Answers
Answer:
a) |sec(θ)|
b) 2cot(2x)
Step-by-step explanation:
Trig identities are used to simplify these expressions. Several are used:
tan(180°-x) = -tan(x)cot(90°-x) = tan(x)1 +tan(x)² = sec(x)²tan(x) = sin(x)/cos(x)sin(2x) = 2sin(x)cos(x)cot(x) = cos(x)/sin(x)__
a.[tex]\sqrt{1-\tan(180^\circ-\theta)\cot(90^\circ-\theta)}=\sqrt{1-(-\tan(\theta))\tan(\theta)}\\\\=\sqrt{1+\tan^2(\theta)}=\sqrt{\sec^2(\theta)}=\boxed{|\sec(\theta)|}[/tex]
__
b.[tex]\dfrac{\cos(2x)\tan(x)}{\sin^2(x)}=\dfrac{\cos(2x)}{\sin^2(x)}\cdot\dfrac{\sin(x)}{\cos(x)}=\dfrac{\cos(2x)}{\sin(x)\cos(x)}\\\\=\dfrac{\cos(2x)}{\left(\dfrac{\sin(2x)}{2}\right)}=2\dfrac{\cos(2x)}{\sin(2x)}=\boxed{2\cot(2x)}[/tex]
Related Questions
Josh wants to spend less than $80 to buy
4 shirts and a pair of pants. The pants cost $24.
The shirts he wants all cost the same.
2. Which inequality can be used to find how
much Josh will spend on each shirt?
A. 4s + 24 > 80
B. 4s + 24 < 80
C. 4s + 24 = 80
D. 4s + 24 = 80
Answers
Answer:
B
Step-by-step explanation:
b because everything must cost less than 80 and
< 80 means the unknown number will be less than 80.
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
is it possible to write vector (-5,6) as a linear combination of vectors (1,2) and (3,4)
Answers
Answer:
Step-by-step explanation:
-5i+6j=x(1i+2j)+y(3i+4j)
-5=x+3y(multiply by 2)
6=2x+4y
-10=2x+6y
subtract
16=-2y
y=-8
-5=x+3(-8)
x=-5+24=19
-5i+6j=19(i+2j)-8(3i+4j)
so we can write (-5,6) as a linear combination of (1,2) and (3,4)
In a right triangle, A = 90 degrees, with side AC = 17 and angle B = 38
degrees, find BC. Round your answer to 1 decimal. Show the labeled figure and all your
work.
Answers
Answer:
The answer is 27.6
Step-by-step explanation:
I've attached a picture with the labelled figured and working steps. Hope it'll help =)
Melanie is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4 and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
Answers
Answer:
20 possible outcomes
Step-by-step explanation:
5 equal-sized sections x 4 sides of the die = 20
What is the equation of the line that passes through the point (-6, -3) and has a
slope of 0
Answers
Answer:
Answer: the equation of the line is y=−3.
Step-by-step explanation:
Since the slope equals 0, then the line is horizontal.
This means that the equation of the line doesn't contain x.
Thus, the equation of the line is y=−3.
Evaluate the expression 8-5xy3 for x=3 and y=-2.
Answers
Answer:
-54
Step-by-step explanation:
8-5xy3 x=3 y=-2
3xy3
3(3)(-2)3
9(-2)3
-18*3
-54
4. In 2003, Mississippi’s labor force totaled
1,312,700 persons. The unemployment rate in
the state was 5.6 percent. Approximately how
many people were employed in that year?
Round your answer to the nearest thousand.
Answers
employed: 1,312,700 people
total people : 1,312,700 unemployment : 5.6%employed : 100% - 5.6% = 94.4%employed people:
94.4% * 1,312,700 1239188.8≈ 1239189 peopleUnemployed persons
5.6% of 13127000.056(1312700)73511Employed persons
1312700-735111238989A rectangle has a length of 10 cm and a width of 7 cm. What is its perimeter?
44 cm
70 cm
34 cm
17 cm
Answers
Answer:
34 cm
Step-by-step explanation:
Keep in mind that the perimeter of a rectangle is the sum of the measures of its sides. This means that the sum of the longer sides and the shorter sides is the perimeter of the rectangle.
Let "L" represent the longer side (length) of the rectangle and "S" represent the shorter side (width) of the rectangle.
⇒ Perimeter of rectangle = L + S + L + S
⇒ Perimeter of rectangle = 2(L) + 2(S)
⇒ Perimeter of rectangle = 2(L + S)
Now, let's substitute the length and the width in the perimeter and simplify.
⇒ Perimeter of rectangle = 2(10 + 7) [L = 10; S = 7]
⇒ Perimeter of rectangle = 2(17)
⇒ Perimeter of rectangle = 34 cm
Answer: 70 cm
Step-by-step explanation: 10 x 7 = 70
hope this helps
Select one: A. 31.7 percent complete. B. 32.5 percent complete. C. 25.0 percent complete. D. 15.0 percent complete.
Answers
Can you please provide the question that goes with the answers? There can be no answer if there isn't a question
why does a week have seven days
Answers
Hi!the week has seven days because the Babylonians, who lived in modern-day Iraq, were astute observers and interpreters of the heavens, and it is largely thanks to them that our weeks are seven days long. The reason they adopted the number seven was that they observed seven celestial bodies — the Sun, the Moon, Mercury, Venus, Mars, Jupiter and Saturn.
the main reason is :
Avid astronomers and astrologers, the developed a kind of horoscope around 500 where each day of the week was assigned to one of the classical planets – the seven celestial bodies visible to the eye. These are the Sun, the Moon, Mars, Mercury, Jupiter, Venus, and saturn
determine the elements of the relation A × A if -
A = { 1 , 2 , 3 }
thankyou ~
Answers
If X and Y are two sets, then X × Y is the Cartesian product of X and Y, which is the set of all pairs (x, y) such that x ∈ X and y ∈ Y.
This means
A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
Solve for X
5х – 1 = 6x — 9
Answers
Answer:
5x-1=6x-9
5x-1-6x= -9
5x-6x= -9+1
-x= -8
(-1)*(-x)= (-1)*(-8)
x=8
a) Write an expression to represent the amount of money you
should have in the following situation.
Angela has $29 in her wallet. She gets paid $19 per hour and she
worked 8 hours last week and 6 hours this week. Then her friend
friend Tom borrowed $58.
b) How much money does Angela have left ?
PLEASE ANSWER THIS. I have an assignment due soon :((
Answers
Answer: $237
Step-by-step explanation:
Angela: 29 + 19(6 + 8) - 58
= -29 + 19(14) = -29 + 266 = $237
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
What is the recursive rule?
Answers
The required recursive function will be expressed as an = 3000 + 500n
How to write recursive functionsGiven the following parameters
First year salary = $30,000
If it increases by $500 each year, let the number of years be "n", then the increment after "n" years is 500n
The required recursive function will be expressed as an = 3000 + 500n
Learn more on recursive function here: https://brainly.com/question/489759
Which recursive sequence would produce the sequence 2, 11, 38,...?
Answers
Answer:
[tex]a_{1} =2[/tex] and [tex]a_{n} =4a_{n-1} + 3[/tex]
Step-by-step explanation:
hope this helps!! p.s. i really need brainliest :)
Which value for Y makes this sentence true?
y = 1/5
Answers
Answer:
[tex] \frac{1}{5} [/tex]
making both sides d same value makes d sentence true
Divide and simplify the answer to lowest terms. Write the answer as a fraction or a whole number.
17/10 ÷ 11/4
17/10 ÷ 11/4=______?
Answers
When you divide by a fraction, flip the second fraction over and change divide to multiply:
17/10 / 11/4 = 17/10 x 4/11
Now multiply straight across:
(17 x 4) / (10 x 11) = 68/110
Simplify:
68/110 = 34/55
Answer: 34/55
Find the area of the shaded region.
Answers
Answer:
3316
Step-by-step explanation:
Hope it will help you
a bag og of grass seed weigh 5.8 pounds. how many
pounds would 2.5 weighs?
Answers
Answer:
the answer is 8.3 it weigh
1. Abe and Malik both stayed after school on
Wednesday to practice their instruments. Abe
practiced for 30 minutes. Malik practiced 10
minutes longer than Abe. Select all the ratios
that compare Abe's practice time to Malik's practice time
Answers
Answer:
Step-by-step explanation:
If Abe practiced 30 minutes,
Malik practiced 40 minutes.
It's 30:40 minutes;
3:4
The Arctic Ocean has an area of about 5×106 square miles. The Atlantic Ocean has an area of about 3×107 square miles. Use these numbers to complete the sentence below. Write your answer in standard form, without using exponents.
The Atlantic Ocean is about how many times as large as the Arctic Ocean?
Answers
Answer:
1.65x
Step-by-step explanation:
multiply 3x107 to get 321.
multiply 5x106 to get 530.
divide 530 by 321 to get 1.65x
Write an equation in point-slope form for the line that passes through the points (f, g) and (h,j).
Answers
Point-slope form is a form of a linear equation: [tex]y-y_1=m(x-x_1)[/tex]
[tex](x_1,y_1)[/tex] is a point that falls on the linem is the slope of the lineTo write an equation in point-slope form:
Calculate the slope of the line by solving for mPlug m into the general equationPlug a point that falls on the line in the general equation as [tex](x_1,y_1)[/tex]Solving the QuestionWe're given:
The line passes through the points (f,g) and (h,j)Solve for the slope (m):
[tex]y-y_1=m(x-x_1)[/tex]
⇒ Plug in the point (f,g) as (x,y):
[tex]g-y_1=m(f-x_1)[/tex]
⇒ Plug in the point (h,j) as (x₁,y₁):
[tex]g-j=m(f-h)[/tex]
⇒ Isolate m by dividing both sides by (f-h):
[tex]\dfrac{g-j}{f-h}=m[/tex]
⇒ Therefore, the slope of the line is [tex]\dfrac{g-j}{f-h}[/tex].
Plug the slope into the general equation:
[tex]y-y_1=\dfrac{g-j}{f-h}(x-x_1)[/tex]
Plug one of the points, (f,g) or (h,j) into the equation as (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
AnswerThere can be multiple answers for this question, depending on what we consider to be (x,y) and what we consider to be (x₁,y₁). This is one of the possible answers, for (f,g) is (x,y) and (h,j) is (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
Amy, Bob, and Carl were using flour from a 7 cup container. Amy used 0.15 of the total container , Bob used 30% of the total container, and Carl used .5 cups of the container. Determine the amount that each person uses and list them from least to greatest.
Answers
Answer:
Amy, Carl, bob
Step-by-step explanation:
Amy = 7 - 0.15 = 6.45
Bob = 7 - 0.30 = 6.70
Carl = 7 - 0.5 = 6.5
Order from least to greatest is:
Amy (6.45)
Carl (6.5)
Bob (6.7)
Find the unit cost (i.e. dollars per unit). Round the answer to 3 decimal places when necessary. A package of 3 AAA batteries costs $3.36.
Answers
Cost per unit = cost /units
please help :) brainliest for helpful answers!
tree is casting a 35 ft shadow when the sun is at a 56° angle of elevation. How tall is the tree?
Answers
Plot the image of triangle AABC under a reflection across the y-axis.
Answers
Answer:
(6,4) (4,4) (2,3) or (2,2)
Step-by-step explanation:
hope it helps
You deposit $2500 into an account that pay 4%. How much is your account after 15 years if compounded continuously?
Answers
Answer:
I think it is 11875
Sorry if im wrong
Hope This Helps
Use the Pythagorean Theorem to find which one of the
following is the hypotenuse c of a right triangle with side
lengths of a = 9 cm and b = 12 cm.
a 12 cm
b 15 cm
C 14 cm
d 17 cm
Answers
Altitude (AB) = 9cm
Base (BC) = 12cm
To FindHypotenuse (AC) = ?
[tex] \fbox \text{According To Pythagoras Theorem = }[/tex]
[tex] \text{(Hypotenuse)² = (Altitude)² + (Base)²}[/tex]
Inserting The Values
[tex] \text{(Hypotenuse)²} =( {9})^{2} + (12) {}^{2} \\ \\ \implies \text{(AC)} {}^{2} = 81 + 144 \\ \\ \implies \text{(AC}) {}^{2} = 225 \\ \\ \implies \text{AC} = \sqrt{225} \\ \\ \implies \text{AC} = 15[/tex]
[tex] \therefore \text{Hypotenuse \: (AC)} = 15 \text{cm}[/tex]
Option B= 15cm is the correct answer
Hope This HelpsMr. Walters asked his students to order 89, 708, 37, and 93 from least to greatest, and to be ready to explain the process they used to order the numbers.One student, Brianna, ordered the numbers correctly, and when Mr. Walters asked her to explain her process, she said, “The numbers 89, 37, and 93 are less than 100, so they are all less than 708, since that is greater than 100. Also, 37 is the least because it comes before 50 and the other two numbers are close to 100. Then 89 is less than 90, but 93 is greater than 90.”Which of the following best describes the strategy on which Brianna’s explanation is based?
Answers
Brianna first indicates that 708 is the greatest number because it is greater than 100, while 37, 89, and 93 are all less than 100.
Next, Brianna indicates that 37 is the least number because it is less than 50, while 89 and 93 are greater than 50. Finally, Brianna recognizes that 89 is less than 93 because 89 is less than 90, while 93 is greater than 90.
Thus, over the course of her explanation, Brianna used 100, then 50, and then 90 as points of reference for comparisons, which is exactly what benchmark numbers are points of reference for comparison.
Brianna did not count between any of the numbers, estimate the numbers, or use the place values in any of the numbers to make her comparisons, so the other options do not describe the strategy on which Brianna's explanation is based. :)
A basket contains 40 mangoes out of which 8 are rotten. Find the percentage of the mangoes that are in good condition
Answers
So 32/40 are good
32/40 as a percentage is 80%
There are 80% of mangoes which are good condition.
What is percentage?Percentage is a relative value indicating hundredth parts of any quantity.
Given that, A basket contains 40 mangoes out of which 8 are rotten.
Mangoes in total = 40
Number of mangoes which are rotten = 8
Mangoes which are good condition = 40-8 = 32
Percentage of good mangoes = 32/40x100 = 80%
Hence, 80% of mangoes are not rotten.
For more references on percentage, click;
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