Fill out the following table. Do you see a pattern? Do you think this will always be true? Why or why not?
*Trolling answers will be flagged & reported, thank you.*
Answers
Answer:
Please see table completed attached
Yes, there are several patterns, since these two trigonometric functions are periodic with same periodicity, and also satisfy the Pythagorean identity for the same angle.
Step-by-step explanation:
Notice that we are asked about a table of trigonometric functions for the so called "special angles" which render values associated with half of the square root of a counting number between 0 and 4:
[tex]\frac{\sqrt{0} }{2}=0 \\\frac{\sqrt{1} }{2}=\frac{1}{2} \\\frac{\sqrt{2} }{2}\\ \frac{\sqrt{3} }{2}\\ \frac{\sqrt{4} }{2}=\frac{2}{2} =1[/tex]
These two trigonometric functions also satisfy the Pythagorean identity for any angle [tex]\theta[/tex] in the unit circle, so the equality to one will always be true:
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]
They are also periodic functions of period [tex]2\,\pi[/tex], so their resulting values will be repeated with that periodicity.
Related Questions
A square tile has a piece broken off it with 7cm².If the area of the remaining rule is 137cm²,what were the dimensions of the original tile?
Answers
Answer:
12 cm × 12 cm.
Step-by-step explanation:
It is given that a square tile has a piece broken off it with 7 cm². The area of the remaining rule is 137 cm².
Total area of square = 7 + 137 = 144 cm² ...(1)
Area of a square is
[tex]Area=a^2[/tex] ...(2)
where, a is side length of square.
From (1) and (2), we get
[tex]a^2=144[/tex]
Taking square root on both sides.
[tex]a=\sqrt{144}[/tex]
[tex]a=12\ cm[/tex]
Therefore, the dimensions of the original tile are 12 cm × 12 cm.
Consider the line . y = 7/3x +2 Find the equation of the line that is parallel to this line and passes through the point . (-9,4) Find the equation of the line that is perpendicular to this line and passes through the point (-9,4)
Answers
Answer:
parallel lines have the same slope. so your new equation will be y = 7/3x + b
to find b, plug in the (x, y) values of (-9, 4) since the line has to pass through this point.
a. 4 = (7/3)(-9) + b
b. 4 = -21 + b
c. b = 4 +21
d. b = 25
your equation is y = 7/3x + 25
perpendicular lines have reciprocated slopes. so your new equation will be y = -3/7x + b
to find b, plug in the (x, y) values of (-9, 4) since the line has to pass through this point.
a. 4 = (-3/7)(-9) + b
b. 4 = (27/7) + b
c. b = 4 - (27/7)
i. (112/28) - (108/28) = 4/28
d. b = 1/7
your equation is y = -3/7x + 1/7
hope this helps :)
3. Daniel is a very good television salesperson. His annual sales average at $187,400. His
commission on sales is 30% and his annual base salary is $40,000. On average what is his
annual gross income?
Answers
Answer:
$96,220
Step-by-step explanation:
Daniel is a very good sales person
His annual sales average is $187,400
His commission on sales is 30%
= 30/100
= 0.3
His annual base salary is $40,000
Therefore, Daniel's annual gross income can be calculated as follows
Annual gross income= Annual base salary + Commission on sales
= $40,000 + (30/100 × $187,400)
= $40,000 + 0.3×$187,400
= $40,000+$56,220
= $96,220
Hence Daniel's annual gross income is $96,220
Answer this question
Answers
Answer:
9120(b)
Step-by-step explanation:
95×96
(90+5)×(90+6)
(90×90)+(5+6) (90)+(5)(6)
(90) square+(5+6) (90)+(5)(6)
I am using identity 4
=8100+990+30=9120
A student accidentally added five to both the numerator and denominator of a fraction, changing the fraction's value to $\frac12$. If the original numerator was a 2, what was the original denominator
Answers
Answer:
Original denominator=9
Step-by-step explanation:
A student accidentally added five to both the numerator and denominator of a fraction, changing the fraction's value to 1/2. If the original numerator was a 2, what was the original denominator.
Original Numerator=2
The new numerator after the addition of 5 will be 2+5=7
New Numerator=7
New denominator=x
Value of the fraction=1/2
The Fraction is written in the form:
7/x=1/2
Cross product
7*2=1*x
14=x
x=14
Therefore, the new denominator (x)=14
Check:
7/14=1/2
Original denominator before 5 was accidentally added
=14-5
=9
Which equation is modeled below?
4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles.
2 x + (negative 2) = negative 2 x + 6
4 x + (negative 2) = negative 2 x + 6
2 x + 4 = 6 x + 2
Negative 2 x + 4 = 6 x + (negative 2)
(Ignore the filled in bubble)
Answers
Answer:
B
Step-by-step explanation:
4 (x) + 2 (-1) = 2 (-x) + 6(1)
4x + -2 = -2x + 6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given figure,
x+x+x+x+(-1-1)=(-x-x)+(1+1+1+1+1+1)
⇒ 4x-2=-2x+6
So, equation modeled as 4x-2=-2x+6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ6
PLZZ HELPP WILL GIVE 100 POINTS Which ordered pairs are solutions to the inequality −2x+y≥−4? Select each correct answer. (0, −5) (1, −2) (3, −1) (0, 1) (−1, 1)
Answers
Answer:
(1, −2) (0, 1) (−1, 1)
Step-by-step explanation:
−2x+y≥−4
Substitute the points into the inequality and see if it is true
(0, −5)
-2(0) + -5 ≥−4
0-5 ≥−4
-5≥−4
False not a solution
(1, −2)
-2(1) -2 ≥−4
-2-2 ≥−4
-4≥−4
True it is a solution
(3, −1)
-2(3) -1 ≥−4
-6 -1 ≥−4
-7 ≥−4
False, not a solution
(0, 1)
-2(0) +1 ≥−4
0+1 ≥−4
1 ≥−4
True it is a solution
(−1, 1)
-2(-1) +1≥−4
2+1≥−4
3≥−4
True it is a solution
Answer:
(1.-2)
(0.1)
(-1,.-1)
Step-by-step explanation:
To solve this we have to plug in each point to see which one would work.
Inequality: -2x + y >= -4
First let's plugin (0,-5):
-2x + y >= -4
-2(0) + (-5) >= -4
0 - 5 >= -4
-5 >= -4 is wrong.
Now let's plugin (1,-2)
-2x + y >= -4
-2(1) + (-2) >= -4
-2 - 2 >= -4
-4 >= -4 is correct
Now let's plugin (3,-1):
-2x + y >= -4
-2(3) + (-1) >= -4
-6 - 1 >= -4
-7 >= -4 is wrong
Now let's plugin (0,1):
-2x + y >= -4
-2(0) + (1) >= -4
0 + 1 >= -4
1 >= -4 is correct
Now let's plugin (-1,1):
-2x + y >= -4
-2(-1) + (1) >= -4
2 + 1 >= -4
3 >= -4 is correct
Would appreciate if you gave me brainliest :)
Caisha has a circular garden with a radius of 4 ft. She needs to put a layer of soil on top. Each bag of soil covers 9.42 square feet. How many bags of soil will she need to buy? 5 bag 6 bags 7 bags 8 bags
Answers
Answer:
6 bags
Step-by-step explanation:
Hey there!
Well first we need to find the area of the circle using,
π r^2
4*4 = 16
16 * pi ≅ 50.27
So now to find how much bags needed we do,
50.27 ÷ 9.42 = 5.34
Meaning 6 bags of soil is needed.
Hope this helps :)
Answer:
Caisha will need 6 bags of soil.
(B.) 6 bags :)
Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answers
Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.
Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g
Help!! I WILL GIVE BRAINLIEST I NEED HELPPPPPPPPPPPPPPPPPPP PLEASE PLEASE PLEASE PLEASEEEEEEEEEEEEE IM DEADD I REALLY NEED HELP ASAP ITS URGENT
Answers
Answer:
arc axb=4.938
Step-by-step explanation:
to find the measure of arc AXB find angle P first
length of the arc=rФ
in triangle APQ sin angle APQ= opp/hyp=AQ(radius)/PQ=5/√5+√21
in traingle PQB sin angle BPQ= opp/hyp.=5/√5+√21
angle P"
2arcsin 5/√5+√21= 94.324 degrees=(π*94.324)/180=1.64626 rad.
arc AXB=Фr (Ф=94.324 , r=3)
arc axb=4.938
if a student is selected at random find the probability the student is a male given that it's a senior. Round to the nearest whole percent.
Answers
Answer: 40%.
Step-by-step explanation:
From the table : Total Seniors = 2+3= 5
Number of male seniors = 2
If a student is selected at random find the probability the student is a male given that it's a senior:
P(Male | senior)[tex]=\dfrac{\text{Number of male seniors}}{\text{Total seniors}}[/tex]
[tex]=\dfrac{2}{5}[/tex]
In percent, [tex]\dfrac{2}{5}\times100=40\%[/tex]
Hence, the probability the student is a male given that it's a senior. =40%.
The probability of the student is a male senior is 7%.
Given, here from the 2- way table the total no. students will be 30.
We have to find out the probability of the student select at random, student is a senior male .
We know that, the probability of an event E, will be
[tex]P(E)=\dfrac{No.\ of \ favaurable\ outcomes}{Total\ outcomes}[/tex]
Now,
[tex]P( Senior\ male)= \dfrac{2}{30} \\\\P( Senior\ male)=0.06\\[/tex]
Representing it in percentage as,
[tex]P( Senior\ male)=0.06666\times100\%\\P( Senior\ male=6.66\%[/tex]
Hence the nearest whole percent will be 7%.
Thus probability of the student is a male senior is 7%.
For more details on probability follow the link:
https://brainly.com/question/795909
after 15 years mary age will be fourtimes of her present age find her present age
Answers
1. In triangle ABC. A-54.2° B=71.5º, a=12 4cm. Find b
Answers
Answer:
13
Step-by-step explanation:
Hassan built a fence around a square yard. It took 48 m^2 of lumber to build the fence. The fence is 1.5 meters tall.
Answers
Answer:
Step-by-step explanation:
Please check ones more because this might be incorrect.
The area is in square meters...Let's change it
Square 48= 48*48 =2304
2304 divided by 4( 4 since the formula for the area of a sqaure is s*s and square has 4 sides)
2304 divided by 4 = 576
The formula for area of a square is S*S(side times side)
Let's apply the formula here.
so, 576 times 576
331776 square meters
Hope this is right and helps! :)
( This just my point of view. Please check this onces again)
Answer:
the answer is 64
Step-by-step explanation:
khan
i cant see the answers anyone else has the problem
Answers
Answer: im having the same problem
Step-by-step explanation:
The side length of an equilateral triangle is 6 cm. What is the height of the triangle? 2
Answers
Answer:
h=3√3 cm
Step-by-step explanation:
An equilateral triangle has 3 Equal sides
The height of an equilateral triangle with side a =a√3/2
That is,
h=a√3/2
Where,
h=height of the equilateral triangle
a=side length
From the triangle given,
a=6cm
Therefore,
h=6√3/2
=3√3
h=3√3 cm
Given the function [tex]h:x=px-\frac{5}{2}[/tex] and the inverse function [tex]h^{-1} :x=q+2x[/tex], where p and q are constants, find a) the value of p and q c)[tex]h^{-1} h(-3)[/tex]
Answers
Answer:
[tex]p = \frac{1}{2}[/tex]
[tex]q = 5[/tex]
[tex]h^{-1}(h(3)) = 3[/tex]
Step-by-step explanation:
Given
[tex]h(x) = px - \frac{5}{2}[/tex]
[tex]h^{-1}(x) = q + 2x[/tex]
Solving for p and q
Replace h(x) with y in [tex]h(x) = px - \frac{5}{2}[/tex]
[tex]y = px - \frac{5}{2}[/tex]
Swap the position of y and d
[tex]x = py - \frac{5}{2}[/tex]
Make y the subject of formula
[tex]py = x + \frac{5}{2}[/tex]
Divide through by p
[tex]y = \frac{x}{p} + \frac{5}{2p}[/tex]
Now, we've solved for the inverse of h(x);
Replace y with [tex]h^{-1}(x)[/tex]
[tex]h^{-1}(x) = \frac{x}{p} + \frac{5}{2p}[/tex]
Compare this with [tex]h^{-1}(x) = q + 2x[/tex]
We have that
[tex]\frac{x}{p} + \frac{5}{2p} = q + 2x[/tex]
By direct comparison
[tex]\frac{x}{p} = 2x[/tex] --- Equation 1
[tex]\frac{5}{2p} = q[/tex] --- Equation 2
Solving equation 1
[tex]\frac{x}{p} = 2x[/tex]
Divide both sides by x
[tex]\frac{1}{p} = 2[/tex]
Take inverse of both sides
[tex]p = \frac{1}{2}[/tex]
Substitute [tex]p = \frac{1}{2}[/tex] in equation 2
[tex]\frac{5}{2 * \frac{1}{2}} = q[/tex]
[tex]\frac{5}{1} = q[/tex]
[tex]5 = q[/tex]
[tex]q = 5[/tex]
Hence, the values of p and q are:[tex]p = \frac{1}{2}[/tex]; [tex]q = 5[/tex]
Solving for [tex]h^{-1}(h(3))[/tex]
First, we'll solve for h(3) using [tex]h(x) = px - \frac{5}{2}[/tex]
Substitute [tex]p = \frac{1}{2}[/tex]; and [tex]x = 3[/tex]
[tex]h(3) = \frac{1}{2} * 3 - \frac{5}{2}[/tex]
[tex]h(3) = \frac{3}{2} - \frac{5}{2}[/tex]
[tex]h(3) = \frac{3 - 5}{2}[/tex]
[tex]h(3) = \frac{-2}{2}[/tex]
[tex]h(3) = -1[/tex]
So; [tex]h^{-1}(h(3))[/tex] becomes
[tex]h^{-1}(-1)[/tex]
Solving for [tex]h^{-1}(-1)[/tex] using [tex]h^{-1}(x) = q + 2x[/tex]
Substitute [tex]q = 5[/tex] and [tex]x = -1[/tex]
[tex]h^{-1}(x) = q + 2x[/tex] becomes
[tex]h^{-1}(-1) = 5 + 2 * -1[/tex]
[tex]h^{-1}(-1) = 5 - 2[/tex]
[tex]h^{-1}(-1) = 3[/tex]
Hence;
[tex]h^{-1}(h(3)) = 3[/tex]
Please explain: Find the measure of angle A. a. 32 b. 57 c. 59 d. No angle exists.
Answers
Answer:
The answer is option B.
57°Step-by-step explanation:
To find Angle A we use cosine
cos ∅ = adjacent / hypotenuse
From the question
The adjacent is 14
The hypotenuse is 26
So we have
cos A = 14/26
cos A = 7/13
A = cos-¹ 7/13
A = 57.42
A = 57° to the nearest degreeHope this helps you
Answer:
57 deg
Step-by-step explanation:
(see attached for reference)
we are given a right triangle together with the lengths of one side (= 14 units) and the hypotenuse (= 26 units)
Using the trigonometry formulas, we can find angle A
cos A = adjacent length / hypotenuse
cos A = 14 / 26
A = cos⁻¹ (14/26) (use calculator)
A = 57.42 deg
A = 57 deg (rounded to nearest whole degree)
Analyze the diagram below and complete the instructions that follow.
Find the value of M angle 2 + M angle 4
Answers
Answer:
200°
Step-by-step explanation:
<2 = 90° (right angle)
<3 = 70° (vertically opposite angles)
<4 + <3 = 180° ( angles on a straight line)
<4 + 70 = 180°
<4 = 180° - 70°
<4 = 110°
<2 + < 4
= 90 ° + 110° = 200°
Jake is going to call one person from his contacts at random. He has 30 total contacts. 16 of those contacts are people he met at school.
What is P(Call a person from school)
Answers
Explanation:
There are 30 contact in total
And there are 16 contacts are people he met at school
P = 16/30 = 8/15
Answer:16/30
Step-by-step explanation:
Exercise topic: Permutations and Combinations. A company wants to hire 3 new employees, but there are 8 candidates, 6 of them which are men and 2 are women. If the selection is random: a) In how many different ways can choose new employees? b) In how many different ways can choose a single male candidate? c) In how many different ways can choose at least one male candidate? with procedures. Help me please..
Answers
Answer:
(a) 56 ways
(b) 6 ways
(c) 56 ways
Step-by-step explanation:
Given:
candidates: 6 mail, 1 female
number to hire : 3
a) In how many different ways can choose new employees?
use the combination formula to choose r to hire out of n candidates
C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways
b) In how many different ways can choose a single male candidate?
6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways
c) In how many different ways can choose at least one male candidate?
To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.
Since there are only two females, there is no way to choose 3 female candidates.
In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.
Jordon will play a triangle at his school’s music program. As its name suggests, the musical instrument is shaped like a triangle. Jordon has customized the dimensions to produce a unique melody, which is played when the shortest side is hanging down, parallel to the ground. Which side of the musical instrument should be parallel to the ground if its dimensions are as shown in the diagram?
Answers
Answer:
A. AB
Step-by-step explanation:
Given that the musical instrument has a shape of ∆ABC, we can determine the shortest side that would be parallel to the ground by comparison of the 3 angles of the triangle corresponding to each side that is opposite each of them.
What this means is that, the larger angle would have the largest side opposite it. The medium angle will have medium length side opposite it, while the smallest angle will have the smallest side opposite it.
m < A = 59°
m < C = 57°
m < C = 180 - (59+57) (sum of angles in a triangle)
m < C = 64°
The smallest angle out of the three angles is angle C = 57°.
The side opposite it, is side AB.
Side AB is the shortest side of ∆ABC.
Therefore, AB should be parallel to the ground.
The
side
of the musical instrument that should be parallel to the ground if the
dimensions
are as given is side AB, which is option A.
Given that:
Jordon will play a
triangle
in his school’s music program.
When playing, the shortest side
is hanging down,
parallel
to the ground.
From the figure:
m∠A = 59°
m∠C = 57°
By the
angle sum
property,
m∠A + m∠B + m∠C = 180°
59° + m∠B + 57° = 180°
m∠B + 116° = 180°
m∠B = 180° - 116°
= 64°
The
shortest side
will be the side that is opposite to the smallest angle.
So, the smallest side is the side opposite to C.
So, the side is AB.
Hence, the side is AB, which is option A.
Learn more about
Triangles
here :
https://brainly.com/question/2773823
#SPJ6
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far (in miles) is it from Jeremy's home to school?
Answers
Answer:
Step-by-step explanation:
18/60-12/60= 4 miles
just my guess
An ancient Greek was born on April 1st, 35 B.C. and died on April 1st, 35 A.D. How many years did he live?
Answers
Answer:
69 years
Step-by-step explanation:
Data provided in the question
Born date of an Ancient Greek = April 1st 35 BC
Diet date of an Ancient Greek = Aril 1st 35 AD
Based on the above information
We can say that
35 + 35 = 70
We deduct 1 as there is no zero
So, it would be
= 70 - 1 year
= 69 years
Hence, An ancient greek lives 69 years and the same is to be considered
can someone please help me
Answers
Explanation:
Since it’s > not _> then we use dash line
And since y > 1/3x - 2 the inequalities will go up cuz y is bigger than 1/3x - 2
Answer:
B
Step-by-step explanation:
Because this equation is just a normal greater than symbol, it has to be a dotted line.
This graph starts at -2 and goes up 1 and right 3(this cancels out C as an option)
Than you shade the region with the larger number vaules, since it is greater than.
Please help! "Create a real-life scenario involving an angle of elevation or depression. Draw an appropriate diagram and explain how to solve your example."
Answers
Answer:
Height of the kite = 86.60 meter (Approx)
Step-by-step explanation:
The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.
Given:
Length of thread = 100 meter
Angle of elevation = 60°
Find:
Height of the kite.
Computation:
Using trigonometry application:
Height of the kite / Length of thread = Sin 60°
Height of the kite / 100 = √3 / 2
Height of the kite = [√3 / 2]100
Height of the kite = 50√3
Height of the kite = 86.60 meter (Approx)
Solve: d |6n+7|=8 can you guys answer me plezzzzzzzz
Answers
Answer: -5/2 or 1/6
Step-by-step explanation:
I6n + 7I = 8
Therefore (6n + 7) = 8 or -8 because modulus means we're only getting it's absolute value, (it's positive value) meaning it could equal 8 or -8 before it's modulus'ed.
Therefore 6n + 7 = 8
or 6n + 7 = -8
Leaving us with:
6n = 1
6n = -15
So n = 1/6
or n = -5/2 (-2.5)
Answer:
n = 1/6 n = -5/2
Step-by-step explanation:
|6n+7|=8
This has two solutions, one positive and one negative
6n+7 = 8 and 6n+7 = -8
Subtract 7 from each side
6n+7-7 = 8-7 6n+7-7 =-8-7
6n =1 6n = -15
Divide by 6
6n/6 = 1/6 6n/6 = -15/6
n = 1/6 n = -5/2
f(x) = 5x - 3
f(5) =_____
Answers
Answer:
22
Step-by-step explanation:
Evaluate!
5(5)-3
25-3
22
Tina had d dollars. She bought three cupcakes for her and her friends, which cost c dollars each. How much money does she have left after being so nice?
Answers
Answer: $(d-3c)
Step-by-step explanation:
Total amount Tina had = $d
Cost of cupcakes = $c
Number of cupcakes purchased = 3
Therefore,
Total cost of cupcakes = cost per cupcake × number of cupcakes
Total cost of cupcakes = $c × 3 = $3c
Amount left after cupcake purchase:
Total amount Tina had - total cost of cupcakes :
$d - $3c
HELP ME PLEASSSSEE On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?
Answers
Answer:
3 degrees F
Step-by-step explanation:
if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.
i hope this helped?