 7 = 21 - 7
7j = 14
Divide both sides by 7
7j/7 = 14/7
j = 2
Answer:
j = 2
Step-by-step explanation:
6j + 7 = 21 - j
6j + j = 21 - 7
7j = 14
j = 14/7
j = 2
KELLY Connect
Deidra Roberts
CONTACT CENTER OUTSOURCING
Supervisor: "You are currently scheduled to work Monday through Friday of next
week. I need you to try to assist 9 more customers per day to hit your goal for the
week."
Employee: "That seems very realistic. I currently assist an average of 52 customers
per day, so the total number of customers l assist per week would be
295
300
304
305
Answers
Answer:
305
Step-by-step explanation:
52 customers per day * 5 days per week
260 currently
Now add the 9 per day to find you new goal
52+9 = 61 per day
61 *5 = 30
305 per week is your goal
Every 7th person who enters a store is given a survey to complete. Which type of sampling method is described in this situation?
A. voluntary sample
B. convenience sample
C. simple random sampling
D. systematic random sampling
Answers
Answer:
D. Systematic Random Sampling
Pls mark as Brainliest
Use the matrix tool to solve the system of equations. Choose the correct ordered pair. 4x-7y=-12 and -2+6y=11 plz help!!
Answers
Answer:
Option C.
Step-by-step explanation:
Note: x is missing in the second equation.
The given equations are
[tex]4x-7y=-12[/tex]
[tex]-2x+6y=11[/tex]
It can we written as
[tex]\left[\left.\begin{matrix}4 & -7\\ -2 & 6\end{matrix}\right|\begin{matrix}-12\\ 11\end{matrix}\right][/tex]
Divide row 1 be 4.
[tex]\left[\left.\begin{matrix}1 & -\dfrac{7}{4}\\ -2 & 6\end{matrix}\right|\begin{matrix}-3\\ 11\end{matrix}\right][/tex]
Applying [tex]R_2\to R_2+2R_1[/tex], we get
[tex]\left[\left.\begin{matrix}1 & -\dfrac{7}{4}\\ 0 & \dfrac{5}{2}\end{matrix}\right|\begin{matrix}-3\\ 5\end{matrix}\right][/tex]
Applying [tex]R_2\to \dfrac{2}{5}R_2[/tex], we get
[tex]\left[\left.\begin{matrix}1 & -\dfrac{7}{4}\\ 0 & 1\end{matrix}\right|\begin{matrix}-3\\ 2\end{matrix}\right][/tex]
Applying [tex]R_1\to R_1+\dfrac{7}{4}R_2[/tex], we get
[tex]\left[\left.\begin{matrix}1 & 0\\ 0 & 1\end{matrix}\right|\begin{matrix}\dfrac{1}{2}\\ 2\end{matrix}\right][/tex]
Since [tex]x=\dfrac{1}{2}\text{ and }y=2[/tex], therefore required ordered pair is [tex](\dfrac{1}{2},2)[/tex].
Hence, option C is correct.
if a square is dilated by a factor of 2 what is the measure of each individual angle
Answers
Answer:
4:1
Step-by-step explanation:
If the side length x is dilated to 2x, the area x² will dilate to (2x)² = 4x², which is 4 times the original x².
The measure of each individual angle will be of 90°
What is a quadrilateral ?A quadrilateral is a 2D figure which has 4 sides.
According to the given question a square is dilated by a factor of 2.
Suppose the side of the original square was x cm.
∴ We know the area of he square will be side² which is
= (x)²
= x².
Now the square is dilated by a factor of 2.
∴ Side of the new square will be 2x and the area of the new square will be (2x)² which is 4x².
But the measure of each individual angle will be same and they are all of 90°.
learn more about quadrilateral here :
https://brainly.com/question/13805601
#SPJ2