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Kryger [21]
2 years ago
14

if A and B together can do a piece of work in 10 days and B along can do it in 15 days, how many part of the work does A complet

e in 6 days ​
Mathematics
1 answer:
anzhelika [568]2 years ago
8 0

Answer:

1/5

Step-by-step explanation:

Well work can be defined as: work = rate \ *\ time

where rate=amount of work that can be done in one unit of time

let a = rate of work A does in a day

let b = rate of work B does in a day

this means that: 10a + 10b=1 where work=1 and it just means the entire job has been completed.

Since b can do it alone in 15 days, this means that: 15b=1

If we divide by 15 here, we get the equation: b=\frac{1}{15}

We can now use this definition to substitute it into the first equation we made.

10a + 10(\frac{1}{15}) = 1

Multiply the 10 and 1/15

10a+\frac{2}{3}=1

subtract 2/3 from both sides

10a=\frac{1}{3}

Now divide both sides by 10

a=\frac{1}{30}

Now multiply this by 6, since we a represents the amount of work that can be done in a day, we want to find how many parts of the work can be done by a in 6 days

6a=\frac{6}{30}

Now divide both the numerator and denominator by 6

a=\frac{1}{5}

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algol13
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3 0
3 years ago
A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
Dima020 [189]

Answer:

Part A) y=\frac{3}{4}x-\frac{1}{4}  

Part B)  y=\frac{2}{7}x-\frac{5}{7}

Part C) y=\frac{2}{7}x+\frac{8}{7}

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the  median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

we have

L(-3, 6) and P(1, -8)

substitute the values

M(\frac{-3+1}{2},\frac{6-8}{2})

M(-1,-1)

step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}  

we have

N(3, 2) and M(-1,-1)

substitute the values

m=\frac{-1-2}{-1-3}

m=\frac{-3}{-4}

m=\frac{3}{4}

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{3}{4}

point\ N(3, 2)

substitute

y-2=\frac{3}{4}(x-3)

step 4

Convert to slope intercept form

Isolate the variable y

y-2=\frac{3}{4}x-\frac{9}{4}

y=\frac{3}{4}x-\frac{9}{4}+2

y=\frac{3}{4}x-\frac{1}{4}  

Part B) Find the equation of the  right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

we have

L(-3, 6) and P(1, -8)

substitute the values

M(\frac{-3+1}{2},\frac{6-8}{2})

M(-1,-1)

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}  

we have

L(-3, 6) and P(1, -8)

substitute the values

m=\frac{-8-6}{1+3}

m=\frac{-14}{4}

m=-\frac{14}{4}

m=-\frac{7}{2}

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m_1*m_2=-1

we have

m_1=-\frac{7}{2}

so

m_2=\frac{2}{7}

step 4

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{2}{7}

point\ M(-1,-1) ----> midpoint LP

substitute

y+1=\frac{2}{7}(x+1)

step 5

Convert to slope intercept form

Isolate the variable y

y+1=\frac{2}{7}x+\frac{2}{7}

y=\frac{2}{7}x+\frac{2}{7}-1

y=\frac{2}{7}x-\frac{5}{7}

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}  

we have

L(-3, 6) and P(1, -8)

substitute the values

m=\frac{-8-6}{1+3}

m=\frac{-14}{4}

m=-\frac{14}{4}

m=-\frac{7}{2}

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m_1*m_2=-1

we have

m_1=-\frac{7}{2}

so

m_2=\frac{2}{7}

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{2}{7}

point\ N(3,2)

substitute

y-2=\frac{2}{7}(x-3)

step 4

Convert to slope intercept form

Isolate the variable y

y-2=\frac{2}{7}x-\frac{6}{7}

y=\frac{2}{7}x-\frac{6}{7}+2

y=\frac{2}{7}x+\frac{8}{7}

7 0
3 years ago
if you took 7 hours to mow 4 lawns, then at that rate, how many lawns could be lawns could be mowed in 35 hours? at what rate we
liraira [26]
It takes 7 hours to mow 4 lawns
Therefore every hour, (4 ÷ 7) or 4/7 lawns are mowed. This gives the rate.

For 35 hours, 4/7 x 35 lawns are mowed.
=35 ÷ 7 = 5
= 4 × 5
= 20 lawns
3 0
3 years ago
Are you study of a population of 1200 frogs you feel that sold out of every 180 frogs in the population has spots on the back ba
Vsevolod [243]

Answer: 1,120 frogs

Step-by-step explanation:

If 12 out of every 180 frogs in the population have spots on their backs, the number that do not are;

= 180 - 12

= 168 frogs

168 frogs out of every 180 do not have spots. Out of 1,200 that would be;

= 168/180 * 1,200

= 1,120 frogs

5 0
3 years ago
3.<br>What is the<br>distributive property<br>of<br>40 + 64?​
Ivan

Answer:

104

Step-by-step explanation:

This is not a distributive property question though.

A distributive property has a number (a) outside the parenthesis

a(b+c)

so in this case a(40+64)

then you would multiply a by both numbers

40a+64a

then add them together

104a

However if it is a number outside the parenthesis and not a variable, it will come out different

For example

5(40+64)

(5*40)+(5*64)

200+320

520

Hope this helps!

8 0
3 years ago
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