Answer:
Here we want to solve:
(cos(A) + sin(A))^2 + ( sin(A) - cos(A))^2 = 2
First, remember the two expansions:
(a + b)^2 = a^2 + 2*a*b + b^2
(a - b)^2 = a^2 - 2*a*b - b^2
Using these relations, we can expand:
(cos(A) + sin(A))^2 = cos(A)^2 + 2*cos(A)*sin(A) + sin(A)^2
( sin(A) - cos(A))^2 = sin(A)^2 - 2*sin(A)*cos(A) + cos(A)^2
Replacing that in our equation, we geT:
(cos(A)^2 + 2*cos(A)*sin(A) + sin(A)^2) + (sin(A)^2 - 2*sin(A)*cos(A) + cos(A)^2) = 2
We can simplify this to get:
2*cos(A)^2 + 2*sin(A)^2 + 2*cos(A)*sin(A) - 2*cos(A)*sin(A) = 2
2*cos(A)^2 + 2*sin(A)^2 = 2
We can take the 2 as a common factor to get:
2*cos(A)^2 + 2*sin(A)^2 = 2*( cos(A)^2 + sin(A)^2) = 2
Now we can divide both sides by 2:
2*( cos(A)^2 + sin(A)^2)/2 = 2/2
cos(A)^2 + sin(A)^2 = 1
And this is a trigonometric property that is true for any value of A.
So the equality:
(cos(A) + sin(A))^2 + ( sin(A) - cos(A))^2 = 2
is true for any real value of A.
There are 3000 student in the school 30% of the student are girls find
A) The total number of girl
B) The total number of student
Step-by-step explanation:
3000 [tex] 3000 \div 30 = 1000[/tex][tex]3000 \times 30 = 90000[/tex]Evaluate the following expression when x = 4 and y = 2.
x²+y3
3
Answer:
24
Step-by-step explanation:
x^2+y^3
(4)^2+(2)^3
(4)(4)+(2)(2)(2)
16+8=24
Simplify the algebraic expression:
7(x + 3)20
Answer:
140x+420
Step-by-step explanation:
7(x+3)20
=140x+420
Answer:
14x+420
Step-by-step explanation:
7(x+3)(20)
=140x+420
Sally can paint a room in 9 hours while it takes Steve 5 hours to paint the same room. How long would it take them to paint the room if they worked together?
Answer: About 3 hours and 5 minutes to paint the room together.
Step-by-step explanation:
Sally can paint 1/5 of the room in an hour and Steve can paint 1/8 of the room in an hour.
Room/Hour
1/5 ± 1/8 =8/40
8/40+5/40=13/40
How long to paint the room?
13/40 x 1= 40/13
40÷13=3.0777
So the answer will be Sally and Steve can paint the room in about 3 hours and 5 minutes
Noah says, "If I try to write 100 expanded, it should have zero factors that are 10, so it must be equal to 0." Do you agree? Why or why not?
Answer:
Disagree
Step-by-step explanation:
10^0
According to the laws of indices, anything raised to the power of 0 will equate to 1. Therefore, based on this established mathematical principle, Noah's assertion about 10^0 being equal to 0 is false.
Hence, I disagree.
Find the measure of
А
E
103°
270
50°
35°
D
B
C
Answer:B
Step-by-step explanation:
The piper family arrived at the campground at the time shown on the clock. I took the family 2 hours and 15 minutes to get to the campground. What time did the family leave their house?
Answer:
As you included no picture, I do not know the time on the clock. We can however, work with assumed figures which you can then relate to your question.
Assuming the time on the clock was 10:45 am, if the family took 2 hours and 15 minutes to get to the camp ground, simply subtract this from 10:45 to find out what time they arrived.
Subtract the 2 hours from 10am:
= 10 - 2
= 8am
Subtract the 15 minutes from 45:
= 45 - 15
= 30
Put that together:
= 8:30 am
They left their house at 8:30 am using this scenario.
Two phone companies one is 11/+.16/ min And another is 20+.11/min How many minutes will make both equal amounts
Answer:
Company one charges $11 + $0.16 per min.
Then if you talk for x minutes, the cost will be:
C₁(x) = $11 + ($0.16 per min)*x
For company two, the prize is $20 + $0.11 per min, and if yo talk for x minutes, the cost will be:
C₂(x) = $20 + ($0.11 per min)*x
Now we want to find the value of x, the number of minutes, such that the cost is the same with both companies.
C₁(x) = C₂(x)
$11 + ($0.16 per min)*x = $20 + ($0.11 per min)*x
($0.16 per min)*x - ($0.11 per min)*x = $20 - $11
($0.05 per min)*x = $9
x = $9/($0.05 per min) = 180 mins
If you speak for 180 minutes, the cost is the same in both companies.
does anybody know the answer to this?
Answer:
C (136)
Step-by-step explanation:
The triangle is only rotated, the measure of <D doesn't change
Given that (√3)^n = 3^x/27^y^1
express n in terms of x and y.
A simple impact crater on the moon has a diameter of 15 kilometers. A complex impact crater has
a radius of 30 kilometers. How much greater is the circumference of the complex impact crater than
the simple impact craters?
Answer:
141.3 km
Step-by-step explanation:
First crater has the radius (that is, half the diameter) of 7.5 km; the circumference of this crater is C = 2(pi)r, or 2(3.14)(7.5 km) = 47.1 km;
Second crater radius is C = 2(pi)(30 km) = 188.4 km
The circumference of the complex (larger) impact crater is
(188.4 - 47.1) km greater than the circumference of the simple (smaller) crater:
141.3 km
The local water slides have 72
employees, of which 25% are
temporary. How many
temporary employees are
there?
Answer:
18
Step-by-step explanation:
Step 1: Convert 25% to a fraction
[tex]\frac{25}{100}[/tex]
Simplify
[tex]\frac{1}{4}[/tex]
Step 2: Convert 72 to a fraction
[tex]72 = \frac{72}{1}[/tex]
Step 3: Set it up
[tex]\frac{1}{4}\times \frac{72}{1}[/tex]
Step 4: Cross divide
[tex]72 \div 4 = 18[/tex]
[tex]1 \div 1 = 1[/tex]
[tex]\frac{18}{1} = 18[/tex]
Therefore, the are 18 temporary employees in the local water slides.
I need to know the surface area of this prism please help !!!! I will give brainlist !
Answer:
614
Step-by-step explanation:
15 x 13 = 195 two times 195 x 2 = 390
4 x 15 = 60 two times 60 x 2 = 120
4 x 13 = 52 two times 52 x 2 = 104
104 + 120 + 390 = 614
Answer:
SA = 2(l·w)+2(w·h)+2(l·h)
SA = 614 sq in
Step-by-step explanation:
SA = 2(4x13)+2(13x15)+2(4x15)
= 2(52)+2(195)+2(60)
= 104 + 390 + 120
= 614
how many sixths are in 2 5/6?
Answer:
Respuesta. el resultado (17) va ser el numerdaor de la fraccion y el denominador se mantiene.
Step-by-step explanation:
Find the value of x.
:]]
Answer:
144
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
This is a right angle (complementary angles) so 90-43 is 47 and the angel is x - 7 so you have to add 7. Answer is 54 <3
Johnny took a math quiz last week. He got 9 problems correct and 11 problems incorrect. What percentage did Johnny get correct?
Answer:
The answer is 45%
Step-by-step explanation:
9+11=20
9/20
=4.5/10
=45/100
=45%
Which of the following are roots of the polynomial function
Answer:
its a and b
Step-by-step explanation:
HELP ME PLS♀️‼️
What rational number subset(s) do 2, 5, 7, 9, 13 belong to??
Answer:
Natural numbers , whole numbers, Integers
What is the surface area of this composite solid?
Use 11.3 meters for the slant height of the triangular prism.
Enter your answer in the box.
__m²
Composite made up of a rectangular prism surmounted by a triangular prism. The rectangular prism has dimensions of 16 meters wide by 20 meters long by 12 meters high. The triangular prism has dimensions of 16 meters wide by 20 meters long with a triangular altitude of 8 meters high.
Answer:
1764 m²Step-by-step explanation:
Refer to attached picture.
All given dimensions are given on the picture (not to scale).
Since altitude of the triangle and slant height is given, we can find the base of the triangle using Pythagorean:
[tex]b/2 = \sqrt{11.3^2-8^2} = \sqrt{64} = 8m, \\b = 16 m[/tex]It has 9 faces and the total surface area is:
S = 16*20 + 2(20*12) + 2(20*11.3) + 2(16*12) + 2(1/2*8*16) = 1764 m²How would you find the missing value? 15/4=5/x
15(4) = 5x
15(x) = 5(4)
15 14 =5+x
Using the intersecting chord theorem you multiply the two lengths of one line together to equal the multiplication of the two dimensions on the second line.
The answer would be 15(4) = 5x
5x−4y=−10
y=2x−5
x=x=x, equals
y=y=y, equals
Answer:
✎ ANSWER:-[tex]y = 2x - 5[/tex]
Substitute the value of y as 2x - 5 in the equation.
[tex]5x - 4y = - 10 \\ 5x - 4(2x - 5) = - 10 \\ 5x - 8x + 20 = - 10 \\ 5x - 8x = - 10 - 20 \\ - 3x = - 30 \\ x = \frac{ - 30}{ - 3} \\ x = 10[/tex]
Now, find the value of y
[tex]y = 2x - 5 \\ y = 2(10) - 5 \\ y = 20 - 5 \\ y = 15[/tex]
⎇ x = x = x, equals 10
⎇ y = y = y, equals 15
Answer:
if y = 2x-5
then in the second equation we can find the value of x
5x-4(2x-5) = -10
5x-8x+20 = -10
-3x = -30
x = 10
then the value of y = 20-5 = 15
therefore the value of x = 10 and y =15 (ans)
Hope it helps
The average commute times for employees of a large company is 23 minutes.
The commute time of 12 employees are
25, 33, 26, 29, 17, 29, 42, 19, 15, 52, 11, and 14.
Enter the sample mean and the population mean in the boxes.
x¯ =
min
μ =
min
Answer:
x¯ = 26 min
μ = 23 min
Step-by-step explanation:
I took the test and these were the answers.
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
5x=0
X=0 only one solution
Answer:
5x=0
x= 0 anly solution. helpful answer
When a graph is symmetric about the origin, it is an function.
When a graph is symmetric about the y-axis, it is an function.
A function is considered if f(-x) =
f(x), and it is considered
=
if f(-x) = -f(x).
Answer:
odd; even; even; odd
Step-by-step explanation:
The answers are odd, even, even, and odd respectively the graph is symmetric about the y axis it is an even function.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We know when the graph is symmetric about the origin it is an off function.
When the graph is symmetric about the y axis it is an even function.
When f(-x) = f(x) it is an even function
When f(-x) = -f(x) it is an odd function.
Thus, the answers are odd, even, even, and odd respectively the graph is symmetric about the y axis it is an even function.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
Use the distributive property to remove the parentheses. 5(v+6)
Answer:
5 x 6v
Step-by-step explanation:
4. My son's age is of my wife's age, my wife's age is of my age, and my age is of my father's age. Find
age of my son, if my father is 50 years old
Answer:
50?
Step-by-step explanation:
Answer:
The age of son is 50.THANK YOU.
You and your friends go to the state fair. It costs $6 to get into the fair
and $2 each time you go on a ride. Consider the relationship between
number of rides and total cost.
Model the equation to show the linear relationship.
Answer:
[tex]let \: number \: of \: rides \: be \: \: n \\ let \: cost \: be \: \: c \\ n \: \alpha \: c \\ n = kc \\ k \: is \: a \: costant \: of \: proportionality \\ when \: n = 1. \: \: c = 2 \\ 1 = (k \times 2) \\ k = \frac{1}{2} \\ therefore : \\ n = 0.5c[/tex]
Answer:
[tex]\huge\boxed{\sf x = 6 + 2y}[/tex]
Step-by-step explanation:
Let the total cost be x and number of rides be y
It costs $2 on each ride. So, the rides' cost will be:
=> Number of rides * One rides' cost
=> y * 2
=> 2 y
So, The total cost will be:
Total cost = Entrance cost + Rides' cost
Total cost = $6 + $2(Number of rides)
x = 6 + 2y
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Someone please please help and
Thanks so much
Ashton estimates the square root of 50 in the following way: Complete sentences √50= 2√25=2×5=10
Answer:
[tex]\sqrt{50} = \sqrt{2*5*5}= 5\sqrt{2}[/tex]
can anyone do all my work for me before Wednesday i
Answer:
sure I can help with that.....