Answers
Answer:
the first component of ordered pair is domain and second component is range
Answer:
In its simplest form the domain is all the values that go into a function, and the range is all the values that come out
Related Questions
what is cross products
Answers
Please help me to prove this!
Answers
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A = π - (B + C)
→ B + C = π - A
Use the Pythagorean Identity: cos² A + sin² A = 1 → sin² A = 1 - cos² A
Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2
→ cos A = 1 - 2 sin² (A/2)
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]
Use Cofunction Identities: cos (π/2 - A) = sin (A)
sin (π/2 - A) = cos A
cos (-A) = cos (A)
Proof LHS → RHS:
[tex]\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A][/tex]
[tex]\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]
[tex]\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]
[tex]\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]
[tex]\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg][/tex]
[tex]\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg][/tex]
[tex]\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg][/tex]
[tex]\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)[/tex][tex]\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)[/tex]
[tex]\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad[/tex]
I’m order of greatest to least with the numbers .875,.6,.5&.8 would it be .875,.8.6&.5
Answers
Answer:
Yes!
Step-by-step explanation:
Answer:
Yes Of course.This always confuses but you are correctIf you need further explanation, don't hesitate to ask mePlease, I need a BrainliestHelp pls i need help !!
Answers
Answer:
Ray, Line, Transversal?, Plane, Segment
Step-by-step explanation:
Using words, express x< 7
Answers
Answer:
X is less than seven
Step-by-step explanation:
"<" means less than, and shows that x is less than 7
Alex's wardrobe is 2 yards tall. How tall is the wardrobe in feet?
feet
Answers
Find the midpoint between each pair of points.
(7,-2) and (-4,2)
Answers
Answer:
Midpoint: [tex](\frac{3}{2} ,0 )[/tex]
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Step 1: Define variables
x₁ = 7
x₂ = -4
y₁ = -2
y₂ = 2
Step 2: Plug into midpoint formula
[tex](\frac{7-4}{2} ,\frac{-2+2}{2} )[/tex]
Step 3: Simplify/Evaluate
[tex](\frac{3}{2} ,\frac{0}{2} )[/tex]
[tex](\frac{3}{2} ,0 )[/tex]
Drag the tiles to the right places
PLEASE HELPPP FASSTTTTTTTT
I WILL MARK YOU AS THE BRAINLYEST IF I GET IT RIGHT JUST HELPPPPP
Answers
(4^2)^4 = 4^-8
(4^2)^-1 = 4^-2
4^2 x 4^6 = 4^8
4^5 x 4^-3 = 4^2
solve for T
10t = -50
Answers
Answer: t=-5
Step-by-step explanation:
if 10t=-50, you have to solve for the equation. to solve, you have to get the variable by itself. to get the variable by itself, you have to divide both sides by 10. 10t/10=-50/10. t=-5
Find the distance between (5,3)and(9,7)
Answers
Answer:
wouldnt it be 4,4?
Step-by-step explanation:
Answer:
Step-by-step explanation:
Calculate the distance between two points by filling in the x and y values of both coordinates. How do you find the distance between two points? Distance Formula : Example: For two points, (3,2) and (15, 10) the distance is calculated as: Distance = 14.42 (rounded to the nearest 100th)
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept and what is the y-intercept of the line? Choices are as follows: b = y + mx b = y - mx b = [tex]\frac{y-m}{x}[/tex] b = -12 b = -4 b = 2
Answers
Answer:
b=y-mx
Step-by-step explanation:
We know that y=mx+b is the slope intercept form of a line and we know that the slope of the line is 4. So:y = 4x+bHowever, we need to find the y intercept of the line which is b. Using the point (1,-8), we can find the y intercept. We need to find the equation to find the y-intercept. So:y = mx+b b=y-mxAnd now, we can substitute 4 for m which is the slopeb=y-4xUsing the point (1,-8) we can find the y-intercept b=(-8)-4(1)b=-8-4b=-12the equation of the line is y = 4x - 12 with the slope being 4 and y-intercept is -12. The equation we used is b = y-mx
NEED HELP ASAP SHOW WORK PLSSSS
Answers
Answer:
Hey there!
6x+1+3=8x+1
6x+4=8x+1
6x+3=8x
3=2x
x=1.5
6(1.5)+1
10
SR is 10 units long.
Let me know if this helps :)
Simplify the following: (-83)2
Answers
Use the fraction bar interactive to find the difference: One-third minus StartFraction 5 over 6 EndFraction
Answers
Answer:
-1/2
Step-by-step explanation:
Answer:
common denominator
6
1/3 - 5/6 difference
-1/2
Step-by-step explanation:
hope I wasn't to late
have a good day guys
:)
What is the question to b(x)=3x-1.
Answers
Answer:
x = 1/3
Step-by-step explanation:
Solve using the order of Operations:
- 5- (- 4 + 2)2
O -1
0-9
O 9
O 1
Math
Answers
Hey there! I'm happy to help!
Order of operations is PEMDAS. Parentheses comes first.
(-4+2)=-2
So, now we have -5-(-2)2
The next available option is multiplication.
-5-(-4)
Now we do addition and subtraction.
-5+4
-1.
Have a wonderful day! :D
solve inequality and show work please
Answers
Subtract two from both sides and it will leave you with x>5
No sign change since there is no dividing from a negative sign
( 1.03 x 10^9 ) - ( 4.7 x 10^7 )
Answers
Answer:
983000000
Step-by-step explanation:
can a rational number + a rational number = irrational number
Answers
Answer:
no
Step-by-step explanation:
its just like a positive number + a positive number cannot equil a negitive number.
What is 5000000+2000
Answers
Answer:
Step-by-step explanation:
5000000
+ 2000
5002000 (Answer)
2.9 x 10^5 + 8.7 x 10^5
Answers
Answer:
So this is scientific notation what you do is
2.9x10^5 so you put however many zeros the is powered to 10. See there is a 5 It has to be behind or in front of the decimal you might be saying how do you know if its behind or in front well negative is in front and positive is behind .
290,000 there was a number already behind the decimal so there you go 5 number behind the decimal.
Same for the second one
290,000 870,000 is your answers so now you add hem together
1,160,000 is your final answer
Step-by-step explanation:
helppp first to answer get brainlist
Answers
Answer: c
Step-by-step explanation:
A. 3
B. 4
C. 130
D. 35
Answers
Answer:
a) 3
Step-by-step explanation:
3+10= 13
hope this helped :)
Answer:
A. 3
Step-by-step explanation:
? + 10 = 13
? = 13 - 10
? = 3
2) I have two consecutive numbers. The difference of 4 times the first and 3 times the second number is negative 25. What is the value of your two numbers?
Answers
Answer:
31
Step-by-step explanation:
Answer:
Step-by-step explanation
The anwser should be 30 or 37 because 4 times 3 is 12 then plus 25 is 375w +3w=40 simplify your answer as much as possible
Answers
Answer:
w=5
Step-by-step explanation:
8w=40
/8 /8
w=5
8w= 40
40/8= 5
Mercedes takes out a loan for $ 10 , 000 at a simple interest rate of 3.5 % to be paid back in 42 monthly installments. What is the amount of the monthly payments?
Answers
Answer:
The amount of monthly installments is $267.30
Step-by-step explanation:
Here, we are interested in calculating the amount of the monthly is installments.
To get the amount of the installments, we need to calculate the sum of the interest and the amount borrowed.
Mathematically,
Simple interest = PRT/100
from the question;
P = principal which is the amount borrowed = $10,000
R = rate = 3.5%
T = time = 42 months = 42/12 = 3.5 years
Substitute these values into the formula for simple interest;
We have ;
S.I = (10,000 * 3.5 * 3.5)/100 = $1,225
So the total amount to
payback = interest + principal = 1225 + 10,000 = 11,225
So the amount of installments will be ;
The amount to payback/number of months
Mathematically that would be ; 11,225/42 = $267.26 which is approximately $267.30 per month
Mark wants to put a fence around his square yard.He knows that his yard is shaped like a square and the area of the yard is 110. What would the perimeter be
Answers
Answer:
27.5 is the answer good luck
Step-by-step explanation:
good luck my G
2(3-p)=17=41 show answer.
Answers
this is what I found hope its correct!♀️
find the value of x if h is the midpoint of gj, gj equals 4x-6, and gh=27 - huryyyyyyy please.
Answers
Answer: X=15
Step-by-step explanation:
GH+HJ= GJ
27+27=4x-6
54=4x-6
60=4x
15=x
The perimeter of a rectangular playing field is 280 feet. The length of the field is 20 feet more than the width. What are the dimensions of the playing field? (You need to find the length and the width.)
Answers
Answer:
L =80
w=60
Step-by-step explanation:
P =280
L =w +20
=>L +w=280 :2 =140
w+20+w=140
2w=140 - 20
2w =120
w=120 :2 =60
L=60 +20 =80
P =2L +2w
P =2 ×80 +2 ×60
P=160 +120
P=280
Answer:
L = 80 , w=60
Step-by-step explanation:
l= w+20
perimeter: l+w+l+w=280
Plug in the value of L in place of L
(w+20)+w+(w+20)+w=280
Combine Like terms
and then separate the variables and knowns by subracting 40 from both sides
4w+40=280
-40 -40
Divide by 4 from both sides so (W) would be alone
4w=240
÷4 ÷4
You solved half the question now
w = 60
Remember the L at the top
we now know the value of W
so
L=(60)+20
L=80
just to be sure
80+80+60+60=280
you are welcome