Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:
[tex]\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]
To start, we can multiply the fraction by (1 - sin(θ)). This yields:
[tex]\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta[/tex]
Simplify. The denominator uses the difference of two squares pattern:
[tex]\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta[/tex]
Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:
[tex]\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]
Split into two separate fractions:
[tex]\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta[/tex]
Rewrite the two fractions:
[tex]\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta[/tex]
By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:
[tex]\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta[/tex]
Hence verified.
If the right angle triangle LMN.
L=30°, MN = 4cm and diagonal LM.
Find the LM and LN.
Find the measure of one exterior angle for the following regular polygon that’s for both questions
Answer:
Step-by-step explanation:
HELP ME ASAP!!!
two angles are supplementary. one angle is three less than 4 times it's supplement. what are the measures of the two angles?
Step-by-step explanation:
Two angles are supplementary one angle is 4 degrees less than three times the other find the measures of the angles
x + y = 180
x = 3y - 4
3y - 4 + y = 180
4y = 184
y = 46
x = 134
Answer:
30°，150°
Step-by-step explanation:
Sequence Problem Below
Answer:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}[/tex]
Step-by-step explanation:
[tex]\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4[/tex]
Write the equation of the line with a slope of 4 that contains the point (5, 8).
Answer:
y = 4x - 12
Step-by-step explanation:
y = 4x + b
8 = 4(5) + b
8 = 20 + b
-12 = b
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: \: we \: know \: that \: \\ \sf \: if \: any \: equation\:of \: line \: which \: slope (m) \\ \sf \: and \: passes \: through \: (x_1,y _1) \: \: then \: its \\ \sf equation \: is \: : \\ \\ \red{ \boxed{ \bf y - y_1 = m(x - x_1)}}\bf\end{array}}}}[/tex]
Given that,
A equation of the line with a slope of m = 4 and that contains / passes through the point (5, 8).
So,
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: x_1 = 5 \: \: \: \\ \bf y_1 = 8 \\ \bf \: m \: = 4 \: \: \end{array}}}}[/tex]
NOW,
The equation is :
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: y - 8 = 4(x - 5) \\ \\ = > \bf \: y - 8 = 4x - 20 \\ \\ = > \pink{ \boxed{\bf\:4x - y - 12 = 0}} \end{array}}}}[/tex]
THIS IS TIMED I NEED THE ANSWER NOW
Answer:
114 pi or 359
Step-by-step explanation:
find the perimeter of the isosceles trapezoid
Answer:
A =136 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2( 22+12) *8
A = 1/2 ( 34)*8
A =136 cm^2
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
SEE QUESTION IN IMAGE
Answer:
d) 2y + x = 106Step-by-step explanation:
Mean of the data = sum of the data / number of frequencies:
(40 + 38 + y + y + x + 32)/6 = 362y + x + 110 = 36*62y + x = 216 - 1102y + x = 106Correct choice is d
LOL….HEY
(Btw I’m not new to brainly, but I just forgot my old password) *sigh* ughh I start school August second and it’s gonna be my first year in high-school ….I- first of all summer break was wayyyyyyyyy too short basically 2 months and a half while the rest of the year I have to bust my behind preparing for test that don’t have anything to do with MY future plans….eeeee every time I think about it my anxiety levels raise higher and higher …..if any upper class men have some advice plz tell me…cuz I am legit terrified ngl (I checked out some freshmen tips on yxutube but that didn’t really help that much) *and btw this is kind of academically related so need to report me*
Answer:not a man but I think you should just relax and be yourself, high school isn’t scary at all. When you go in for orientation walk around the school and find your classes so you have a good map of where you need to go in your head already! Best of luck
Step-by-step explanation:
Find the value of x. I need help ASAP
Answer:
x is 30 degrees
Step-by-step explanation:
It is known that the length of time that people wait for a city bus to arrive is right skewed with mean 6 minutes and standard deviation 4 minutes. A sample of 25 wait times is randomly selected. What is the standard deviation of the sampling distribution of the sample wait times
Answer:
The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30. Otherwise, the mean and the standard deviations holds, but the distribution will not be approximately normal.
Standard deviation 4 minutes.
This means that [tex]\sigma = 4[/tex]
A sample of 25 wait times is randomly selected.
This means that [tex]n = 25[/tex]
What is the standard deviation of the sampling distribution of the sample wait times?
[tex]s = \frac{4}{\sqrt{25}} = 0.8[/tex]
The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.
What should be added to twice the rational number
-1/3 to get 4/5
Answer:
[tex]1 \frac{7}{15} [/tex]
Step-by-step explanation:
[tex] - \frac{1}{3} \times 2 + x = \frac{4}{5} \\ - \frac{2}{3} + x = \frac{4}{5} \\ x = \frac{4}{5} + \frac{2}{3} \\ x = \frac{12 + 10}{15} \\ x = \frac{22}{15} \\ x = 1 \frac{7}{15} [/tex]
Given m
n, find the value of x and y.
m
35°
x
yº
X=
y =
PLS HELP I’m kinda really confused
Answer:
x = 145°, y = 35°Step-by-step explanation:
Given,
m || n
So,
35° = y° [Alternate interior angles]
And,
y° + x° = 180° [Since linear pair]
=> x + 35 = 180
=> x = 180 - 35
=> x = 145°
Hence,
x = 145°, y = 35°
Answer:
x = 145
y = 35
Step-by-step explanation:
35 and y are alternate interior angles and alternate interior angles are equal when the lines are parallel
35 = y
x+y = 180 because x and y form a straight line
x+35 = 180
x = 180-35
x = 145
What is the simplified form of ((15xy^2)/(x^2+5x+6))/((5x^2y)/2x^2+7x+3))
Answer:
(27xy +3)/5x^2 +6x
Step-by-step explanation:
((15xy^2 )/ x^2 + 5x + 6 ) × ((2x^2 + 7x + 3) / 5x^2y)
(3y ×(2x+ 7x + 3)) / 5x^2 +6x)
HELP!!!
I need to know if this is Function or not a function.
Answer:
Not a function
Step-by-step explanation:
Since x = 1 produces y = 3 and y = 4 , the relation is not a function.
( − 2 , − 5) , ( − 1 , − 3 ) , ( 0 , 0 ) , ( 1 , 3 ) , ( 1 , 4 )
The domain cannot be the same value.
Write 6.8167 correct to 3 significant figures.
Answer:
6.82
Step-by-step explanation:
Please help me
A person starts walking from home and walks: 6 miles East 6 miles Southeast 3 miles South 5 miles Southwest 2 miles East This person has walked a total of 22Correct miles Find the total displacement vector for this walk: If this person walked straight home, they'd have to walk miles
Answer:
1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)
2) The number of miles they'd have to walk is approximately 13.856 miles
Step-by-step explanation:
1) The distance, direction, and location of the path of the walk the person takes, are listed as follows;
Start location, (0, 0)
6 miles East walk to location, (6, 0)
6 miles Southeast to location, (6 + 3·√2, -3·√2)
3 miles South to location, (6 + 3·√2, -3·√2 - 3)
5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)
2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)
(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)
Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)
The total displacement vector, [tex]\underset{d}{\rightarrow}[/tex] = ((16 + √2)/2, -(6+11·√2)/2)
d = (16 + √2)/2)·i - (6+11·√2)/2)·j
2) If the person walked straight home, the number of miles they'd have to walk, [tex]\left | \underset{d}{\rightarrow} \right |[/tex], is given as follows;
[tex]\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }[/tex]
Therefore;
If the person walked straight home, the number of miles they'd have to walk [tex]\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles[/tex]
Below are the times (in days) it takes for a sample of 6 customers from Sarah's computer store to pay their invoices.
33, 16, 29, 41, 36, 37
Find the standard deviation of this sample of times. Round your answer to two decimal places.
=___
Answer:
8.80
Step-by-step explanation:
(S. D.)^2=summation(x-mean)^2/(n-1)
S. D.=sqrt(388/5)
S. D.=8.80
Can someone help me out I don't understand
Answer:
1/2
Step-by-step explanation:
You need to see how much times bigger or smaller the shape is after it's changed, that's the scale factor
The dialated image (blue one where it says J'K'T'P') seems like half the size of the black one, so we'll say the scale factor is half or 1/2 (if it's double then the scale factor is 2, for triple, it's 3)
Answered by GAUTHMATH
30 POINTS!!!!
Select ALL the correct answers.
Identify the two tables which represent quadratic relationships.
Answer:
Tables 4 and 6Step-by-step explanation:
Look at the y-values as x-values are same for all tables.
We see that:
Tables 1 and 5 - linear function as the differences are same.Tables 2 and 3 - exponential function as the ratios are same.Tables 4 and 6 - seem quadratic as there are repeat values showing the symmetry.which choice is equivalent to the expression below? 7x√2 - 4√2 + x√2
A. 6x√2 - 3√2
B. 5x^2√2
C. 3x√2
D. 8x√2 - 4√2
Answer:
D
Step-by-step explanation:
[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]
SEE QUESTION IN IMAGE
Answer:
46.Total number in favour:
128 + 96 = 224Probability:
P(favour, A) = 128/224 = 4/747.Total number in against:
32 + 48 = 80Probability:
P(against, not B) = 32/80 = 2/5find the quantity whose 15% in 220
Answer:
Step-by-step explanation:
[tex]\frac{15}{100}*220=\frac{15}{10}*22=3*11 = 33[/tex]
đồ thị hàm số có bao nhiêu tiệm cận
Answer:
c
Step-by-step explanation:
which of the following inequalities represents all values of x for which the quotient below is defined? sqrt 21(x-1) divided by sqrt 7x²
A. x < -1
B. x > -1
C. x < 1
D. x > 1
Answer:
the answer to your question is D
Jonathan has a comic book collection.
He tells you he sold half of them, but then bought 9 more new comics.
After this, Jonathan now has 81 comic books. How many comic books did he have before he sold some? a) Let b = the number of Jonathan had before selling some. Write the equation you would use to solve this problem.
Solve the system of equations:
v=2x-4
y=x2 - 4
The choose (D)
(0,-4) and (2,0)
Mr. Denning bought a jacket for $67.50
and a tie for $12.50. If a sales tax of 3%
was added to the price of his purchase,
what was his total bill?
67.50 + 12.50 = 80
80/100 = 0,8 x 3 = 2.4
so, the total bill was 80 + 2.4 = 82.4
hope it helps :)
Find the length of CB
.
Answer:
CB = 7
Step-by-step explanation:
CB = CK
5x - 3 = 3x + 1
5x - 3x = 1 + 3
2x = 4
x = 4 / 2
x = 2
CB = 5x - 3
= 5 ( 2 ) - 3
= 10 - 3
CB = 7
Answer:
CB = 7
Step-by-step explanation:
since the 2 triangles are AAS (B, K, E, CE as shared side) proven congruent, CB and CK must have the same length.
5x - 3 = 3x + 1
2x = 4
x = 2
CB = 5x - 3 = 5×2 - 3 = 10 - 3 = 7
