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3 years ago

Please help!!!!!Solve the equation 5(2y - 1) - 2(3y)= 1

Mathematics

1 answer:

-Dominant- [34]3 years ago

5 0

Answer:

y = 3/2

Step-by-step explanation:

5(2y - 1) - 2(3y) = 1

First we use distributive property:

10y - 5 - 6y = 1

because 5 × 2y = 10y

and -2 × 3y = -6y

Now we combine the like terms:

4y -5 = 1

because 10y - 6y = 4y

Now we have to send the -5 to the other side. (when we send it to the other side it becomes positive because right now it is negative)

4y = 1 + 5

Again we combine the like terms:

4y = 6

(because 5 + 1 = 6)

Now we have to send the 4 to the other side because we need to get the y value. (when we send it to the other sidr it will be divided)

y = 6/4

and we simplify:

y = 3/2

And we cannot simplify or do anything else. So that is the answer.

Hope that helped!

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Write an expression for the 12th partial sum of the series 3/2+7/3+19/6+... using summation notation

lapo4ka [179]

Answer:

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=73$

Step-by-step explanation:

$First\ term\ of\ the\ series(a_1)=\frac{3}{2}\\\\Second\ term\ of\ the\ series(a_2)=\frac{7}{3}\\\\Third\ term\ of\ the\ series(a_3)=\frac{19}{6}\\\\a_2-a_1=\frac{7}{3}-\frac{3}{2}=\frac{5}{6}\\\\a_3-a_2=\frac{19}{6}-\frac{7}{3}=\frac{5}{6}\\\\Hence\ it\ is\ an\ Arithmetic\ Series\ with\ first\ term=\frac{3}{2}\ and\ constant\ difference=\frac{5}{6}$

$a_1=\frac{3}{2}+0\times \frac{5}{6}\\\\a_2=\frac{3}{2}+1\times \frac{5}{6}\\\\a_3=\frac{3}{2}+2\times \frac{5}{6}\\\\.\\.\\.\\a_n=\frac{3}{2}+(n-1)\times \frac{5}{6}\\\\S_n=a_1+a_2+a_3+......+a_n\\\\S_n=(\frac{3}{2}+0\times \frac{5}{6})+(\frac{3}{2}+1\times \frac{5}{6})+(\frac{3}{2}+2\times \frac{5}{6})+....+(\frac{3}{2}+[n-1]\times \frac{5}{6})\\\\S_n=\sum_{i=1}^n [\frac{3}{2}+(i-1)\times \frac{5}{6}]\\\\S_n=(\frac{3}{2}+\frac{3}{2}+\frac{3}{2}+...n\ times)+\frac{5}{6}(1+2+3+4+...+(n-1))\\\\$

$S_n=\frac{3}{2}\times n+\frac{5}{6}\times \frac{n(n-1)}{2}\\\\$

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=\frac{3}{2}\times 12+\frac{5}{6}\times \frac{(12)(12-1)}{2}\\\\S_{12}=18+55\\\\S_{12}=73$

5 0

3 years ago

You are standing 15 ft away from a tree. The angle of elevation from the groumd where you are standing to the top of a tree is 5

Allushta [10]

Answer:

the height of the tree is 19.2 ft

Step-by-step explanation:

Given;

distance from the foot of the tree, d = 15 ft

angle of elevation; θ = 52°

let the height of the tree = h

Make a sketch of the problem as follows;

↑

↑ h

52°---------------------

15 ft

If completed to form a right triangle by adding the hypotenuse side, we can calculate the height of the tree as follows;

$tan (52)= \frac{h}{15} \\\\h = 15 \times tan(52)\\\\h = 19.2 \ ft$

Therefore, the height of the tree is 19.2 ft

4 0

2 years ago

Please help!!!!!Solve the equation 5(2y - 1) - 2(3y)= 1​

Please help!!!!!Solve the equation 5(2y - 1) - 2(3y)= 1