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3 years ago

How To Solve The Equation 3(x-6)=10x+3 ?

Mathematics

2 answers:

dem82 [27]3 years ago

6 0

$3(x-6)=10x+3\\
3x-18=10x+3\\
7x=-21\\
x=-3$

kykrilka [37]3 years ago

4 0

3(x-6)=10x+3

Expand the left side:

3x-18 = 10x + 3

Subtract 3x from each side:

-18 = 7x + 3

Subtract 3 from each side:

-21 = 7x

Divide each side by 7 :

-3 = x

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3 years ago

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3 years ago

You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

Charra [1.4K]

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

$h=\frac{504}{lw}$

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides $C_{s}$ = 3[2(l + w)h] = 6(l + w)h

$C_{s}$ = 3[2(l + w)h]

$C_{s}=6(l+w)(\frac{504}{lw} )$

Cost of the top and the bottom $C_{(t,p)}$ = 4(2lw) = 8lw

Total cost of the box C = $3024\frac{(l+w)}{lw}$ + 8lw

= $3024[\frac{1}{l}+\frac{1}{w}]$ + 8lw

To minimize the cost of the sides

$\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0$

$\frac{3024}{l^{2}}=8w$

$\frac{378}{l^{2}}=w$ ---------(1)

$\frac{dC}{dw}=3024(-w^{-2})+8l=0$

$\frac{3024}{w^{2}}=8l$

$\frac{378}{w^{2}}=l$

$w^{2}=\frac{378}{l}$ -------(2)

Now place the value of w from equation (1) to equation (2)

$(\frac{378}{l^{2}})^{2}=\frac{378}{l}$

$\frac{(378)^{2} }{l^{4}}=\frac{378}{l}$

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

$w^{2}=\frac{378}{7.23}$

$w^{2}=52.28$

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

$h=\frac{504}{(7.23)^{2}}$

h = 9.64 cm

6 0

4 years ago

Is 1/2 or 4/8 bigger???

Stels [109]

1/2 x 2/2 = 4/8

Therefore, 1/2 = 4/8

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3 years ago

A farmer ships oranges in wooden crates that each weigh 15 pounds when they are empty. The total weight of the crate when filled

scoundrel [369]

Answer:

Step-by-step explanation:

Let g represent the weight of the g oranges that were put in the crate in pounds.

From the information given,

The weight of the empty crate is 15 pounds. The total weight of the crate when filled with g oranges is 24.5 pounds.

Therefore, the equation that represents the relationship between the weight of the crate and the number of oranges it contains is

g + 15 = 24.5

g = 24.5 - 15

g = 9.5 pounds

The weight of the g oranges is 9.5 pounds

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3 years ago

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