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dybincka [34]
3 years ago
9

It takes a printer 2 1/2 min to print 24 black-and-white pages and 4 color pages. It takes the same printer 3 1/4 min to print 3

0 black-and-white pages and 6 color pages. Let b represent the time in minutes needed to print a black-and-white page and c represent the time in minutes needed to print a color page.The shown system represents the given problem.
24b+4c=2 1/2
30b+6c=31/4
Solve the system to complete the statement.

It takes the printer min to print a black–and–white page and min to print a color page.
Mathematics
2 answers:
Paul [167]3 years ago
4 0
Multiply the first equation by 1.5, to get:
(1.5)(24b + 4c) = 1.5(2.5)
36b + 6c = 3.75
Subtract the second equation from this:
6b = 1/2
b = 1/12
Substituting into the first equation:
24b + 4c = 2.5
24*(1/12) + 4c = 2.5
2 + 4c = 2.5
4c = 0.5
c = 1/8
Therefore, it takes 1/12 minute to print a black-and-white page, and 1/8 minute to print a colored page.
snow_tiger [21]3 years ago
3 0

Answer:

1/12

1/8

Step-by-step explanation:

E2020 :))))))

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A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amo
Blababa [14]

Answer:

<h2><em>2ft by 2ft by 1 ft</em></h2>

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

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Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

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width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

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Height of the cardboard is 1 ft

<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>

8 0
3 years ago
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Elza [17]

Answer: the answer is x<-4 so the correct answer choice would be D

Step-by-step explanation: Hope this helps :)

7 0
2 years ago
Read 2 more answers
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laila [671]

Answer:

The value of angle is 56.9°

Step-by-step explanation:

First, you have to find the length of hypotenuse using Pythagoras' Theorem, c² = a² + b² :

{c}^{2}  =  {a}^{2}  +  {b}^{2}

let \: a = 8.25 \\ let \: b = 6.45

{c}^{2}  =  {8.25}^{2}  +  {6.45}^{2}

{c}^{2}  = 68.0625 + 41.6025

{c}^{2}  = 109.665

c =  \sqrt{109.665}

c = 10.47cm \: (4s.f)

In order to find θ, you have to apply Sine Rule :

\sin(θ)  =  \frac{opposite}{adjacent}

let \: oppo. = 8.77 \\ let \: hypo. = 10.47

\sin(θ)  =  \frac{8.77}{10.47}

θ =  { \sin( \frac{8.77}{10.47} ) }^{ - 1}

θ = 56.9 \: (1d.p)

4 0
2 years ago
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