HELP 30 pts
Prove this trigonometric identity. Any help is appreciated. Thanks!
Answers
Answer: See the attached image.
I've rearranged the tiles in the proper order
===================================================
Explanation
For step 2, we rewrite each expression in terms of sines and/or cosines. For instance, tan = sin/cos.
In step 3, we focus on the stuff in the numerator only. So we focus on sin/cos+cos/sin. In this step, we multiply top and bottom of the first fraction by sine. We multiply top and bottom of the second fraction by cos. These steps are done to get the LCD.
In step 4, we are able to add the fractions because both fractions have the same denominator.
In step 5, we use the pythagorean trig identity sin^2+cos^2 = 1.
In step 6, we use the idea that (A/B) divide by (C/D) = (A/B)*(D/C).
Related Questions
Determine the general rule for the sequence 19;11;3;.....
Answers
Answer:
Answer 3.0/528 claudiasai 88-2n + 2927,25,23,21,19- 2 difference- 2n + 29-2 x (1 ) + 29 =27-2 x (3) +29 =23
Step-by-step explanation:
Write a recursive formula for each sequence. 3. 1, 6, 11, 16, ... SOLUTION: ... Check for a common ratio by dividing each term by the term that precedes it. = 3 ;. = 3 ; ... 19. 100, 80, 64, 51.2, ... SOLUTION: Subtract each term from the term that follows it. ... Patrick thinks that the sequence can be written as a recursive formula.
Answer:
[tex]a_{n}[/tex] = 27 - 8n
Step-by-step explanation:
There is a common difference between consecutive terms, that is
11 - 19 = 3 - 11 = - 8
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 19 and d = - 8 , then
[tex]a_{n}[/tex] = 19 - 8(n - 1) = 19 - 8n + 8 = 27 - 8n ← general rule
A Department of transportation report about air travel that nationwide, 76% of all flights are on time. In a sample of 12 flights, what is the probability that 3 flights will be late?
Answers
Answer:
The probability of 3 flights are late is 0.25.
Step-by-step explanation:
Total number of flights = 12
Flights on time = 76 % = 0.76 x 12 = 9.12 = 9
flights which are late = 24 % = 0.24 x 12 = 2.88 = 3
The probability of 3 flights are late is
P = 3/12= 1/4 = 0.25
Susan and Katie are running an ultra marathon. Susan averages 5 miles per hour. Katie averages 5.2
miles per hour. If Susan gets a 45 minute head start, then exactly how many hours after Katie begins
running will she catch up to Susan?
Answers
Answer:
Katie will catch up to Susan after running 33.4 h.
Step-by-step explanation:
We can find the time that takes Katie to catch up to Susan by using the following equation:
[tex] x_{f_{k}} = x_{0_{k}} + v_{0_{k}}t + \frac{1}{2}at^{2} [/tex]
Where:
[tex] x_{f_{k}} [/tex]: is the final position of Katie
[tex] x_{0_{k}} [/tex]: is the initial position of Katie = 0
[tex] v_{0_{k}}[/tex]: is the initial speed of Katie = 5.2 mi/h
a: is the acceleration = 0 (she is moving at constant speed)
t: is the time
Since Katie will catch up to Susan, the final distance traveled by Katie will be equal to the final distance traveled by Susan.
[tex] x_{f_{s}} = x_{0_{s}} + v_{0_{s}}t + \frac{1}{2}at^{2} [/tex]
[tex] x_{0_{k}} + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Since Susan gets a 45 minutes head start, in that time she traveled the following distance:
[tex] d = \frac{v}{t} = \frac{5 mi/h}{45 min*\frac{1 h}{60 min}} = 6.67 mi [/tex]
So, this will be the initial position of Susan.
[tex] 0 + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Hence, the time will be:
[tex] 5.2t = 6.67 + 5t [/tex]
[tex] t = 33.4 h [/tex]
Therefore, Katie will catch up to Susan after running 33.4 h.
I hope it helps you!
whats the value of x? 8(-6 + 6x) = 240
Answers
Answer:
x = 6
Step-by-step explanation:
8(-6 + 6x) = 240
Distribute the 8
-48 + 48x = 240
Add 48 to both sides
48x = 288
Divide both sides by 48
x = 6
express 81 as sum of odd numbers.
Answers
Step-by-step explanation:
[tex]1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17[/tex]
Solution all the odd no. show sum is 81In a survey of students , every student studies at least one of the three subjects Maths English and Science . The number of students who study only one subject is twice the number of students who study only two students . If 20 students study all three and 80 students who study only two subjects, find the total number of students in the survey.
Answers
Answer:
80x2=160 20x3=60 160+60=220
Step-by-step explanation:
Oksana wrote the equation below on the whiteboard.
6 b + 6 = 48
What is the value of b?
4
7
8
9
Answers
Answer:
b = 7
Step-by-step explanation:
6 b + 6 = 48
Subtract 6 from each side
6b+6-6 = 48 -6
6b = 42
Divide each side by 6
6b/6 = 42/6
b = 7
Answer:
7Step-by-step explanation:
6b +6 = 48
collect terms that is ,
6b =48 - 6
6b = 42
divide both sides by 6
therefore, b = 42/6 =7
Hope this helps !
Find the area of a regular octagon with
a side length of 10 cm. Round to the
nearest tenth.
10 cm
Answers
Answer:
482.8 cm
Step-by-step explanation:
A=2(1+sqrt2)a^2=2·(1+squrt2)·10^2=482.84271
The odometer on Ed's car shows 8,946 miles. The odometer on Beth's car shows 5,042 miles driven. Which car has traveled the most miles?
(NO LINKS)
Answers
Answer:
since 8946 is more then 5042 we know ed has driven the most miles.
Step-by-step explanation:
Identify the angle between 0 and 360 degrees that is coterminal with the
following angle *
1155°
Answers
Answer:
option 2
Step-by-step explanation:
By repeatedly subtracting 360° from the given angle.
1155° - 360° = 795°
795° - 360° = 435°
435° - 360° = 75° ← coterminal angle
What is the sum of the polynomials below ? 3y^5-2y+8 2y^5 - 4y^3-7
Answers
Answer:
[tex](3 {y}^{5} - 2y + 8) + (2 {y}^{5} - {4y}^{3} - 7) \\ = 5 {y}^{5} - 4 {y}^{3} - 2y + 1[/tex]
Simplify using suitable property. Also name the property used:-3/5 x 4/7 + 8/5x 4/7
Answers
Answer:
The answer is 4/7 and the property used is the distributive property
Step-by-step explanation:
Recall from the distributive property;
a * (b + c) = ab + ac
Applying same here, we have it that;
4/7 (-3/5 + 8/5)
= 4/7 * ((-3 + 8)/5)
= 4/7 * 5/5
= 4/7 * 1 = 4/7
Find the mean absolute deviation of the following numbers. 10, 8, 5, 12, 20
Answers
Step-by-step explanation:
We need to find the mean absolute deviation of the following set of data.
10,20,12,4,18,8,14,18
For finding mean absolute deviation, first we need to find the mean of the given data set.
The formula used to calculate mean is:
Sum of all data points: 10+20+12+4+18+8+14+18 = 104
Number of data points = 8
So, mean is:
Now, we will subtract 13 from the given data points:
10 - 13 = -3
20 - 13 = 7
12 - 13 = -1
4 - 13 = -9
18 -13 = 5
8 - 13 = -5
14 - 13 = 1
18 - 13 = 5
We will take absolute values i.e |-a|=a
So, now the numbers will be:
3,7,1,9,5,5,1,5
We will now find absolute mean deviation by finding mean of newly calculate values
Sum of all data points = 3+7+1+9+5+5+1+5
Number of data points = 8
So, the mean absolute deviation of the following set of data is 4.5
PLEASE HELP How can you make different triangles with the same angle measures?
Form different triangles with angle measures 90°, 75°, and 15°
How can you make different triangles with the same angle measures?
O A. Make triangles with the same angle measures and the same side lengths
OB. It is not possible to make different triangles with the same angle measures.
OC. Make triangles with the same angle measures but different side lengths
OD. Make triangles with the same side lengths but different angle measures
Answers
Reasoning:
The angle measurement has to be the same according to the question. The side lengths only impact the shape of a triangle, making it different even if two triangles have the same measurement.
which of the following is the slope of a line perpendicular to the line y = -2/3 x +5
Answers
Answer:
-2/3x is the slope
Step-by-step explanation:
y=mx+b is the equation to follow
PLEASE I REALLY NEED HELP
Plans for a new school call for classrooms directly across the hall from each other to be congruent. This computer printout shows a math classroom. If the vertices of a science classroom are located at (-3x¹,y¹). (-3x²,y²), (-3x³, y³), and (-3x⁴, y⁴), will the science classroom be congruent to the math classroom?
Answers
The lengths of the horizontal sides of the science class is larger than the
length of the horizontal side of the math class.
The correct option is; No, the the transformation applied was not a rigid motion.
Reasons:
The given vertices of the science classroom are;
(-3·x₁, y₁), (-3·x₂, y₂), (-3·x₃, y₃), and (-3·x₄, y₄)
The coordinates of the vertices math classroom are;
(x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄)
Whereby x₁ = x₄, we have;
Length of the vertical side of the rectangular math class = y₁ - y₄
Length of the horizontal side, [tex]L_M[/tex] = x₂ - x₁
Similarly;
The length of the horizontal side of the science class is, [tex]L_S[/tex] = -3·x₂ - (-3·x₁)
Therefore;
[tex]L_S[/tex] = 3·(x₁ - x₂) = [tex]\mathbf{3 \cdot L_M}[/tex]
The length of a side of the science is three times the length of the side of
the math class, which gives that the dimensions of the science class are not
the same as the the dimensions of the math class.
Therefore;
The science class and the math class are not congruent
The the correct option is, no the transformation that gives the science class from the math class is not a rigid transformation.Learn more about non-rigid transformation here:
https://brainly.com/question/2396426
The president of a small company
made $72,000 last year. She cut her
salary this year to $60,000 because
the company was not doing as well.
What was the percent decrease in
her salary to the nearest percent?
Answers
Answer:
17%
Step-by-step explanation:
Percent decrease
[tex] = \frac{72000 - 60000}{72000} \times 100 \\ \\ = \frac{12000}{72000} \times 100\\ \\ = \frac{1200000}{72000} \\ \\ = 16.67 \% \\ \\ \approx \: 17 \%[/tex]
I need help with this question w2–23w–50
Answers
Answer:
(w - 25)(w + 2)
Step-by-step explanation:
w² - 23w - 50
w² + 2w - 25w - 50
w(w + 2) - 25(w + 2)
(w - 25)(w + 2)
W² – 23 W – 50 =0
(w - 25) ( w+2) =0
As for:
w-25=0
w=25
or :
w+2=0
w=-2
I hope I helped you^_^
James goes to a meeting that lasts 1 hour and 50 minutes. The clock shows the time the meeting ends. What time did the meeting begin？
Answers
The required time, when the meeting begins is given as 11:55 minutes.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
When the meeting end the time was 1:45,
Meeting last for 1 hour and 50 minutes.
Now,
1 hour and 50 minutes. = 01 : 50 minutes
Required time = 12 : 00 + 1:45 - 01:50
= 12 :00 - 00:05
= 11 : 55 minutes
Thus, the time when the meeting begins is given as 11:55 minutes.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
Help,anyone can help me do quetion.
Answers
Answer:
C2- 65° C3- 84°
Step-by-step explanation:
for C2:
the 2 parallel lines and the one cutting fully through form a transversal.
One of the rules for this is that co-interior angles (the 2 on the same side of the intersecting line) add to 180°.
This means that the angle at the top left (still within the triangle) should be 50° (180-121).
The other angle within the triangle (not the x one) is vertically opposite (opposite or "diagonal") with the 65°.
Vertically opposite angles have the same value, meaning the second angle is 65°.
In a triangle, the 3 angles add to 180. In this case, 50+65+x=180, which can be simplified to 115+x=180. Subtracting 115 from both sides gives x=65°.
For C3-
Imagine a parallel line is going through the angle x, splitting it into 2 angles (let's call them a and b).
With a being the top half, you can use the 133° given to help you. Like before, vertically opposite angles are the same, so the value "diagonal" to 133° should also be 133°. Using the co-interior rule, a should be 180-133, which gives 47°.
For b, we can skip this first step entirely. Since 143 and b are co-interior, 180-143=b, therefore b=37°.
To use these, remember a+b=x, which by subbing in the values gives 47+37=x, simplified to x=84°.
** I suggest revising the types of transversal relationships (corresponding, alternate, vertically opposite and co-interior). It's difficult explaining this without diagrams, but if you need more clarification, I'm happy to help!
At the dance shoe store, they sell Tap, Point, and Ballet shoes. A pair of point shoes are double the price of ballet shoes. The tap shoes are $10 more than ballet shoes. If the total price of all the shoes is $648, how much is each shoe
Answers
Answer:
a pair of Tap shoes costs $169.50
a pair of Point shoes costs $319.00
a pair of Ballet shoes costs $159.50
Step-by-step explanation:
first tell your teacher, that the problem description is misleading.
as a shoe store has more than one pair per type. so, "all the shoes" would mean all the sites in the store. but that is for sure not meant here.
what your teacher hopefully meant was that the total price of buying one pair of each of the shoe types is $648.
and your teacher was hopefully asking for the price of pairs of shoes, and not actually single shoes.
my solution bases on these assumptions.
so, we got Tap (t), Point (p) and Ballet (b) shoes.
buying one pair each is
t + p + b = 648
now we know some other information.
p = 2×b (Point shoes are double the price of Ballet shoes)
t = b + 10 (Tap $10 more than Ballet)
so, we can replace t and p by expressions of b and get
b + 10 + 2×b + b = 648
4×b + 10 = 648
4×b = 638
b = 159.50
p = 2×159.50 = 319.00
t = 159.50 + 10 = 169.50
Solve the system of equations below using the elimination method.
Show how you determined your solution.
4x+y=23
3x-y=12
Answers
Answer:
The solution is (5, 3)
Step-by-step explanation:
To solve this system of linear equations, let's use elimination by addition and subtraction. This approach is particularly easy because one equation already has +y and the other -y, summing up to zero:
4x+y=23
3x-y=12
---------------
7x = 35
Then x must be 5.
Substituting 5 for x in the first equation, we get
4(5) + y = 23. Then 20 + y = 23, or y = 3.
The solution is (5, 3)
11.) Evaluate the expression.
Answers
Answer:
- 116
Step-by-step explanation:
Given
28 - ( [tex]\sqrt{144}[/tex] )²
= 28 - (12)²
= 28 - 144
= - 116
Solve the following equation for x.
18 – 4.x = 10 - 2x
A x = -4
B) x = -1
C) x = 1
D) x =4
Answers
Answer:
D) x = 4
Step-by-step explanation:
18 - 4x = 10 - 2x
10 - 2x = 18 - 4x
10 - 2x + 4x = 18 - 4x + 4x
10 + 2x = 18
10 - 10 + 2x = 18 - 10
2x = 8
2x ÷ 2 = 8 ÷ 2
x = 4
CORRECTLY ANSWER PLEASE AND THANK YOU
Answers
9514 1404 393
Answer:
(-3, 4)
Step-by-step explanation:
The midpoints of the diagonals of a parallelogram are coincident. This means the sums of coordinates at the ends of the diagonals are the same. For missing point P, we must have ...
P +(0, -3) = (-6, -6) +(3, 7)
P = (-6, -6) +(3, 7) -(0, -3)
P = (-6 +3 -0, -6 +7 -(-3))
P = (-3, 4)
if cos a>0 and cot a is undefined then where does the terminal side of a located?
A. Quadrant II
B.quadrant III
C.negative x axis
D.negative y axis
E.no such angle a exists
Answers
Answer:C
Therefore: In Quadrant I, cos(θ) > 0, sin(θ) > 0 and tan(θ) > 0 (All positive). For an angle in the second quadrant the point P has negative x
Step-by-step explanation:
Which of the following is the definition of the sine ratio in a right triangle
Answers
Answer:
Oppositeleg
adjacenleg
Answer:
option 1
Step-by-step explanation:
Just remember this to get the trigonometric ratio in a right triangle :
Old Henry And His Old Aunt
O for opposite
H for hypotenuse
A for Adjacent
Sin = O/ H
Cos = A /H
Tan = O /A
The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors?
Answers
This question is incomplete
Complete Question
A varsity boys' basketball team has a ratio of seniors to juniors that is 7:4.
The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors
Answer:
The boys' team has more seniors
Step-by-step explanation:
If each team has 12 juniors,
Step 1
For the boys' basketball team, lets find the total number of people on the team
A varsity boys' basketball team has a ratio of seniors to juniors that is
7:4 = seniors : juniors
Sum of proportion
= 7 + 4 = 11
Let the total number of people on the team = x
Hence:
4/11 × x = 12
4x/11 = 12
Cross Multiply
4x = 11 × 12
x = 11 × 12/4
x = 33 members
The number of seniors is calculated as
33 members - 12 juniors
= 21 seniors
Step 2
For the girls' basketball team, lets find the total number of people on the team
The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2.
= 3:2 = seniors : juniors
Sum of proportion
= 3+2 = 5
Let the total number of people on the team = x
Hence:
2/5 × x = 12
2x/5 = 12
Cross Multiply
2x = 5 × 12
x = 5 × 12/2
x = 30 members
The number of seniors is calculated as
30 members - 12 juniors
= 18 seniors
Therefore, from our above calculations, the boys' team has more seniors
A circle P is circumscribed about a regular hexagon ABCDEF
Arc AB =
Select one:
a. 60
b. 120
c. not enough information
d. 90
Answers
Answer:
angle degrees is 60
so the answer would be A
Step-by-step explanation:
because there are 6 sides, 360 is divided by 6.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli. The correct value of t* to construct a 98% confidence interval for the true mean amount of cheese filling is ________. Group of answer choices 2.797 2.492 2.064 3.467 3.745
Answers
Answer:
The correct value is t* = 2.492.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.492, which is the answer to this question.
