Answer:
just invert the points
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
We are given ...
barrettes : hair ties = 5 : 7
barrettes : hair bands = 5 : 8
Then the combined ratios are ...
barrettes : hair ties : hair bands = 5 : 7 : 8
For every 5 barrettes, there are 7+8 = 15 hair ties and bands, so their ratio is ...
barrettes/(hair ties and bands) = 5/15 = 1/3
Answer:
(x + 1) (3 x^2 + 1)
Step-by-step explanation:
Factor the following:
3 x^3 + 3 x^2 + x + 1
Factor terms by grouping. 3 x^3 + 3 x^2 + x + 1 = (3 x^3 + 3 x^2) + (x + 1) = 3 x^2 (x + 1) + (x + 1):
3 x^2 (x + 1) + (x + 1)
Factor x + 1 from 3 x^2 (x + 1) + (x + 1):
Answer: (x + 1) (3 x^2 + 1)
I'll start 18 and 22 for you, and you should then be able to do the rest on your own!
For 18, what we literally do is apply the distance formula for all the points and add them up. For B to C, we get the distance between them to be
sqrt((x1-x2)^2+(y1-y2)^2)=sqrt((0-4)^2+(3-(-1))^2)=sqrt((-4)^2+4^2)=sqrt(16+16)=sqrt(32). Repeat the process for C to E, E and F, and F to B then add the results up to get your answer!
For 22, since the area of a rectangle is length*width (we know given the right angles and that the opposite sides are equal in how long they are), we can multiply 2 perpendicular lines, for example, BC and CE to get sqrt(32)*sqrt(8)=16 as the area
Answer: proof below
<u>Step-by-step explanation:</u>
Use the Difference formula for sin:
sin (A - B) = sin(A)·cos(B) - cos(A)·sin(B)
sin (180° - θ) = sin(180°)·cos(θ) - cos(180°)·sin(θ)
= 0 · cos(θ) - -1 · sin(θ)
= 0 - -sin(θ)
= + sin(θ)
sin (180° - θ) = sin(θ) 
