The exact value of cos 105° is equals to √2/4 - √6/4.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
In this case, 105 degrees, can be split into 45+60 (cos (45+60))
Use the sum formula for cosine to simplify the expression;
cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).
The exact value of cos(60) is 1/2.
So, multiply 1/2 to cos (45) - sin (60) times sin (45).
The exact value of cos (45) is the square root of 2 over 2
(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)
The Value of sin (60) is √3/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)
The exact value of sin (45) is √2/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2
Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.
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Liam says -() is equivalent to 2. Explain if Liam is correct by completing the
statements below.
Click the arrows to choose an answer from each menu.
The fraction - (2) can be described as the opposite of a positive number divided by a positive
number. A positive number divided by a positive number results in a Choose...
quotient, and its opposite is always Choose...
The fraction can be described as a positive number divided by a negative number, which
-12
always results in a Choose...
quotient.
value, so Liam Choose...
The fractions have
Choose...
Y
correct.
Someone help I am on my big sisters phone
Answer:
I don't understand the format of the questions and choices. I simply made a few observation.
Step-by-step explanation:
The fraction - (2) can be described as the opposite of a positive number divided by a positive number.
-(2/1)?
A positive number divided by a positive number results in a Choose... Negative Number
quotient, and its opposite is always Choose... Opposite? Still a negative number.
I don't understand the following:
The fraction can be described as a positive number divided by a negative number, which
-12
always results in a Choose...
quotient.
value, so Liam Choose...
The fractions have
Choose...
Y
correct.
I need help please with this
Answer:
24
Step-by-step explanation:
thats what i got from the math i did
What is the volume of the rectangular prism?
2 cm
2 cm
2 cm
Answer:
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Since AC, MN, and DB intersect at O,
( A. Transitive property of congruence.)
( B. Linear pair postulate.)
( C. Congruent supplements theorem.)
( D. Vertical angles theorem.)
It is given that
( A. Linear pair postulate.)
( B. Vertical angles theorem.)
( C. Transitive property of congruence.)
( D. Congruent supplements theorem.).
The paragraph looks like:
Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.
In the question, we are asked to convert the given proof to the paragraph format, where the proof is already given to us.
The proof given to us is:
Statements________________________Reasons
1. AC, MN, and DB intersect at O.______1. given
2. ∠AOM ≅ ∠NOC__________________2. vertical angles theorem.
3. ∠MOD ≅ ∠BON__________________3. vertical angles theorem.
4. ∠BON ≅ ∠NOC__________________4. given.
5. ∠AOM ≅ ∠MOD_________________5. transitive property of congruence.
To convert this proof to the paragraph format, we need to translate each statement along with its reason in the paragraph.
Thus, the paragraph looks like:
Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.
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2(x+2y)^2 + 3(x+2y) +1
Answer:
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Step-by-step explanation:
1) Split the second term in [tex]2{(x+2y)}^{2}+3(x+2y)+1[/tex] into two terms.
1 - Multiply the coefficient of the first term by the constant term.
[tex]2\times1=2[/tex]
2 - Ask: Which two numbers add up to 3 and multiply to 2?
2 and 1.
3 - Split [tex]3x+2y[/tex] as the sum of [tex]2(x+y)[/tex] and [tex]x+2y[/tex].
[tex]2x+2y^2+2(x+y)+x+2y+1[/tex]
2) Collect like terms.
[tex](2x+x)+2y^2+2(x+y)+2y+1[/tex]
3) Simplify.
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Thank you,
Eddie
PLEASE PLEASE PLEASE HELP ME ITS A MATH PROBLEM!!! EXPLANATIONS WELCOMED
Answer:
8
Step-by-step explanation:
The given ratios can be combined to a composite ratio using least common multiples.
Given ratiosWe can identify each of the entities with a 2-letter designation:
TT - Tumtum tree; TW - tulgey wood; BS - frumious Bandersnatch;
ST - slithy tove; BG - borogoves; MR - mome raths; JW - Jabberwocky;
JB - Jubjub birds.
Then the given ratios are ...
20 TT : 1 TW1 TW : 1 BS5 ST : 2 BG2 MR : 1 JW2 JB : 200 TT . . . . (reduces to 1 : 100)200 MR : 1 BG5 JB : 1 STComposite ratiosThe path from BS to JW is unique, so we can work our way there one ratio at a time. Having done this once, we can go back and do it again with the least possible multiplier.
Here, that turns out to be 125 Bandersnatches. We can combine these to the composite ratio ...
125 BS : 125 TW : 2500 TT : 25 JB : 5 ST : 2 BG : 400 MR : 200 JW
Then the ratio of Bandersnatches to Jabberwocks is 125 : 200 = 5 : 8.
If there are 5 frumious Bandersnatches, there should be 8 Jabberwocks.
__
Additional comment
We know 1 JW : 2 MR and 200 MR : 1 BG. In order to get a common value of 200 MR in these ratios, we need to multiply the first by 100:
100 JW : 200 MR : 1 BG
Next, we notice the other ratio involving BG is 2 BG : 5 ST, which means we need to multiply by 2 again:
200 JW : 400 MR : 2 BG : 5 ST
The number of JB is 5 times the number of ST, so this extends to ...
... 5 ST : 25 JB
The number of TT is 100 times the number of JB, so we have ...
... 5 ST : 25 JB : 2500 TT
Continuing in like fashion, we get the composite ratio shown above. We originally worked this starting from BS. Reducing the JB/TT ratio from 2/200 to 1/100 helped eliminate an extra factor of 2.
Step-by-step explanation:
it's not really a math problem per se, it is more like a regular riddle with numbers.
true, everything involving numbers is essentially math, but then what will you do in life with things like earning a salary, going shopping, checking a calendar and schedules for bus, train and flights or business meetings, sharing a pizza with friends, playing computer games, ...
life is for a big part numbers and therefore math.
so, don't be afraid, just use your brain and common sense !
let's think this through (just be strict, concentrated, and follow each line literally) :
5 fr. Band. means 5 tulgey woods.
which means 20×5 = 100 tumtum trees.
as there are 2 jubjub birds in 200 tumtum trees, that means that there is 1 jubjub bird in the given 100 tumtum trees.
as there are 5 jubjub birds in 1 slithy toves, but we have only 1 bird, that means we have only 1/5 slithy toves.
there are 5 slithy toves in 2 borogoves. that means 1 slithy toves in 2/5 borogoves. and 1/5 slithy toves in 2/5 / 5 = 2/25 borogoves.
there are 200 mome raths in each borogove. and we have 2/25 borogoves. that means we have
200 × 2/25 = 400/25 = 16 mome raths.
and there are 2 mome raths per jabberwocky. we have 16 raths. how many pairs of raths does that make ?
16/2 = 8 pairs of raths = jabberwocks.
so, there should be 8 jabberwocks.
you see ? that's all that was needed. this was like a labyrinth riddle, where you need to find the way from an inside starting point to the exit without crossing a line (or wall).
O Yes
O No
2. (02.01 LC)
Is the following relation a function? (1 point)
{(3,-2), (1, 2), (-1,-4), (-1, 2)}
Answer:
No
Step-by-step explanation:
Each x can have only ONE y as its partner. In this relation, -1 has TWO different partners: in one point (-1,-4) the y is -4 and in another point (-1,2) the y is 2. Not a function.
A palindrome is a string of characters the reads the same backwards as it does forwards. for example, "mam" is a 3-letter palindrome. how many 6-letter palindromes are there?
If a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes after solving through permutations.
Given that a palindrome is a string of characters the reads the same backwards as it does forwards.
We are required to find the number of 6 letter palindromes.
Permutations is basically finding how many ways in which the some numbers or things can be arranged. It is expressed as [tex]nP_{r}[/tex]=n!/(n-r)!.
If there are 6 letters then in a palindrome 3 alphabets are used here to form a 6 letter word.
=6[tex]P_{3}[/tex]
=6!/(6-3)!
=6*5*4*3!/3!
=120 palindromes.
Hence if a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes.
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The picture has both the graph and the answer choices plesse help
Answer: Option (4)
Step-by-step explanation:
The graph has a y-intercept of 2.
Eliminate options (1) and (3).The graph passes through (2,4).
Eliminate option (2).This leaves option (4) as the correct answer.
Graph h(x)= -4(x-3)(x-1)
Answer:
roots (1,0) (3,) the vertical intercept is (0,-12)
Step-by-step explanation:
A softball player throws a ball into the air with an initial velocity of 32 feet per second. The ball is released at a height of 5 feet. The function h(t) = [tex]-16t^{2}[/tex]+32t+5 models the height h (in feet) of the ball as a function of the time t (in seconds) after it is thrown. Use the equation to find the time that the ball is in the air if the player lets the ball drop
The time that the ball is in the air if the player lets the ball drop is 2.145 sec
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
-16t²+32t+5
by comparing this equation to the standard form of the quadratic equation we get
a=-16 b=32 c=5
the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:
the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)
t = -32/2×-16
t=1sec
by putting h(t) to zero and determining the time (t) when the ball hits the ground:
-16t²+32t+5=0
-16(t²+2t+5/16)=0
t²-2t-5/16=0
(t)²-2×1×t+(1)²-5/16=1
(t-1)²=21/16
t-1=√21/√16
t=1+4.58/4
t=1+1.145
t=2.245sec
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Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1). an algebra tile configuration. 4 tiles are in the factor 1 spot: 2 are labeled negative x and 2 are labeled negative. 3 tiles are in the factor 2 spot: 2 are labeled x and 1 is labeled negative. 12 tiles are in the product spot: 4 are labeled negative x squared, 4 are labeled negative x, 2 are labeled x, and 2 are labeled . which is true regarding adi’s use of algebra tiles?
Answer:
3 tiels are in the factor 2: 2 are labeled x and 1 is labeled negative
Answer: B
Step-by-step explanation:
A boat takes 10 hours to sail a distance of 100 nautical miles with the current.
Against the current, it takes the boat 25 hours to sail the same distance. Find
the rate of the current.
The rate of the current is 6 mile/hour.
What does a rate mean ?In this context, the rate is tantamount to speed o velocity in a linear motion. The S.I unit will be mile per hour.
Given that a boat takes 10 hours to sail a distance of 100 nautical miles with the current. The rate at which the boat move will be
The rate R1 = 100/10
R1 = 10 mile/hour
And when it moves against the current, it takes the boat 25 hours to sail the same distance. The rate at which the boat move will be
The rate R2 = 100/25
R2 = 4 mile/hour
The rate of the current R will be the difference between the two calculated rate. That is,
R = R1 - R2
R = 10 - 4
R = 6 mile/hour
Therefore, the rate of the current is 6 mile/hour.
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calculate the slope of the line in the graphs and show your work
calculate the slope of a line that passes through (1,4) and (5,8)
Answer:
7.a) 5
7.b) 1/2
8. 1
Step-by-step explanation:
7.
a)
Read the points on the graph (0, 0) and (1, 5).
slope = (5 - 0)/(1 - 0) = 5/1 = 5
b)
read the points on the graph (0, 0) and (4, 2).
slope = (2 - 0)/(4 - 0) = 2/4 = 1/2
8.
Points (1, 4) and (5, 8)
slope = (8 - 4)/(5 - 1) = 4/4 = 1
simplify the expression 9^7/ 9^9 60 points
Answer:
1/9^2
Step-by-step explanation:
simplify
9^(7-9)
simplify further
9^-2
simplify even more
1/9^2
Answer:
9^16
Step-by-step explanation:
just took the test
Charles used a chain which was 12.5 metres long, 12 times to measure the breadth of his garden. Stephen used a chain of different length 10 times to cover the breadth of Charles' garden and 18 times to cover its length. What is the area of Charles' garden to the nearest one tenth of a hectare?
A. 4.05 m^2
B. 5.4 m^2
C. 3.6 m^2
D. 4.1 m^2
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Length of Charles garden = 12.5 m * 12 = 150 m
Length of Stephen chain = 150 m /18 = 25/3 m
Breadth of Charles garden - 25/3 * 10 = 250/3 m
Area of Charles garden = 150 m * 250/3 m = 12500 m =
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Select the correct answer. a number is selected at random from the set {2, 3, 4, ... 10}. which event, by definition, covers the entire sample space of this experiment?
[tex]( \: 2 \: 3 \: 4 \: 5 \:6 \: 7 \:8 \: 9 \: 10 \: )[/tex]
[tex]Event \: P \\P:"choosing \: a \: natural \: number \: from \: 2 \: to \: 10 \: inclusive"[/tex]
Find the inverse of function f
f(x)9x+7
The inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9
How to determine the inverse of the function?The function is given as:
f(x) = 9x + 7
Express f(x) as y
y = 9x + 7
Swap the positions of x and y in the above equation
x = 9y + 7
Subtract 7 from both sides
9y = x - 7
Divide through by 9
y = x/9 - 7/9
Express as an inverse function
f-1(x) = x/9 - 7/9
Hence, the inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9
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Find the error with subject-verb agreement. select the incorrect verb and type it correctly. on the ledge there is three potted geraniums that desperately need water. however the hanging ferns in the living room are thriving.
Answer:
Step-by-step explanation:
ggggggg
In whice of the pictures will the string form a knot if you pull on its ends?
Answer:
3
Step-by-step explanation:
i used process of elimination... 1 and 2 looks unreasonable, and 4 doesn't work cus i tried it irl. i might be wrong though, don't rely on me :>
Jason solved the following equation to find the value for x.
-8.5x-3.5x=-78
X=6.5
Describe how Jason can check his answer.
please help this is a math question about geometry !!!! please view the attached images to see the question and the answer choices i am going to give 13 points and a brainlist thank you
Answer:
It is the second picture.
Step-by-step explanation:
HALP AFAP PLSSS
Figure A is a scale image of figure B. what is the value of x?
Using proportions, it is found that the value of x is of 5.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, since Figure A is a scale of Figure B, the side lengths are proportional, hence the following rule of three is established:
x/12.5 = 2/5
Applying cross multiplication:
5x = 25
x = 5.
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Find the measure of angle x in the figure below
57
61
67
Answer:
51°
Step-by-step explanation:
posted answer to the question
work out the value of x
Answer:
x = 36
Step-by-step explanation:
The two lines are parallel and intersected by a transversal line.
The co-interior angles formed will sum up to 180°
Here angles 3x and 2x are the co-interior angles
So 3x + 2x = 180
5x = 180
x = 180/5 = 36
Answer:
x = 18°Step-by-step explanation:
2x + 2x + 3x + 3x = 180°
10x = 180°
x = 180° : 10 =
x = 18°
-----------------------
check
2 × 18 + 2 × 18 + 3 × 18 + 3 × 18 = 180°
the answer is good
HL=
Help me asap!! Thanks so much I appreciate it :)
The value of length HL is 8.
How to find HL when two secant intersect outside a circle?A secant is a line that intersects a circle in exactly two points
When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.
Therefore,
(EF + FL)FL = HL(GH + HL)
(10 + 14)10 = (HL + 30 - HL)HL
240 = 30(HL)
divide both sides by 30
Hence,
240 / 30 = 30HL / 30
8 = HL
Therefore,
HL = 8
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dilate the line segment by a scale factor of 2 with a center of dilation at the origin. Draw the dilated segment on the provided graph.
Answer:
See attached
Step-by-step explanation:
Each point on the line segment moves to 2 times its previous distance from the origin.
Invariant pointThe center of dilation, the origin, is an invariant point. It doesn't move for any dilation factor. One end of the line segment is there, so it will not move.
Dilated pointsThe coordinates of each point are multiplied by the dilation factor. The other end of the line segment is (5, 5), so it moves to 2×(5, 5) = (10, 10).
The dilated line segment extends from (0, 0) to (10, 10). It is shown in red in the attached graph.
Find the total surface area. rectangular prism 2 A. 132 yd² B. 1,238 yd² C. 896 yd² D. 2,736 yd²
The total surface area is 1308 meters square
How to determine the total surface area?From the question, we have the following dimensions
Length = 19 m
Width = 16 m
Height = 10 m
The total surface area is then calculated as:
Total surface area = 2 * (Length * Width + Width * Height + Length * Height)
Substitute the known values in the above equation
Total surface area = 2 * (19 * 16 + 16 * 10 + 19 * 10)
Evaluate the expression
Total surface area = 1308
Hence, the total surface area is 1308 meters square
The question is incomplete, and the resources cannot be found online.
So, I used the attached figure to answer the question
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Answer:1,238yd squared
Step-by-step explanation:
A. Undefined b. Zero c.negative b. Positive
I believe the slope is negative. If it was positive then it would have been " / "
Answer:
C
Step-by-step explanation:
• A vertical line has an undefined slope
• A horizontal line has a slope of zero
• A line sloping downwards from left to right has a negative slope
• A line sloping upwards from left to right has a positive slope
-------------------------------------------------------------------
the line here slopes downwards from left to right and has a negative slope
Chris bought 11 watermelons for his 11th birthday. The first watermelon weighed 1 pound, the second 2 pounds, the third 3 pounds and so on, Can he divide all of his watermelons into two groups with the same weight?
Answer:
ther r 2group 5%
i hope this is helpful to you