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3 years ago

14

A bag is filled with green and blue marbles. There are 97 marbles in the bag. If there are 9 more green marbles than blue marble

s, find the number of green marbles and the number of blue marbles in the bag.

1 answer:

Alenkasestr [34]3 years ago

3 0

Answer:

44 blue and 52 green

Step-by-step explanation:

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The amount of tax for each camera is $5.25 and the tax rate is 6%. Explain how the equation: (Original Cost)(Percent) = Tax Amou

Degger [83]

x(1.06)=5.25

The reason it is 1.06 is because it is the original cost plus tax. You can divide each side by 1.06 to get x roughly equals 4.95.

So $4.95 is roughly what the camera costs rounded to the nearest cent.

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4 years ago

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Which ordered pair is generated from the equation shown below? y = 3x + 2 A. (3, 11) B. (3, 9) C. (5, 15) D. (2, 4)

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Answer:

a

Step-by-step explanation:

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3 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

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3 years ago

Can someone help me with this problem

Alex_Xolod [135]

Answer:

<h2>A = 20</h2><h2>P = 6√10</h2>

Step-by-step explanation:

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

A(-3, 0) , B(3, 2)

$AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}$

A(-3, 0), D(-2, -3)

$AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}$

AB = CD and AD = BC

The area of a rectangle:

$A=(AB)(AD)$

Substitute:

$A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20$

The perimeter of a rectangle:

$P=2(AB+AD)$

Substitute:

$P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}$

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dalvyx [7]

First, we subtract 20% of the amount from x, so the initial cost of the furniture should be 80% of x or 0.80x. Then, due to the sales taxs, this amount should be added with 6.25% of itself. Such that,
A = 0.80x + 0.0625(0.80x)
= 0.85x

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