If a 25 ft rope is cut into two sections with one section 4 times as long as the other section, how long is the shorter piece?

Answers

Answer 1

Answer: x - shorter piece
4x - longer piece

$x+4x=25\n 5x=25\n x=5\hbox{ ft}$

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(a) Solve 7( k - 3 ) = 3k - 5 (b) Expand and simplify (2x + 3 )( x - 8)

(c) Solve 7 - 3 f = 2
4

Answers

a) $7(k-3)=3k-5\n 7k-21=3k-5\n 7k-3k=-5+21\n 4k=16\n k=\frac { 16 }{ 4 } \n k=4$

b) $(2x+3)(x-8)\n 2{ x }^( 2 )-16x+3x-24\n 2{ x }^( 2 )-13x-24$

c) $\frac { 7-3f }{ 4 } =2\n 7-3f=4\cdot 2\n 7-3f=8\n -3f=8-7\n -3f=1\n f=-\frac { 1 }{ 3 }$

$(a)\n7(k-3)=3k-5\n7(k)+7(-3)=3k-5\n7k-21=3k-5\ \ \ \ |add\ 21\ to\ both\ sides\n7k=3k+16\ \ \ \ |subtract\ 3k\ from\ both\ sides\n4k=16\ \ \ \ \ |divide\ both\ sides\ by\ 4\n\boxed{k=4}$

$(b)\n(2x+3)(x-8)=(2x)(x)+(2x)(-8)+(3)(x)+3(-8)\n\n=2x^2-16x+3x-24=\boxed{2x^2-13x-24}$

$(c)\n(7-3f)/(4)=2\ \ \ \ |multiply\ both\ sides\ by\ 4\n\n\not4^1\cdot(7-3f)/(\not4_1)=4\cdot2\n\n7-3f=8\ \ \ \ \ |subtract\ 7\ from\ both\ sides\n\n-3f=1\ \ \ \ \ |divide\ both\ sides\ by\ (-3)\n\n\boxed{f=-(1)/(3)}$

a bookstore sells 617 books on moday ,498 books on tuesday, and 563 books on wednsday. on which two days did the bookstore sell about 600 books

Answers

monday and wednesday

617 rounds to 600
563 rounds to 600
498 rounds to 500

answer would be Monday and Wednesday

Six more than three times a number is less than or equal to 96.

Answers

3x+6≤96
three x plus six is less than or equal to 96.

Wat is the common denominator of 1 and 6/4 and 1

Answers

Answer:

Step-by-step explanation:

4 is the common denominator.

1 and $(6)/(4)$ can be converted into $(4)/(4)$ + $(6)/(4)$ = $(10)/(4)$ we can divide both the numerator and denominator by 2 in order to simplify this fraction to get a fraction of $(5)/(2)$

1 can be converted to a fraction of $(2)/(2)$

Charles can do a job in 1 hour, Bill can do the same job in 2 hours, and Bob can do the jobin 3 hours. How long does it take them to do the job working together?

Answers

1hr +2hr+3hr is 6 hours job done

1+2+3=6 hours
bill Charles and bob

the population of masterton was 23 000 in 2012. Assume that Masterton population increases at a rate of 2% per year. Write an equation to model the population of masterton (y) based on number of years since 2012(x)

Answers

So, after a year, the population will be

23 000*1.02 (which is 23460 people).

And after two years it will be:

23460*1.02, which is 23930 people. Another way of writing it is
23000*1.02*1.02

so we can generalize: the population of the town, y= 23 000* $1.02 ^(x)$

where x is the number of years passed

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