A+B+C=180 so that B+C=180-A A-B-C=A-(B+C)=A-(180-A)=2A-180 tan(x-y)=(tanx-tany)/(1+tanxtany) tan(2A-180)=(tan2A-tan(180))/(1_+tan2Atan(180))=tan2A/1-tan2A) since tan(180)=-1

In triangle ABC, tan(A-B-C)=? (answer)

A+B+C=180 so that B+C=180-A A-B-C=A-(B+C)=A-(180-A)=2A-180 tan(x-y)=(tanx-tany)/(1+tanxtany) tan(2A-180)=(tan2A-tan(180))/(1_+tan2Atan(180))=tan2A/1-tan2A) since tan(180)=-1

− 4 < − 2 x − 14 < 3 This is really two inequalities. -4<-2x-14 and -2x-14<3 -4<-2x-14 multiply by -1 to get 4>2x+14 subtract 14 from each side to get -10>2x or 2x<-10 or x<-5 − 2 x − 14 < 3add 14 to each side to get -2x<17...

I assume that you want the value of sinθ, given the value of cos2θ. The relevant half-angle formula is sinθ=√((1-cos2θ)/2) sinθ=√((1+24/25)/2)=7/(5√2)

The terms of a geometric sequence may be written as a, ar, ar2,...,arn-1 for thre first n terms 8 is the first term, 8r5 is the sixth term 8r5=243/128=35/27 divide by 8=23 r5=35/210 and so r=3/22=3/4

sinθ=2/5. cos2θ=1-sin2θ gives cos2θ=1-4/25=21/25 cosθ<0 gives cosθ=-(√21)/5 sin2θ=2sinθcosθ=2×(2/5)×(-(√21)/5)=-4(√21)/25 cos2θ=cos2θ-sin2θ=21/25-4/25=17/25

How do you compare fractions? (answer)

or you could divide the numbers and see whether the answer is <=>1, as first number 4 3/8=35/8, second number 34/7 35/8÷34/7=35/8×7/34=245/272 <1 so 34/7 is larger.

2x−y=1 −6x+3y=2 multiply the first equation by -3 to-3 get -6x+3y=-3 the two equations are a set of two parallel lines −6x+3y=2 and -6x+3y=-3 No solution.

15(n+(n+1)+(n+2)+(n+3))=390 15(4n+6)=390 4n+6=26 4n=20 n=5 15(n+3)=120

Algebra Question (answer)

Total cost = $25+$10S Total payment $40 Change $40-($25+$10S)=$(15-10S)

The area of the circle is, as a function of time, A(t)=πr2(t) We are given that dr/dt = 7 cm/min and seek to find dA/dt Differentiating the equation for the area we have dA/dt = 2πr(t)dr/dt which gives that dA/dt=2π×12cm×7cm/min=168π cm2/min

If the bond pays its interest yearly then after one year the owner receives $600×.045=$27 For the final six months the bond will accrue $600×.045×1/2=$13.50 The total interest earned is $40.50

Similar triangles. The right triangle formed by the lamp post and the (24+6) foot side on the ground is similar to the right triangle formed by the person, of height h and his 6 foot shadow. h/25=6/30 h=5

The number pairs you state are in the form of A+B and A-B. Their average is A. For the first that means 23, and for the second that means -b/2.

let x be an irrational number. show that for every k>0 there exist n,m ∈Z such that 0<|nx-m|<k (answer)

Since x is irrational there exists an integer N for which N<x<N+1. Divide the interval [N,N+1] into n2 parts as xj=N+j/n2 for j=0,1,2,...,n2, (xn2=N+1) All of the xj are rational. xj+1-xj=1/n2. No xj is x. There is a j* such that xj*<x<xj*+1 That...

1/(3×22) 1/(3×32) 1/(3×2¹) 1/(3×3¹) 1/(3×20) 1/(3×30) The missing number is 1/(3×20)=1/3

Total distance traveled Time 90×2=180 miles 2 hrs 72×1/2=36 miles ...

1/|×-4|<1/|×+7| multiply both sides by |×-4|×|×+7| to get |×+7|<|×-4| which says that the points you are looking for are those whose distance from -7 is less than their distance from 4. The middle of that interval is the point -3/2. The points we want...

Now find the range of N as N/(-5) + 1 ≤ 7 subtract 1 from each side N/(-5)≤6 now multiply each side by -5 N≥-30 NOTE: multiplying an inequality by a negative number flips the inequality.

equation find m and n (answer)

(m-n)2=m2-2mn+n2=140-2(49)=140-98=42 You only asked for m-n. The question title asks for more.

write the equation of the line in general form whose x-intercept is 3 and y- intercept of -4. (answer)

There is a double intercept form x/3+y/(-4)=1