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 .
A DVD that originally cost $30 is on sale for 10 percent off. Complete the steps to solve the problem.
Answer:
$27
Step-by-step explanation:
10% of 30 = 3, so if we take 3 or 10% away from 30, you will get 27.
Answer:
27$
Step-by-step explanation:
0% of 30 = 3, so if we take 3 or 10% away from 30, you will get 27.
What is 3.18 written as a rational?
Answer:
[tex]\frac{318}{100}[/tex]
Step-by-step explanation:
A rational number can be expressed as
[tex]\frac{a}{b}[/tex] ← where a and b are integers
The 8 in 3.18 is in the hundredths position, thus
3.18 = [tex]\frac{318}{100}[/tex] ← as a rational number
what type of angle is <CEB?
Answer:
obtuse angle
Step-by-step explanation:
m(<CEA)=m(<BED)=88 (vertically opposite angles)
So m(<CEB)+m(<AED)=360-(88+88)=182
m(<CEB)=m(<AED)= 182÷2=92
You need a piece of paper to measure 64 Dash 25 cylinders if you take two together that each measure 38.4 silver meters how much do you need to cut off
Answer:
The length needed to cut off is 12.55 cm
Step-by-step explanation:
The corrected question is:
you need a piece of paper to measure 64.25 cm. If you tape two together that each measure 38.4 cm, how much do you need to cut off?
Solution:
measurement/length of each paper piece = 38.4 cm
measurement/ length required = 64.25 cm
If length of one paper piece is 38.4 cm then if we tape 2 pieces together then the measurement or length is calculated as:
38.4 + 38.4 = 76.8 cm
So to calculate how much we need to cut off:
length required to cutoff = total length of two pieces - length required
= 76.8 - 64.25
= 12.55 cm
So the length required to cut off is 12.55 cm
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.
Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
Answer:
10
Step-by-step explanation:
This is the answer because:
1) First, insert all the numbers into the expression
Expression: I -2(2) + -3(2) I
2) Next, do -2 x 2 and -3 x 2
-2 x 2 = -4
-3 x 2 = -6
3) Then, do -4 + -6
-4 + -6 = -10
4) Finally, the absolute value of -10 is 10
Therefore the answer is 10
Hope this helps!
Walk me through solving this one-step equation for x.
-18 + x = -11
-18 + x = -11
Let's add 18 to both sides
x = 7
Answer:
7
Step-by-step explanation:
Step 1:
- 18 + x = - 11
Step 2:
x = - 11 + 18
Answer:
x = 7
Hope This Helps :)
A wheel whose radius is 50 centimeters completes 6 radians in 1 seconds. What is the linear speed of a point on the rim of the wheel? Convert your answer to meters per second (m/s).
Answer:
3m/seconds
Step-by-step explanation:
In this problem we are required to solve for linear speed of the rotating wheel
The linear speed =angular speed x raduis
Given data
Radius r= 50cm
Converting from cm to m
50/100= 0.5m
Angular velocity w= 6rad/s
V=wr
V= 6*0.5m
V=3m/s
The linear speed is 3m/seconds
Answer:
get from (4,1) to (2,9) go up 8 and over 2 left (-2) - (4 - 2, 1 + 8), do this again (2 - 2, 9+8) and end up at (0,17) which is the y how do you change 7x+3y=3 into slope intercept form.
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PLEASE help me at 1 B !!!!
Answer:
a = 1, b = 4
Step-by-step explanation:
You have worked out part (a) correctly, that is
0.7575... = [tex]\frac{75}{99}[/tex] = [tex]\frac{25}{33}[/tex]
(b)
[tex]\frac{a}{11}[/tex] + [tex]\frac{b}{6}[/tex] = [tex]\frac{25}{33}[/tex]
[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{25}{33}[/tex]
Multiply numerator/ denominator of [tex]\frac{25}{33}[/tex] by 2, thus
[tex]\frac{25(2)}{33(2)}[/tex] = [tex]\frac{50}{66}[/tex] , then
[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{50}{66}[/tex] , thus
6a + 11b = 50
Choose a = 1 ( a positive integer ), then
6(1) + 11b = 50
6 + 11b = 50 ( subtract 6 from both sides )
11b = 44 ( divide both sides by 11 )
b = 4
a = 1, b = 4, so
[tex]\frac{1}{11}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{25}{33\\}[/tex]
what does ^2 mean????????????????????????????????????????????????????????????
Answer and Step-by-step explanation:
What does ^2 mean? Well, first let's find out what ^ means, this is "squaring". So, ^2 means two is squared by another number. Such as 6^2. Six is squared by two.
Hope you found this helpful! Have a wonderful day!
Question 2 of 5 Consider the polynomials given below. P(x) = 11x5 + 9x4 – 4x3 – 7x2 + 5 Q(x) = (2x2 + 1)(4x2– 3) Determine the operation that results in the simplified expression below. 11x5 + x4 – 4x3 – 5x2 + 8 PQ
Q-P
P+Q
P-Q
Answer: p-q
Step-by-step explanation:
Answer: P-Q is correct
Step-by-step explanation:
What would 489,000,000,000,000,000 in scientific notation
Pls help me on question 15
Solve for k.
12/k = 3
Answer:
k=3/12
k=.25
Step-by-step explanation:
we need to get k by itself
because 12 is over k we need to get rid of it by moving it to the other side (multiplying) because it is 12/k we need to multiply it by 1/12
This eliminates 12 and leaves us with k=3/12
Find the area of a triangle with a 21 cm base and 4 cm height
Answer:
42 cm^2
Step-by-step explanation:
Base = 21 cm
Height = 4 cm
Area = [tex]\frac{base\times height}{2}[/tex]
Substitute values into the given equation
[tex]A = \frac{21\times 4}{2} \\\\A = \frac{84}{2} \\\\A = 42cm^2[/tex]
You ask a friend to think of a number from 7 to 14. What is the probability that his number will be an even number? Answer as a fraction in simplest form.
Answer:
1/2
Step-by-step explanation:
Not sure but
I am assuming we have 8 integers :
All or (A) = {7,8,9,10,11,12,13,14} = n(A) = 8
Hence, the probability of any one outcome is 1/8.
Therefore, as you can detect, there are 4 numbers that are even numbers which means :
Even or (E) = {8, 10, 12, 14} = n(E) = 4
So, let E imply this occurrence
E x A
= 4 x 1/8
= 4/8
= 1/2
Probability of getting an even number from7 to 14 is equals to ( 1/ 2).
What is probability?
" Probability is defined as the mathematical calculation to represents the ratio of number of favourable outcomes to the total number of outcomes."
Formula used
[tex]Probability = \frac{Number of favourable outcome }{Total number of outcomes}[/tex]
According to the question,
Given,
Total number from 7 to 14 = { 7, 8, 9, 10, 11, 12, 13, 14}
⇒Total number of outcomes = 8
Possible outcomes of even number ={ 8, 10, 12, 14}
⇒ Number of favourable outcomes = 4
Substitute the value in the formula we get,
Probability = ( 4 / 8)
= ( 1 / 2) ( fraction in simplest form)
Hence, probability of getting an even number from7 to 14 is equals to ( 1/ 2).
Learn more about probability here
https://brainly.com/question/11234923
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What is the product of 2x - 5 and 3x2 + 5x - 7? Write your answer in standard form.
(a) Show your work.
(b) is the product of 2x - 5 and 3x2 + 5x - 7equal to the product of 5x - 2 and 3x2 + 5x - 7? Explain your
answer.
Answer:
a) 6x³ − 5x² − 39x + 35
b) no
Step-by-step explanation:
(2x − 5) (3x² + 5x − 7)
Distribute:
3x² (2x − 5) + 5x (2x − 5) − 7 (2x − 5)
Distribute again:
6x³ − 15x² + 10x² − 25x − 14x + 35
Combine like terms:
6x³ − 5x² − 39x + 35
5x − 2 is the opposite of 2x − 5, so you would get the negative of the answer from part (a).
20 points
5. Convert the following standard equation to slope-intercept form (y =
mx + b) and identify the slope: 8x + 2y = 20 *
Answer:
y = -4x +10
Slope = -4
Step-by-step explanation:
[tex]8x + 2y = 20[/tex]
Slope intercept form =
[tex]y = mx + b[/tex]
[tex]2y = - 8x + 20[/tex]
Divide both sides of the equation by 2
[tex] \frac{2y}{2} = \frac{ - 8x}{2} + \frac{20}{2} [/tex]
Simplify
[tex]y = - 4x + 10[/tex]
In y= mx+b , m is the slope and the coefficient of x
[tex]m = - 4[/tex]
6*10^-2 is how many times as large as 2*10^-8
Answer:
3000000
Step-by-step explanation:
6×[tex]10^{-2}[/tex] = 6 × 1/(10)² = 6 × 1/100 = 6/1002×[tex]10^{-8}[/tex] = 2 × 1/[tex]10^{8}[/tex] = 2 × 1/100000000 = 2/100000000Divide 6/100 and 2/100000000 to find how many times as large
The answer is 3000000
10x − 4.5 + 3x = 12x − 1.1
(2,-4) and (6,2).
Find the mid point
Answer:
The answer is
( 4 , - 1)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(2,-4) and (6,2)
The midpoint is
[tex]M = ( \frac{2 + 6}{ 2} , \: \frac{ - 4 + 2}{2} ) \\ = ( \frac{8}{2} \: , \: - \frac{2}{2} )[/tex]
We have the final answer as
( 4 , - 1)Hope this helps you
Answer:
The mid point must be (4,-1)
Step-by-step explanation:
mid point= [(X1+X2)/2 , (Y1+Y2)/2]
= [ (2+6)/2 , (-4+2)/2]
= [ 8/4 , -2/2]
= (4, -1)
Harvey is 3 times as old as Jane. The sum of their ages is 52 years. Find the age of each.
Jane is 13 and Harvey is 39
Jane is 12 and Harvey is 48
Jane is 13 and Harvey is 48
Answer:
13, 39
Step-by-step explanation:
H +J =52
H =3J
3J +J =52
4J =52
J =52 :4 =13 (Jane is 13
H =3 ×13 =39 (Harvey is 39
Answer:
Jane is 13 and Harvey is 39
Step-by-step explanation:
you save $150 per month for 2 years. what is the total amount you have saved?
The answer is 300 because 2 times 15 is 30 than you just add the zero
Answer:
$300
Step-by-step explanation:
i think you multiply 150 by 2 to get 300
What is the first step in evaluating the expression shown below?
12 ÷ (74 – 36) + 8 – 2
a
Subtract 74 – 36.
b
Divide 12 ÷ 74.
c
Add 36 + 8.
d
Subtract 8 – 2.
Answer:
A
Step-by-step explanation:
because it is is parenthesis
Consider the function represented by 9x+3y = 12 with x as the independent variable. How can this function be
written using function notation?
ORD=-v+
O f(x) = -3x+4
OF) = -3y+ 4
Answer:
f(x) = - 3x + 4
Step-by-step explanation:
letting y = f(x) , rearrange making y the subject
Given
9x + 3y = 12 ( subtract 9x from both sides )
3y = - 9x + 12 ( divide all terms by 3 )
y = - 3x + 4, thus
f(x) = - 3x + 4 ← in functional notation
please help!! Two sides of a triangle, a and b, have lengths 1 in
Answer:
Angle A and B: tan^-1 (1/1) = 45°
Angle C: 90°
Side C:
[tex] \sqrt{ {1}^{2} + {1}^{2} } = \sqrt{2} [/tex]
PLEASE MARK AS BRAINLIEST
Need help with this question!!!
Pls explain!!!
3=-(4x+7)+3x
Answer:
x=-10
Step-by-step explanation:
3=-(4x+7)+3x
move all terms to the left:
3-(-(4x+7)+3x)=0
calculate terms in parentheses: -(-(4x+7)+3x), so:
-(4x+7)+3x
add all the numbers together, and all the variables
3x-(4x+7)
get rid of parentheses
3x-4x-7
add all the numbers together, and all the variables
-1x-7
Back to the equation:
-(-1x-7)
get rid of parentheses
1x+7+3=0
add all the numbers together, and all the variables
x+10=0
move all terms containing x to the left, all other terms to the right
x=-10
PLEASE HELP!!!
Use the figure and find PT.
PT = 7x - 24 and TQ = 6x-2
Answer:
PT= 130
Step-by-step explanation:
Since T is the midpoint of segment PQ,
PT = TQ
7x - 24 = 6x-2
Subtract 6x both sides and add 24 both sides
7x -6x - 24 = 6x -6x -2
x - 24 + 24 = -2 + 24
x= 22
Substitue x into PT
7(22) - 24
154 - 24
PT= 130
2(4m + 1) = 4(3 + 2m) what os the value of m in the equation below?
Answer:
No solution.
Step-by-step explanation:
[tex]2(4m + 1) = 4(3 + 2m)\\[/tex]
Expand:
[tex]2\times4m+2\times1=4\times3+4\times2m[/tex]
[tex]8m+2=12+8m[/tex]
Subtract 2 from both sides:
[tex]8m+2-2=12+8m-2[/tex]
[tex]8m=8m+10[/tex]
Subtract 8m from both sides:
[tex]8m-8m=8m+10-8m[/tex]
[tex]0=10[/tex]
Since both sides are not equal, there is no solution, because the value of m will not affect this end result of [tex]0=10[/tex] which is false.
Answer:
any or all real number, meaning anything works, the equations are equal!
Step-by-step explanation:
2(4m + 1) = 4(3 + 2m)
8m+2=12+8m
8m=10+8m
0=10
this means that m can be any real number
hope this helped!
whats he approximete value of the square root of 8
Answer:
the approximate value of the square root of 8 is 2.828