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

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

solve the system (answer)

y=-x+7 y=(x-3)2/2=(x2-6x+9)/2 So -x+7=(x2-6x+9)/2 or -2x+14=x2-6x+9 or 0=x2-4x-5 competing the square we have (x-2)2-9=0 or x-2=±3 or x=5, or x=-1 In which cases y=2 or y= 8 (5,2) and (-1,8) are the solutions

The answer is 19. The explanation is bG = number of boys Gordon plays bJ = number of boys Jayanthi plays gG = number of girls Gordon plays gJ = number of girls Jayanthi plays There are a total of nC2 games...

A circle centered at the origin containing the point (-6,0) has the equation x2+y2=36. Any other question about the circle may be answered using this. Exactly what is your question. What you posted is incomplete.

H = 21 + 979e^−0.1t. For t=60 is 21+979e-6=23.4267 Average over first hour is (1/60)∫060Hdt=21+(979/60)∫060e-.1tdt ∫060e-.1tdt=-10e-.1t|060=10(1-e-6) Average over first hour is 21+(979/6)(1-e-6)=21+162.7622=183.7622 The 21 is simply added because (1/60)∫06021dt...

There are two similar triangles involved. The man's distance is 1.2t from the lamp post. The length of his shadow is s(t). The right triangle formed by the lamp post and (the distance of the man from the lamp post+his shadow length) is similar to the right triangle formed by the...

1 2 3 4 5 6 7 L L L L L L L O O O O O O O O C O C O C O O C C O C O C This diagram gives the pattern. A locker changes state from being...

x and y are two numbers each greater than 3, the highest common factor of x and y is 3, the lowest common multiple of x and y is 36, find x and y xy = product of greatest common divisor and least common multiple=3×36=108 Since GCD is 3 we may write x=3a, y=3b since...

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