x, x+1, x+2 are the consecutive integers x+x+1=x+2+47 2x+1=x+49 2x-x=49-1 x=48 x+1=49 x+2=50

x, x+1, x+2 are the consecutive integers x+x+1=x+2+47 2x+1=x+49 2x-x=49-1 x=48 x+1=49 x+2=50

Arithmetic Series (answer)

1+2+3+4+...+97+98+99+100 S(n)=(100/2)(2*1+[100-1]*1) S(n)=50(2+99) S(n)=50*101 S(n)=5050 3,6,9,12,...,96,99 there are 33 of these numbers that are divisible by 3 S(n)=(33/2)(2*3+[33-1]*3) S(n)=(33/2)(6+96...

Arithmetic series (answer)

Proof by mathematical induction: an odd number can by written as 2n-1 where n=1, 2, 3, ... prove that 1+3+5+7+...+2n-1=n2 show that this is true for k=1, assume this is true for some odd integer 2k-1, and finally show this is true for 2(k+1)-1 if...

Here's part a) using different reasoning. Row 5 starts with the 11th odd number. The previous rows have 4, 3, 2, and 1 odd numbers for a total of 10 odd numbers. The 99th row will begin with which odd number ? Add the number of odd numbers from each row. 1+2+3+4+...

Determine the y-intercept of the line that passes through the point (-2,1) with a slope of 5 (answer)

y=mx+b y=5x+b using the point (-2,1) 1=5(-2)+b 1=-10+b 1+10=b b=11 is the y-intercept and the equation is y=5x+11

if there is a discount of 30%, then this means that you pay only 70% of the original price 70%*$450=0.7*450 0.7*450=$315 is the new price

algebra story problem (answer)

V=(4/3)(∏)(r3) 62,000=(4/3)(∏)(r3) multiply both sides by 3/4 46,500=∏(r3) (46,500/∏)=r3 take the cube root of both sides (46,500/∏)^(1/3)=r factor 46,500 46,500=5*3*31*2*2*5*5=2*2*3*31*53 the cube root of 53 is 5 5[(2*2*3*31)/∏]^(1/3)=r 5[(372/∏)^(1/3)]=r...

25x+35y=340 x+y=12 simplify the first equation 5x+7y=68 x+y=12 ------>y=12-x substitute 5x+7(12-x)=68 5x+84-7x=68 -2x+84=68 -2x=68-84 -2x=-16 2x=16 x=8 months he paid $25

b=base 8b+16=height A=(1/2)(b)(h) 60=(1/2)(b)(8b+16) 120=(b)(8b16) 120=8b^2+16b 8b^2+16b-120=0 divide all terms by 8 b^2+2b-15=0 factor (b+5)(b-3)=0 b-3=0 b=3 inches (answer) h=8*3+16=40 inches

Solving using the quadratic formula (answer)

Jessica, you did this correctly. The only thing is that it says to use the quadratic formula. (-50±√3364)/6 (-50±58)/6 8/6=4/3 -108/6=-18

Arithmetic Series (answer)

3-5+7-9+11-13+15-17+19-21... find the sum to 80 terms break this up into two parts 3+7+11+15+19.... (there will be 40 numbers ) -5-9-13-17-21... (there will be 40 numbers ) add the first numbers in each sequence...

w=width 3w=length P=2l+2w 44=2(3w)+2(w) 44=6w+2w 44=8w w=44/8 w=5.5 cm l=3*5.5=16.5 cm

algebra 2 high school (answer)

(4/7)^0=1 (anything raised to the 0 power is equal to 1 except 0^0 which does not exist in mathematics) (3/5)^3=(3/5)(3/5)(3/5)=27/125 2^(-5)=1/25=1/32

algebra story problem (answer)

26=64 possible combinations of true-false answers the probability is 1/64 suppose you had 3 questions (R=right and W=wrong) RRR RRW WRR RWR WWW WWR RWW WRW the probability of getting all 3 right is 1/8 (23=8 and only 1 is RRR)

Can anyone solve this ? (answer)

w=width w+10=length A=lw 119=(w+10)(w) 119=w^2+10w w^2+10w-119=0 119=7*17 you can really stop here because you have the answer: w=7 feet and l=17 feet however... (w+17)(w-7)=0 w-7=0 w=7 and w+10=17 basically what you are doing...

draw rhombus ABCD with point A at the top and point C at the bottom point D is at the left and point B is at the right draw the segment joining the midpoints of AB and AD label the midpoint of AB point F on the right label the midpoint of AD point E on the left points E and F...

find the slope of the line containing these 2 points, (-3,1) and (1,25) slope=rise/run slope=(25-1)/(1-[-3]) slope=24/4 slope=6 y=mx+b where m=slope and b=y-intercept, which is what you want y=6x+b use either point 1=6(-3)+b 1=-18+b 1+18=b b=19,...

√6x2-x-√6=0 (√2x-√3)(√3x+√2)=0 √2x-√3=0 x=√3/√2 x=√6/2 √3x+√2=0 x=-√2/√3 x=-√6/3

Prove divisibility 25^7+5^13 by 30 (answer)

257+513 (52)7+513 514+513 513(5+1) 513(6) 512(5)(6) 512(30)

517-516 516(51-1) 516(50) 516(2*25) (516*2)25 by the same reasoning as the others

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