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3 years ago

Solve the formula S=n/2(a+L) for L

Mathematics

1 answer:

Maru [420]3 years ago

4 0

$\frac{n}{2(a+l)}$

$\frac{S}{N} = 2(A+L)$

$\frac{S}{2N} = A+L$

$L= \frac{S}{2N} - A$

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The expression 24y+36 represents the cost of a dozen eggs. Use factoring to write an expression that is equivalent to 24y+36. Th

andriy [413]

$12eggs \: = 24y + 36 \\ 1egg \: = \frac{24y + 36}{12} \\ = 2y + 3$

5 0

3 years ago

Two planes start flying towards each other simultaneously from two different cities. The distance between the cities is 960 mile

Eddi Din [679]

Answer:

The speed of one plane = 257.5 miles per hour

And speed of second plane = 332.5 miles per hour

Step-by-step explanation:

We have given,

Distance between two cities = 960 miles

Two planes are flying towards each other.

Let the speed of one plane be x.

Then,

Speed of second plane = x+75 {Following this "one of the planes' speed exceeds the other by 75 mph"]

After 1.5 hours they are still 75 miles apart.

i.e Relative distance between two planes = Relative speed of plane × Time

Here

relative speed = x + (x+75) , and relative distance left to cover = 960-75.

i.e

(960 - 75) = {x+(x+75)}×1.5

885 = (2x+75)×1.5

or $\frac{885}{1.5} =2x+75$

or 590-75 = 2x

or 515 = 2x

or x = $\frac{515}{2}$ = 257.5

Hence the speed of one plane = x = 257.5 miles per hour

And speed of second plane = (x+75) = 257.5 + 75 = 332.5 miles per hour

6 0

3 years ago

Question -

Sauron [17]

$\rule{200}4$

Answer : The required ratio is (14m-6):(8m+23) .

$\rule{200}4$

Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .

That is.

$\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{7n +1}{4n +27} \\$

As , we know that the sum of n terms of an AP is given by ,

$\small\sf\longrightarrow \pink{ S_n =\dfrac{n}{2}[2a +(n-1)d]} \\$

Assume that ,

First term of 1st AP = a
First term of 2nd AP = a'
Common difference of 1st AP = d
Common difference of 2nd AP = d'

Using this we have ,

$\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{\dfrac{n}{2}[2a + (n-1)d]}{\dfrac{n}{2}[2a' +(n-1)d'] } \\$

$\small\sf\longrightarrow \dfrac{7n+1}{4n+27}=\dfrac{2a + (n -1)d}{2a' + (n -1)d' } . . . . . (i) \\$

Now also we know that the nth term of an AP is given by ,

$\longrightarrow\sf\small \pink{ T_n = a + (n-1)d}\\$

Therefore,

$\longrightarrow\sf\small \dfrac{T_{m_1}}{T_{m_2}}= \dfrac{ a + (n-1)d }{a'+(n-1)d'}. . . . . (ii)\\$

$\longrightarrow\sf\small \dfrac{T_1}{T_2}=\dfrac{2a + (2n-2)d}{2a'+(2n-2)d'} . . . . . (iii)\\$

From equation (i) and (iii) ,

$\longrightarrow\sf\small n-1 = 2m-2\\$

$\longrightarrow\sf\small n = 2m -2+1 \\$

$\longrightarrow\sf\small n = 2m -1 \\$

Substitute this value in equation (i) ,

$\longrightarrow \sf\small \dfrac{2a+ (2m-1-1)d}{2a' +(2m-1-1)d'}=\dfrac{7(2m-1)+1}{4(2m-1) +27}\\$

Simplify,

$\longrightarrow\sf\small \dfrac{ 2a + (2m-2)d}{2a' +(2m-2)d'}=\dfrac{14m-7+1}{8m-4+27}\\$

$\longrightarrow\sf\small \dfrac{2[a + (m-1)d]}{2[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\$

$\longrightarrow\sf\small \dfrac{[a + (m-1)d]}{[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\$

From equation (ii) ,

$\longrightarrow\sf\small \underline{\underline{\blue{ \dfrac{T_{m_1}}{T_{m_2}}=\dfrac{ 14m-6}{8m+23}}}}\\$

$\rule{200}4$

8 0

3 years ago

HELP GEOMETRY URGENT

LenaWriter [7]

Answer:

z = 16

y = 9

Step-by-step explanation:

4 0

3 years ago

Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using

MArishka [77]

Answer:

f(x) = -3x + 4

Step-by-step explanation:

Step 1: Write it in slope-intercept form

9x + 3y = 12

3y = -9x + 12

y = -3x + 4

Step 2: Replace y with f(x)

f(x) = -3x + 4

In math, function f(x) is equal to the variable y.

3 0

3 years ago