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3 years ago

Answer please for 15pts

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

5 0

Simplify the equation

√363 becomes 11 √3

3 √27 becomes 9 √3

11 √3 - 9 √3 = 2 √3

Explanation: Find the factors of each number

363 factors are 33, and 11

Find which one you can take the square root from which is 33 and that is how you get 11 √3

3 √27 can be simplified more because the factors of 27 are 9, 3 take the square root of 9. And multiply the leftover 3 with the outside number which is also 3. Then you get 9 √3

Now just subtract

11 √3 - 9 √3

= 2 √3

Sorry if this is confusing but I hope it helps !!

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A paper store sells wrapping paper rolls and bags. In the spring, they order a ratio of 3:7 in wrapping paper and bags. However,

34kurt

Answer:

250 bags

Step-by-step explanation:

Spring 3:7

150:x

3x = 1050

x = 350 bags in spring

Total order = 150 + 350 = 500

Holiday Season 5:5

(5+5)x = 10x = 500

x = 50

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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

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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

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3 years ago

Toby exercises 14 hours a week. John exercises 20% more than Toby and Jenny exercises two more hours than John. Which expression

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Answer: C. 18.8w

Step-by-step explanation:

Since Toby exercise 14hours a week, and John exercises 20% more than Toby

John increment in number of hours compared to Tobi will be;

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This shows John exercises 2.8hrs more than Tobi. Total number of hours exercised by John will become;

14+2.8 = 16.8hrs

Since Jenny exercises two more hours than John, Total number of hours exercised by Jenny will be;

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If Jenny exercise 18.8hrs in a week, it means she will exercise 18.8×w/1 in w weeks which gives 18.8w weeks.

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3 years ago

Read 2 more answers

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If 39 = (1 3/10)b, we could simplify this by writing 39 - (13/10)b.

Solve this for b by mult. both terms by (10/13):

(10*39)
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