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dalvyx [7]
2 years ago
8

Solving equations-variables on both sides!

Mathematics
1 answer:
scZoUnD [109]2 years ago
5 0

Simplifying

64 + -12w = 6w

Solving

64 + -12w = 6w

Solving for variable 'w'.

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

Add '-6w' to each side of the equation.

64 + -12w + -6w = 6w + -6w

Combine like terms: -12w + -6w = -18w

64 + -18w = 6w + -6w

Combine like terms: 6w + -6w = 0

64 + -18w = 0

Add '-64' to each side of the equation.

64 + -64 + -18w = 0 + -64

Combine like terms: 64 + -64 = 0

0 + -18w = 0 + -64

-18w = 0 + -64

Combine like terms: 0 + -64 = -64

-18w = -64

Divide each side by '-18'.

w = 3.555555556

Simplifying

w = 3.555555556

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Please help me! Need answer quick!
aksik [14]

Let h = height of triangle


h^2 + 12^2 = 15^2


h^2 + 144 = 225


h^2 = 225 - 144



h^2 = 81


sqrt{h^2} = sqrt{81}


h = 9 cm


For part B, we need to find surface area because it represents the perimeter of this 3-D figure. The formula needed is SA = B + LA.


1. First find the lateral area.


LA = perimeter of triangle • height


LA = ph


p = 15 + 15 + 24


p = 30 + 24


p = 54 cm


LA = (54)(9)


LA = 486 cm^2


2. We now find the base of each triangle. This is found by finding the area of each triangle and multiplying by 2.


A = (1/2)bh


A = (1/2)(24)(9)


A = 108 cm^2


A = 2•108 cm^2


A = 216 cm^2 = our B in the surface area formula.


SA = B + LA


SA = 216 cm^2 + 486 cm^2


SA = 702 cm^2


The amount of cardboard needed is 702 cm^2.






6 0
3 years ago
The figure shows △ABC . BD is the angle bisector of ∠ABC .
Misha Larkins [42]
From angle bisector theorem, we know that:

\dfrac{|AD|}{|DC|}=\dfrac{|BA|}{|BC|}\\\\\\\dfrac{|AD|}{|DC|}=\dfrac{8}{10}=\dfrac{4}{5}

Moreover:

|AD|+|DC|=6

so:

|DC|=6-|AD|

and

\dfrac{|AD|}{|DC|}=\dfrac{4}{5}\\\\\\\dfrac{|AD|}{6-|AD|}=\dfrac{4}{5}\qquad\qquad\text{cross multiplying}\\\\\\ 5\cdot|AD|=4\cdot\big(6-|AD|\big)\\\\5\cdot|AD|=24-4\cdot|AD|\\\\5\cdot|AD|+4\cdot|AD|=24\\\\9\cdot|AD|=24\qquad|:9\\\\\\|AD|=\dfrac{24}{9}=\boxed{\dfrac{8}{3}}

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Step-by-step explanation:

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3 0
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