Given :
An expression sin(140°)cos(20°) – cos(140°)sin(20°) .
To Find :
The value of given expression .
Solution :
We know ,
sin(A - B) = sin A cos B - cos A sin B
By comparing with above formula , we get :
A = 140° and B = 20° .
So , sin(140°)cos(20°) – cos(140°)sin(20°) = sin ( 140°- 20°) = sin 120° .
Now , [tex]sin 120^\circ{} = \dfrac{\sqrt{3}}{2}[/tex]
Therefore , the value of expression is [tex]\dfrac{\sqrt{3}}{2}[/tex] .
Hence , this is the required solution .
Please answer these with lots of detail. I want to be able to understand the topic and material well.
Step-by-step explanation:
Q3
(a) If 0 < |x − 1| < δ, then |f(x) − 2| < 2
What this means is, how far can x stray from the x=1 line such that f(x) stays within 2 units of the y=2 line (0 < f(x) < 4).
If we move 2 units left of x=1, we get f(x) = 4.
If we move about 3.5 units right of x=1, we get f(x) = 4.
Therefore, δ can't be more than 2.
(b) If 0 < |x| < δ, then |f(x) − 3| < 1
What this means is, how far can x stray from the x=0 line such that f(x) stays within 1 unit of the y=3 line (2 < f(x) < 4).
If we move 1 unit left of x=0, we get f(x) = 4.
If we move 1 unts right of x=0, we get f(x) = 2.
Therefore, δ can't be more than 1.
Since f(x) isn't continuous within this domain, we can't conclude that the limit exists.
Q4
(a) Yes. If δ = 0.25, then 0.75 < x < 1.25, and f(x) > 200.
(b) No. f(1) = 300, so even if δ = 0, f(x) will be less than 400.
(c) Yes. If δ ≈ 0.1, then 0.9 < x < 1, and f(x) > 450.
[ 28 - (16 + 3) ] ÷ 3
Answer:
3
Step-by-step explanation:
By order of PEMDAS, perform math within parentheses first.
[tex](28 - 19) \div 3[/tex]
Continue with PEMDAS
[tex](9) \div 3[/tex]
Now, simply divide
[tex]9 \div 3 = 3[/tex]
8cm 10cm 10cm 12cm 34cm what’s the volume
find the midpoint of a line segment with the given endpoints.(8,-3) (-8,1)
Answer:
(0,-1)
Step-by-step explanation:
When Bryan was 11 years old he was 150.25 centimeters tall. For the next 4 years, he grew 65 centimeters a year. How tall was Bryan when he was 15 years old? Help PLEASE
Step-by-step explanation:
He grew 65cm a year??? Omg
I think it is
65cm x 4(years)= 260cm
150.25 + 260= 410.25cm
So, when he was 15 years old he was 410.25cm tall
3 things to keep 1: It takes a garage owner 45 minutes to travel between his two garages 60 miles apart. Travelling at the same speed, how long would it take him to travel to his home 25 miles away? here it is 45/60 not 60/45 so minutes on top of miles 2: A jet travels 320 km in 20 minutes. How far will it fly in 30 minutes? here minutes is bottom, so 320/20 3: A boy cycles 20km in 140 minutes. How long would it take him to cycle 8km, at the same speed? km is bottom and minutes is on top, so 140/20 why is does it exactly does it keep changing what's on top? Is miles the only one allowed to have the smaller number on top, meanwhile km or under has to have the highest number first?
Answer:
Distance=Speed×Time
When speed is 40 kmph
Distance traveled by car =40×9
=360 km
When speed is 60 kmph
Time taken to complete the journey =
60
360
=6 hours
Use the number line to find the coordinate of the midpoint of segment DE
Answer:
x1+x2/2
7+11/2
18/2=9
Step-by-step explanation:
The midpoint of segment DE is 9 units.
It is required to find the midpoint of segment DE.
What is midpoint ?The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Given:
By mid point formula we get,
The midpoint formula is applied when one is required to find the exact center point between two defined points.
The coordinate of point D is 7 units.
The coordinate of point E is 11 units.
According to given question we have,
The midpoint of segment DE
[tex]=\frac{x_{1} +x_{2} }{2} \\=(7+11)/2\\\\=18/2\\\\=9[/tex]
Therefore , the midpoint of segment DE is 9 units.
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What is the value of m?
O 10
O 30
O 70
O 150
Multiply (3)x(−4)x(2).
Answer:
-24x²
Step-by-step explanation:
remove the parentheses, multiply the numbers, apply exponent rule and add the numbers
Evaluate the expression for x=4
3x^2
Answer:
Step-by-step explanation:
x = 4
3x^2
3(4)^2
3(16)= 48
how to subtract 5/8 from 1 7/8
Answer:
7/8 - 5/8 = 2/8. Therefore the answer is 1 2/8.
Step-by-step explanation:
Answer: 1 2/8
Step-by-step explanation:
you take away 5 from seven so it becomes 2 then you put the 8 under and you still keep the one there
What is 0.6 repeating as a fraction
Answer:
2/3
Step-by-step explanation:
0.6 repeating as a fraction is 2/3
Answer:
The answer is 2/3 or
Step-by-step explanation:
[tex]\frac{2}{3}[/tex]
Max got 6 problems wrong on a 50 question test. What percent of the questions did
he miss?
Answer:
8.33333333333%
Step-by-step explanation:
50/6
Answer:
12%
Step-by-step explanation:
the sales per tax on a printer that cost $180 is 6%. What is the total cost of the printer including the sales tax? Show work and explain your answer
Answer:
10.8
Step-by-step explanation:
6% of 180 is 10.8
What is the sum of the terms of the series 4 + 7 + 10 + . . . + 22? 91 43 104
Answer:
91Step-by-step explanation:
This is an arithmetic sequence, in which a set number is added to the previous term to get the next term. The number added is figured out by subtracting the 1st term from the 2nd term and the 2nd term from the 3rd term.
Now that we know the number is 3, we can complete the sequence:
4, 7, 10, 13, 16, 19, 22
We will add all the terms up to get 91.
___________________________________________________I AM ALWAYS HAPPY TO HELP :)Problem
3x + 5 + 2x = 12 + 4x
Answer:
x=7
Step-by-step explanation:
because u add the like terms so
3x+2x
which would be
5× so now its
5x+5=12+4x
-4. -4
x+5=12
-5. -5
x=7
how do i solve the equation [tex](2a^{3} b^{4}c^{0})^{3}[/tex]
Answer:
[tex]8\frac{-2x}{-2}=\frac{0}{-2}[/tex]
Step-by-step explanation:
[tex]\left(2a^3b^4c^0\right)^3[/tex]
Cube each portion:
[tex]2^3\left(a^3\right)^3\left(b^4\right)^3\left(c^0\right)^3[/tex]
[tex]8\left(a^3\right)^3\left(b^4\right)^3\left(c^0\right)^3[/tex]
[tex]8a^9\left(b^4\right)^3\left(c^0\right)^3[/tex]
[tex]8a^9b^{12}\left(c^0\right)^3[/tex]
[tex]8a^9b^{12}\times1[/tex]
[tex]8a^9b^{12}[/tex]
The area of a trapezoid is given by the formula A 1/2= (b 1 + b 2)h, solve the formula for h
h=A 6/b or 6 divided b = h
find the product (-4)(-2) , find the product (-8)(-3) which product is greater
DIFFERENT ANWSER BTW
next Some friends played a board game. During the game, one unlucky player had to move back 8 spaces 5 turns in a row. Find a number to represent that player's movements for those 5 turns. AND YES I HAVE A TEST DUE TONIGHT
Answer: 8, 24, and 24 is greater
Step-by-step explanation:
(-4)(-2) = 8
(-8)(-3) = 24
8 < 24
74°F, 65°F, 71°F, 65°F. 68°F, 78°F, 72°F. 67°F
What is the mean absolute deviation of this data set?
Answer:
3.75jgfbvuekdfb
Step-by-step explanation:
Can someone help me with number 7 and 8. Thank you
Answer:
Q7) ( 2,-2)
Q8) (- 0.5 , -2)
Step-by-step explanation:
As we have to find the mid-points of the line segments, the line segments will be divided in same ratio i.e. 1:1 (∵ A Mid-point divides a line segment into equal parts )
According to Section formula ,
[tex]( x' , y') = (\frac{mx^2 + nx^1}{m+n} , \frac{my^2+ny^1}{m+n} )[/tex]
where (m,n) are the ratios in which a line segment is divided & ( x¹ , y¹ ) ( x², y²) are the co-ordinates of a line segment.
In Q7 ,
x¹ = 3 , y¹ = -9 , x² = 1 , y² = 5 & m = n = 1
So putting the section formula here gives :-
[tex]( x' , y') = (\frac{1*1 + 1*3}{1+1} , \frac{1*5+1*(-9)}{1+1} ) = ( 2 , -2)[/tex]
In Q8 ,
x¹ = 5 , y¹ = -1 , x² = -6 , y² = -3
So putting the section formula here gives :-
[tex](x' , y') = (\frac{1*(-6) + 1*5}{1+1} , \frac{1*(-3) + 1*(-1)}{1+1}) = ( -0.5 , -2)[/tex]
Jack works at a sporting goods store and makes a commission of 20 percent. His sales for each week are shown below. How much did Jack make in total in commission during all four weeks?
Week
Sales
1
$3,000
2
$2,500
3
$3,500
4
$4,000
$200.00
$260.00
$2,000.00
$2,600.00
Answer: The answer is D 2,6000.00
Answer:
D
Step-by-step explanation:
Solve for x: 2x−7=5x+8
if I am 9 years old how old will i be in 29 years
Answer:
YOU will be 38 yrs old, but I will be 29 years older than my 29 year-younger self
Step-by-step explanation:
Answer:
you would be 38
Step-by-step explanation:
29 plus 9 equals 38
a square patio has an area of 200 square ft. how long is each side of the patio to the nearest foot? please answer quickly! will give brainliest.
Answer:
100
Step-by-step explanation:
cause they its 100
Answer:
14 feet
Step-by-step explanation:
Use the square area formula, A = s², where s is the side length
Plug in the area and solve for s:
A = s²
200 = s²
14 = s
So, each side of the patio is 14 feet
is this statement true or false? If AB+BC=AC, then AB=BC
Answer:
true
Step-by-step explanation:
The given statement AB+BC=AC, then AB=BC is false for the line segment.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
If AC is the line segment and B is in between AC somewhere then the given statement AB+BC=AC, then AB=BC is not necessarily true.
As the two diagrams below;
Diagram 01) →
Here B is the midpoint of AC so AB = BC
Diagram 02) →
Here B is not the midpoint of AC so AB ≠ BC
Hence "The given statement AB+BC=AC, then AB=BC is false for the line segment".
For more about line segment,
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Point L is on line segment KM . Given KM = 5x + 10 , LM = 4x , and KL = 3x , determine the numerical length of KL
Answer:15
I know Bc I got it wrong that was the answer
Can someone help me?
Answer:
3 and 6 5and 4
Step-by-step explanation:
means to find the only possible answer.
20 POINTS
Rewrite the following equation in the center-radius form of the equation of a circle.
x2 + 16x + y2 + 18y = -120
A.
(x + 8)2 + (y + 10)2 = 25
B.
(x + 10)2 + (y + 8)2 = 25
C.
(x - 9)2 + (y - 8)2 = 25
D.
(x + 8)2 + (y + 9)2 = 25
Answer:
Substitute (x+4)2−16 ( x + 4 ) 2 - 16 for x2+8x x 2 + 8 x in the equation x2+y2+8x−6y=24 x 2 + y 2 + 8 x - 6 y = 24 . (x+4)2−16+y2−6y=24 ( x + 4 ) 2 - 16 + y 2 ...
Step-by-step explanation:
Answer:
your answer would be C
Step-by-step explanation: