Answers
Answer:
hope it helps mark me brainlieast!
Step-by-step explanation:
For triangle ABC with sides a,b,c labeled in the usual way,
c2=a2+b2−2abcosC
We can easily solve for angle C .
2abcosC=a2+b2−c2
cosC=a2+b2−c22ab
C=arccosa2+b2−c22ab
That’s the formula for getting the angle of a triangle from its sides.
The Law of Cosines has no exceptions and ambiguities, unlike many other trig formulas. Each possible value for a cosine maps uniquely to a triangle angle, and vice versa, a true bijection between cosines and triangle angles. Increasing cosines corresponds to smaller angles.
−1≤cosC≤1
0∘≤C≤180∘
We needed to include the degenerate triangle angles, 0∘ and 180∘, among the triangle angles to capture the full range of the cosine. Degenerate triangles aren’t triangles, but they do correspond to a valid configuration of three points, namely three collinear points.
The Law of Cosines, together with sin2θ+cos2θ=1 , is all we need to derive most of trigonometry. C=90∘ gives the Pythagorean Theorem; C=0 and C=180∘ give the foundational but often unnamed Segment Addition Theorem, and the Law of Sines is in there as well, which I’ll leave for you to find, just a few steps from cosC= … above. (Hint: the Law of Cosines applies to all three angles in a triangle.)
The Triangle Angle Sum Theorem, A+B+C=180∘ , is a bit hard to tease out. Substituting the Law of Sines into the Law of Cosines we get the very cool
2sinAsinBcosC=sin2A+sin2B−sin2C
Showing that’s the same as A+B+C=180∘ is a challenge I’ll leave for you.
In Rational Trigonometry instead of angle we use spreads, squared sines, and the squared form of the formula we just found is the Triple Spread Formula,
4sin2Asin2B(1−sin2C)=(sin2A+sin2B−sin2C)2
true precisely when ±A±B±C=180∘k , integer k, for some k and combination of signs.
This is written in RT in an inverted notation, for triangle abc with vertices little a,b,c which we conflate with spreads a,b,c,
(a+b−c)2=4ab(1−c)
Very tidy. It’s an often challenging third degree equation to find the spreads corresponding to angles that add to 180∘ or zero, but it’s a whole lot cleaner than the trip through the transcendental tunnel and back, which almost inevitably forces approximation.
Related Questions
Which equation represents a line that passes through ( -2 , 4 ) and has the slope of 2/5
Answers
Answer:
y = 2/5x +24/5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/5 x +b
Substitute the point into the equation and solve for b
4 = 2/5(-2)+b
4 = -4/5 +b
Add 4/5 to each side
20/5 +4/5 = b
24/5 = b
y = 2/5x +24/5
Building 1 (Circle) : Rotate 270 degrees counterclockwise around the origin. Building 2 (Square): Reflect across the y axis. Building 3 (Triangle): Reflect across the y axis, then translate 3 up and 2 to the left. Building 4 (L-Shape) : The points A (3, 8), B (6, 8), C (6, 3), and D (5, 3) need to be transformed to points A'' (–3, 1), B'' (–6, 1), C'' (–6, –4), and D'' (–5, –4). Avoid the pond, which is an oval with an origin at (0, 0), a width of 4 units, and a height of 2 units.
Answers
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as some coordinates to transform are not given.
I will, however, give a general explanation.
Rotate circle 270 degrees counterclockwise
This implies that, we rotate the center of the circle and the rule of this rotation is:
[tex](x,y) \to (y,-x)[/tex]
Assume the center is: (5,3), the new center will be: (3,-5)
Reflect square across y-axis
The rule is:
[tex](x,y) \to (-x,y)[/tex]
If the square has (3,5) as one of its vertices before rotation, the new point will be (-3,5).
Reflect triangle across y-axis, then 3 units up and 2 units left
The rule of reflection is:
[tex](x,y) \to (-x,y)[/tex]
If the triangle has (3,5) as one of its vertices before rotation, the new point will be (-3,5).
The rule of translating a point up is:
[tex](x,y) \to (x,y+h)[/tex] where h is the unit of translation
In this case, h = 3; So, we have:
[tex](-3,5) \to (-3,5+3)[/tex]
[tex](-3,5) \to (-3,8)[/tex]
The rule of translating a point left is:
[tex](x,y) \to (x-b,y)[/tex] where b is the unit of translation
In this case, b = 2; So, we have:
[tex](-3,8) \to (-3+2,8)[/tex]
[tex](-3,8) \to (-1,8)[/tex]
The L shape
[tex]A = (3, 8)[/tex] [tex]A" = (-3, 1)[/tex]
[tex]B = (6, 8)[/tex] [tex]B"= (-6, 1)[/tex]
[tex]C = (6, 3)[/tex] [tex]C" = (-6, -4)[/tex]
[tex]D = (5, 3)[/tex] [tex]D" = (-5, -4)[/tex]
Required
The transformation from ABCD to A"B"C"D"
First, ABCD is reflected across the y-axis.
The rule is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]A' = (-3,8)[/tex]
[tex]B' = (-6,8)[/tex]
[tex]C' = (-6,3)[/tex]
[tex]D' = (-5,3)[/tex]
Next A'B'C'D' is translated 7 units down
The rule is:
[tex](x,y) \to (x,y-7)[/tex]
So, we have:
[tex]A"= (-3,8-7) = (-3,1)[/tex]
[tex]B"= (-6,8-7) = (-6,1)[/tex]
[tex]C"= (-6,3-7) = (-6,-4)[/tex]
[tex]D"= (-5,3-7) = (-5,-4)[/tex]
If the point A at (5, 3) is rotated clockwise about the origin through 90°, what
will be the coordinates of the new point?
Answers
Answer:
(5,-3) in the 4th quadrant
Step-by-step explanation:
pls help me solve this multiplication fractions. (show work)
Answers
Answer:
32:3/4
33:4/3
34:40
35:48
32. 3/4
33. 4/3
34. 40
35. 384/7
Step-by-step explanation:
32. 9/10 • 5/6
Multiply 9 x 5/10 x 6
9 x 5/10 x 6 = 45/60
Then simplify 45/60 “by factoring out 45 and 60 and finding the Greatest Common Factor (GCF)”
45/60 = 3/4
•••••••••••••••••••••••••••••••••••••••••••••••••••
33. 16/21 • 7/4
Multiply 16 x 7/21 x 4
16 x 7/21 x 4 = 112/84
Then simplify 112/84 “by factoring out 112 and 84 and finding the Greatest Common Factor (GCF)”
112/84 = 4/3
•••••••••••••••••••••••••••••••••••••••••••••••••••
34. 8 4/7 • 4 4/6
Multiply 7 by 8 and add 4
7 x 8 + 4 = 60
Then add the denominator back
60/7
Multiply 6 x 4 and add 4
6 x 4 + 4 = 28
Then add the denominator back
28/6
We’re left with 60/7 • 28/6
Multiply 60 x 28/7 x 6
60 x 28/7 x 6 = 1680/42
Then simplify 1680/42 “by factoring out 1680 and 42 and finding the Greatest Common Factor (GCF)”
1680/42 = 40
••••••••••••••••••••••••••••••••••••••••••••••••
35. 7 4/8 • 6 2/5
Multiply 8 by 7 and add 4
8 x 7 + 4 = 60
Then add the denominator back
60/7
Multiply 5 x 6 and add 2
5 x 6 + 2 = 32
Then add the denominator back
32/5
We’re left with 60/7 and 32/5
Multiply 60 x 32/7 x 5
60 x 32/7 x 5 = 1920/35
Then simplify 1920/35 “by factoring out 1920 and 35 and finding the Greatest Common Factor (GCF)”
1920/35 = 384/7
••••••••••••••••••••••••••••••••••••••••••••••••
please mark me as brainliest! This took me effort
Please help, explain too and I will give brainliest :)
Answers
Answer:
c
Step-by-step explanation:
Answer:
C. 37 degrees
Step-by-step explanation:
27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.
I'm sure you can do it with an actual formula, but i can't recall. Cheers
which algebraic expression represents this word description?
the product of two and the difference between eleven and a number
a. 2(11-x)
b. 11-2x
c. 2x-11
d. 2(x-11)
Answers
Step-by-step explanation:
c. 2x-11 this is the answer
hope this helps you
have a nice day:)
Can Anyone please tell me How to Multiply 18√2×18√2...
Please show steps aslo..
Answers
Answer:
648
Step-by-step explanation:
18√2×18√2= (18√2)²
= (18)²×(√2)²
= 324×2
= 648
Mrs. Ella bought something's bought 3 lb of apples. The price is $2.49 per pound. How much did she pay for the three pounds of apples ?
Answers
Answer:
$7.47
Step-by-step explanation:
Take the number of pounds and multiply by the price per pound
3 * 2.49
7.47 for 3 pounds of apples
Answer:
7.49
Step-by-step explanation:
Given: 3 pounds, and 2.49 for each pound
Multiply:
2.49 × 3
₁ ₂
2.49
× 3
----------
7. 47
Mrs. Ella bought 3 pounds of apples for $7.49
Does this graph show a function? Explain how you know.
Answers
Answer:
A is the correct one
cause according to function rule the vertical line should cut only on a one point to be function
as here we can see that vertical line cuts here at two point
In English auction, an item is auctioned. People increase bids in increments of $10, and the player giving the highest bid gets the item for that amount of money. Give reasons why the auctioneer would be considered a player of the game, or reasons why he or she would not. Does the game contain random moves
Answers
Given a circle with centre O and radius 2.4cm. P is a point such that the lenght of the tengent from Q to the circle is 4.5cm. Find the lenght of OP
Answers
Answer:
5.1 cm
Step-by-step explanation:
(Probable) Question;
Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP
The given parameters are;
The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm
The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm
The length of OP = Required
By Pythagoras's theorem, we have;
[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²
∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01
[tex]\overline{OP}[/tex] = √26.01 = 5.1
The length of OP = 5.1 cm
Help!! Please! appreciate it !!
Answers
Answer:
I'm pretty sure you are intended to pick AAS.
Step-by-step explanation:
As it stands, AAS. But this can be an unreliable theorem. If you show that the third angles are equal (which they are) using the fact that if two angles of a triangle are equal to the corresponding angles of another triangle, then the third angle is as well. That means that you can use the much more reliable ASA.
Work out the circumference of this circle 7.5
Answers
Answer:
47.12
Step-by-step explanation:
C=2πr=2·π·7.5≈47.12389
PLEASE HELP URGENTLY!!
Answers
Answer:
x = 69
Step-by-step explanation:
since AB is parallel to CD we can find the value of y with the following equation :
2y - 40 = 66 add 40 to both sides
2y = 110 divide both sides by 2
y = 55
from supplementary angles, we know that the exterior angle's measure is 124
since the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle
y + x = 124 we found value of y earlier
55 + x = 124 subtract 55 from both sides
x = 69
Delta math please help
Answers
Answer:
[tex]\approx 13.0[/tex]
Step-by-step explanation:
The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the triangle angle of the right triangle. Parameter (c) represents the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown:
[tex]a = 7\\b = 11[/tex]
[tex]a^2+b^2=c^2[/tex]
[tex]7^2+11^2=c^2[/tex]
Simplify,
[tex]7^2+11^2=c^2\\\\49 + 121= c^2\\\\170=c^2[/tex]
Inverse operations,
[tex]170=c^2\\\\\sqrt{170}=c\\\\\\c \approx 13.0384[/tex]
one morning sam cycles 5km in 20 mins and Dwight cycles 6km in 30mins Determain who cycles faster. Show your work
Answers
Answer:
5 + 20 + 6
Step-by-step explanation:
that's how you get
The floor is in the shape of square. Louis measures the area as 445 square feet. Find the diagonal of the floor.
Answers
Answer:
29.83 ft
Step-by-step explanation:
First, you find the square root of 445, which is 21.09.
Then you use the Pythagorean theorem, which is a^2 + b^2 = c^2
because a and b are the same value you plug it in
21.09^2+21.09^2 = c^2
You end up getting:
c^2=889/5762
You then square root both sides to get:
c = 29.83, which is option 3
Find the volume
Help me please
Answers
Answer:
54piecm^3
Step-by-step explanation:
pie x radius ^2 x h
= v
pie x 9
= 9pie x 6
= 54pie
54pi cm^3
Step-by-step explanation:
V = (pi)r^2h
V = (pi)(3^2)(6)
V = (pi)(9)(6)
V = 54pi cm^3
Question 2 (1 point)
Match each situation to a linear system below.
A child has a piggy bank full
of $1 and $2 coins totalling
$37.
There are 25 more $1 coins
than there are $2 coins.
1. x + 2y = 37
x - y = 25
An exam that is worth 37
marks contains 25
questions.
The questions are either
worth 1 mark or 2 marks.
2. x + 2y = 37
x + y = 25
18
3. x - 2y = 37
x + y = 25
The sum of two numbers is
25.
The first number is 37 more
than 2 times the second
number
Answers
Answer:
See answers below
Step-by-step explanation:
For the expression
The sum of two numbers is 25. The first number is 37 more than 2 times the second number
Let the two numbers be x and y
If the sum is 25, then;
x + y = 25 .... 1
37 more than 2 times the second the number is expressed as;
37+2y
If the first number is 37 more than 2 times the second number, then;
x = 37 + 2y
x - 2y = 37 ...2
This shows that the simultaneous equation that fits the expressions are;
x - 2y = 37
x + y = 25
For the expression
A child has a piggy bank full of $1 and $2 coins totaling $37. There are 25 more $1 coins than there are $2 coins.
Let x be the $1 coins
Let y be the $2 coins
If a child has a piggy bank full of $1 and $2 coins totaling $37, then;
x + 2y = 37 ... 1
Also, if there are 25 more $1 coins than there are $2 coins, then;
x = 25 + y
x - y = 25 ...2
The equivalent expressions for the statement will be;
x + 2y = 37
x - y = 25
This hence leaves us with the last;
An exam that is worth 37 marks contain 25 questions. The questions are either worth 1 mark or 2 marks. The resulting simultaneous equation will be;
x + 2y = 37
x + y = 25
Hellllllllp plsss!! Due in very soon maths
Answers
Answer: 23, 27,29
Those im absolutely positive about.
Im not sure abt the rest
Step-by-step explanation:
geometry help translations
Answers
Answer:
A' (9,4)
B' (8,-1)
C' (5,1)
Answered by GAUTHMATH
Answer:
A' = 9,4
B' = 8,-1
C' = 5,1
Step-by-step explanation:
PLEASE HELP ITS TIMED!!!!
Answers
Answer:
It's A
Step-by-step explanation:
DO FOIL
-10d^4+(5+12)d^2s-6s^2=-10d^4+17d^2s-6s^2
Answer:
the first answer: -10a^4 + 17a^2s-6s^2
Step-by-step explanation:
how can the graph of g(x) =x2+4 be obtained from the graph of f(x) =x2
Answers
Answer:
see explanation
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
The graph of g(x) is the graph of f(x) shifted up by 4 units
Fill in the blank and dropdown menus to form a true statement below.
Answers
Answer:
the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .
Answer:
the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .
Step-by-step explanation:
Which table shows a proportional relationship between a and b?
Answers
Answer:
It is c
Step-by-step explanation:
what would be the u to usub and what would be the steps to solving this integral?
Answers
Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).
Then substituting u = ln(x) and du = dx/x gives
[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]
The slope of a line is 5/9 and the slope of another line is -975. The two lines
are
Answers
Answer:
the third option - they are perpendicular to each other.
Step-by-step explanation:
for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.
and that is exactly what happened here.
Solve 7x + 1 < 4(x - 2).
A. {x | x > 3}
B. {x | x > -3}
C. {x | x < -3}
D. {x | x < 3}
Answers
Given:- 7x + 1 < 4(x - 2)
Solving It:-7x + 1 < 4(x - 2)
7x + 1 < 4x - 8
7x - 4x < -8 -1
3x < -9
x < -9/3
x < -3
So Correct Solution Set Will BeC. {x | x < -3}Hope This Helps YouSolve: f(x) = (x + 1)(x + 1)
Answers
Answer:
f(x) = x² + 2x + 1
Step-by-step explanation:
you know how to multiply 2 expressions ?
let's say in general we have
(a + b)(c + d)
you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).
so, we get for this simple generic example
a×c + b×c + a×d + b×d
now we use that understanding for our question here.
(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1
The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?
PLS HELP WILL GIVE BRAINLIEST
Answers
Answer:
-6
Step-by-step explanation:
2n can be the smallest integer, and 2n + 18 will be the largest integer.
The sum of this, divided by two, will result in the average/mean.
(2n + 2n + 18)/2 = 3
Multiply each side by 2:
(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2
2n + 2n + 18 = 6
Combine the like terms:
4n + 18 = 6
Subtract 18 from both sides:
4n + 18 - 18 = 6 - 18
4n = -12
Divide each side by 4:
4n/4 = -12/4
n = -3
Since we decided to go by 2n:
2n = 2(-3) = -6
