x=Sheila's age x+32=Sudha's age x+(x+32)=40 2x+32=40 2x=40-32 2x=8 x=8/2 x=4 years old

x=Sheila's age x+32=Sudha's age x+(x+32)=40 2x+32=40 2x=40-32 2x=8 x=8/2 x=4 years old

sin(26)+sin(24)=sin(A) sin(a)+sin(b)=2sin[(a+b)/2]cos[(a-b)/2] a=26, b=24 2sin(26+24)/2*cos(26-24)/2 2sin(25)*cos(1) 2(0.42261)(0.99984) 0.845084=sin(A) arcsin(0.845084)=57.6809369º or 57º 40' 51.373"

Good question (answer)

a substance is 99% water some water evaporated leaving a substance that is 98% water how much water evaporated ? assume the substance weighs 100 lbs, 1%, or 1 pound is solid and 99% is water some water evaporated and the substance is now 98% water but still 1 pound solid the...

x+y=336 and the GCF of x and y is 24 24x+24y=336 and x and y are relatively prime (they have no common factors other than 1) 24(x+y)=336 divide both sides by 24 x+y=14 x=1, y=13, 24+312=336 x=2, y=12 cannot be used because the GCF would be 48 x=3,...

28=2*2*7 42=2*3*7 56=2*2*2*7 to be a multiple of 56 you need all of 56's prime factors LCM=2*2*2*7 so far to be a multiple of 42 you need only the 3 because you have the 2 and the 7 LCM=2*2*2*7*3 so far you don't need anything from the factorization of 28 because you...

Word Problem Help! (answer)

P=2l+2w but one length is not used because of the school so P=l+2w 32=l+2w and l=32-2w A=l*w A=(32-2w)(w) 0=32w-2w2 this is a parabola that opens downward so there is a maximum at (h,k) where h is the "maximizing point" and k is the maximum area use...

5x-3y=2 -3y=-5x+2 y=(5/3)x-2/3 if you want integers... x=1, y=1 x=4, y=6 x=7, y=11 x=10, y=16 x=13, y=21 do you see the pattern ?

x=3, y=5 x=5, y=-3 x=7, y=-11 as x increases by 2, y decreases by 8 if x increases by 1, y decreases by 4 if x=4, y=1 if x=6, y=-7 if x=2, the previous y must be 4 more, or y=9 if x=1, the previous y must be 4 more, or y=13 if x=0, the previous y must be 4 more,...

find the length of an arc of a circle with radius 6/pi cm that substends a central angle of 99° (answer)

you asked for the length of the arc; you find the area of a sector L=(q/180)(∏)(r) is the formula to use L=(99/180)(∏)(6/∏) simplify first L=(11/20)(6) the ∏'s cancel L=66/20 L=3.3 cm

The ages of three brothers are consecutive integers with the sum of 96. How old are the brothers (answer)

x+x+1+x+2=96 3x+3=96 3x=96-3 3x=93 x=93/3 x=31 x+1=32 x+2=33 using arithmetic... 96/3=32 32-1=31 and 32+1=33

x+y=480 x-y=140 add 2x=620 x=620/2 x=310 310+y=480 y=480-310 y=170 310 and 170 are the numbers if you don't understand algebra... 480/2=240 240 and 240 no 200 and 280 no 180 and 300 no 170 and 310 yes subtract a number from...

the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments of the hypotenuse draw the triangle ABC where A is at the top, B is at the bottom left and C is at the bottom right <ABC is a right angle draw the altitude to the hypotenuse and call this...

Help Help Help (answer)

x=shortest side y=middle side z=longest side x+y+z=70 z=x+y-6 2x=z-4 in this last equation replace z by x+y-6 2x=x+y-6-4 this becomes... 2x-x-y=-10 x-y=-10 from x+y+z=70, replace z by 2x+4 from equation 2x=z-4 which becomes...

google it and you'll find... biquadratic numbers a biquadratic number is a fourth power, n4

P=y+2x because one side is the existing fence 240=y+2x y=240-2x A=lw or A=xy A=x(240-2x) A=240x-2x2 0=240x-2x2 this is a parabola that opens downward so there is a maximum point (h,k) h=-b/2a h=-240/-4 h=60 the rectangle should be a 60 by 60 meter...

1/3=0.33333333333333... 2/3=2*(1/3)=2*0.33333333333...=0.6666666666666666.....

there is a formula that you can use the median from point A=(1/2)√(2c^2+2b^2-a^2) where a, b, and c are the lengths of the sides opposite the angles A, B, and C similarly the formula changes for each different median you can use the formula or do the following... draw right triangle...

tan=opposite/adjacent draw a triangle in quadrant lll the legs are 7 and √32=4√2 find the hypotenuse H^2=7^2+(4√2)^2 H^2=49+32=81 H=√81=9 the hypotenuse is 9 the adjacent is 4√2 cos=adjacent/hypotenuse cos=-4√2/9 tan(θ/2)=±√[(1-cosθ)/(1+cosθ)] tan(θ/2)=±√[(1+4√2/9)/(1-4√2/9)] tan(θ/2)=±√([9+4√2]/9)/[9-4√2]/9) tan(θ/2)=±√[(9+4√2)/(9-4√2)] multiply...

x can be any distance to make it easier to understand, let x=40 miles distance=rate*time total distance=rate*total time d=rt 40=10t t=40/10 t=4 hours to someplace d=rt 40=8t t=40/8 t=5 hours returning from someplace total distance=40+40=80 miles total...

If X is the sum of the integers from 21 to 70 and Y is the sum from 121 to 170, what is Y -X ? (answer)

X=21+22+23+24+...+69+70 (there are 50 numbers) Y=121+122+123+...+168+169+170 (there are also 50 numbers) notice that each number from 121 to 170 are all of the numbers from 21 to 70 with 100 added to each one Y-X=121-21+122-22+123-23+...