Answer:
- 23
Step-by-step explanation:
We could do this the long way and expand the whole product or note that the 
terms arise from the product of the a³ and a terms and the product of the a² and a² terms, that is
4a³ × 3a = 12
+ 5a² × - 7a² = - 35
Summing gives
12 - 35 = - 23
with coefficient - 23
D + 3n = 1 Subtract d from both sides
3n = 1 - d Divide both sides by 3
n = 
Answer:
m∠ABE = 27°
Step-by-step explanation:
* Lets look to the figure to solve the problem
- AC is a line
- Ray BF intersects the line AC at B
- Ray BF ⊥ line AC
∴ ∠ABF and ∠CBF are right angles
∴ m∠ABF = m∠CBF = 90°
- Rays BE and BD intersect the line AC at B
∵ m∠ABE = m∠DBE ⇒ have same symbol on the figure
∴ BE is the bisector of angle ABD
∵ m∠EBF = 117°
∵ m∠EBF = m∠ABE + m∠ABF
∵ m∠ABF = 90°
∴ 117° = m∠ABE + 90°
- Subtract 90 from both sides
∴ m∠ABE = 27°
(a) there are 8C2 = 28 ways of picking 2 girls from 8
And there are 21C4 = 5985 ways of picking 4 boys
Required number of ways for 2g / 4b = 28 * 5985 = 167,580
(b) at least 2 girls means combinations of 2g/4b , 3g,3b , 4g/2b , 5g 1b or
6 girls.
2g/4b = 167,580 ways
3g/3b = 8C3 * 21C3 = 56 * 1330 = 74,480
4g/2b = 8C4* 21C2 = 70 * 210 = 14,700
5g 1b = 8C5* 21 = 56*21 = 1176
6 girls = 8C6 = 28
adding these up we get the answer to (b) which is 257,964
The first term of an arithmetic sequence is 5. the eleventh term is 125. what is the common difference of the arithemetic sequence?
(1,5);(11,125)
Rate of change=change in y/change in x
=125-5/11-1=120/10=12
☆☆☆☆☆common difference of the arithemetic sequence is 12
