Mathematics, 15.01.2020 04:31 crystalclear99

Expand and simplify the equation 5(m+2)+9(n+4)

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Answer from: natajaeecarr

5.4

Step-by-step explanation:3 (m-2)-5=8-2 (m-4)

Simplifying

3(m + -2) + -5 = 8 + -2(m + -4)

Reorder the terms:

3(-2 + m) + -5 = 8 + -2(m + -4)

(-2 * 3 + m * 3) + -5 = 8 + -2(m + -4)

(-6 + 3m) + -5 = 8 + -2(m + -4)

Reorder the terms:

-6 + -5 + 3m = 8 + -2(m + -4)

Combine like terms: -6 + -5 = -11

-11 + 3m = 8 + -2(m + -4)

Reorder the terms:

-11 + 3m = 8 + -2(-4 + m)

-11 + 3m = 8 + (-4 * -2 + m * -2)

-11 + 3m = 8 + (8 + -2m)

Combine like terms: 8 + 8 = 16

-11 + 3m = 16 + -2m

Solving

-11 + 3m = 16 + -2m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '2m' to each side of the equation.

-11 + 3m + 2m = 16 + -2m + 2m

Combine like terms: 3m + 2m = 5m

-11 + 5m = 16 + -2m + 2m

Combine like terms: -2m + 2m = 0

-11 + 5m = 16 + 0

-11 + 5m = 16

Add '11' to each side of the equation.

-11 + 11 + 5m = 16 + 11

Combine like terms: -11 + 11 = 0

0 + 5m = 16 + 11

5m = 16 + 11

Combine like terms: 16 + 11 = 27

5m = 27

Divide each side by '5'.

m = 5.4

Simplifying

m = 5.4

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where, $a = \frac{\sum y \sum x^2 - \sum x\sum xy}{n\sum x^2 - (\sum x)^2}$