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3 years ago

Determine whether the inequality is always, sometimes, or never true.

2 answers:

6 0

Treat this as an ordinary linear equation. Try to isolate x, as some value. Also remember the basic rules of inequalities: If you're dividing, or multiplying, by a negative, you flip the inequality.

Gemiola [76]3 years ago

3 0

You get −4x−18>−4x+9 now you can add 4x to both sides, which means all the x's are gone, and you get −18>9

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Find the area and the perimeter. 6.4 yd 5 yd 6.7 yd Area: Perimeter:

lesya [120]

Answer:

The area of the parallelogram is base*height, so the area would be 5*6.7=33.5yd^2

The perimeter of the shape would be 6.4+6.4+6.7+6.7=26.2yd

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3 years ago

Find an angle between 0° and 360° that is coterminal with 880°.

Minchanka [31]

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2 years ago

a) Saturn is 9.1 * 10^8 miles from the sun and earth is 9.3 * 10^7 miles from the sun. By what distance is one planet closer to

Sonbull [250]

Answer:

8.17 * 10^8

Step-by-step explanation:

Saturn is 9.1 * 10^8 miles from the sun, and earth is 9.3 * 10^7 miles from the sun. From this, we can see that Saturn is much farther from the sun than the earth.

To find the distance of one planet closer to the sun than the other planet, we can subtract 9.3 * 10^7 from 9.1 * 10^8.

Original expression: 9.1 * 10^8 - 9.3 * 10^7

Convert both sides to 10^7: 91 * 10^7 - 9.3 * 10^7

Subtract: 81.7 * 10^7

Simplify: 8.17 * 10^8

Let me know if this helps!

6 0

2 years ago

Is 4.70 greater than 4.07

Aleks [24]

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3 years ago

Read 2 more answers

A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

2 years ago