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3 years ago

The length of a rectangle is 2 times the width. If the perimeter is to be less than 96 meters. What are the possible

Mathematics

1 answer:

tiny-mole [99]3 years ago

7 0

Answer:

W>16

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle:

P = 2L+2W

L is the length of the rectangle

W is the width of the rectangle:

Given

P = 96m

If the length of a rectangle is 2 times the width, then L = 2W

Substitute into the formula:

Since the perimeter is less than 96m

96 < 2(2W)+2W

96 < 4W+2W

96 < 6W

Divide both sides by 6:

96/6 < 6W/6

16 < W

W>16

Hence the possible values of the width are all values greater than 16.

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There are 47 people attending a play at an outdoor theater. There are 11 groups of people sitting in groups of 3 or 5. How many

iVinArrow [24]

Answer:

The number of groups in 3 is 4 groups.
The number of groups in 5 is 7 groups.

Step-by-step explanation:

Let the number of groups in 3 ⇒ x

Let the number of groups in 5 ⇒ y

There are 11 groups. ⇒ x + y = 11 →(1)

There are 47 people. ⇒ 3x + 5y = 47 →(2)

Solve (1) and (2) to get x and y.

From (1) ⇒ y = 11 - x →(3)

By substitution from (3) at (2) with y

∴ 3x + 5(11-x) = 47

3x + 55 - 5x = 47

-2x = 47 - 55 = -8

∴ x = -8/-2 = 4

∴ y = 11 - x = 11 - 4 = 7

So, the number of groups in 3 is 4 groups.

the number of groups in 5 is 7 groups.

4 0

3 years ago

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2x+3=x+15 Help ASAP!

stiv31 [10]

Answer: x=12

2x + 3 = x + 15
- 3 - 3
————————
2x = x +12
- x - x
—————
x = 12

5 0

3 years ago

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...... trying to find domain, range rel max rel min end behavior inc intervals dec intervals. zeros..... I'm a mom trying to hel

Fiesta28 [93]

Answer:

The values are evaluated below.

Step-by-step explanation:

Given function is

$-x^4-7x^3-12x^2$

We have to find the domain, range, rel max, rel min, end behaviour, increasing or decreasing intervals and zeros of polynomial.

Domain:

The domain of a function is the set of all possible values of x for the given function.

Here domain is set of all real numbers R.

Range:

The range is the resulting y-values we get after substituting all the possible x-values.From the graph we see that

The range is $-\infty$

Relative maxima and minima of a function, are the largest and smallest value of the function on an entire domain of function.

Relative max of $-x^4-7x^3-12x^2$ is 0 at x=0

and $\frac{3}{512}(133\sqrt57-471)$ at $x=\frac{-21}{8}-\frac{\sqrt57}{8}$

Relative min is

$\frac{-3}{512}(471+133\sqrt57)$ at $x=\frac{-21}{8}+\frac{\sqrt57}{8}$

From the graph we see that

End behaviour is As $\\x->\infty, f(x)->-\infty\\x->-\infty, f(x)->-\infty\\$

Increasing intervals and decreasing intervals are

Increasing: $\frac{1}{8}(\sqrt57-21)$

Decreasing: $\frac{1}{8}(-21-\sqrt57)$

Zeroes are :

$-x^4-7x^3-12x^2=0$

⇒ $(-x^2)(x^2+7x+12)=0$

⇒ $(-x^2)(x+3)(x+4)=0$

Hence, zeroes are 0, 0, -3, -4

3 0

3 years ago

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A truck can travel 1200 miles on 80 gallons of gasoline. how far can it travel on 240 gallons of gasoline ? Show your work

pogonyaev

Answer:

3600 miles on 240 gal

Step-by-step explanation:

80 gal can go 1200

160 gal can go 2400

240 gal can go 3600

7 0

3 years ago

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Which value satisfies the inequality 5x + 7 ≤ 8x - 3 + 2x?

QveST [7]

Answer:

D) 2

Step-by-step explanation:

5x + 7 $\leq$ 8x -3 +2x

5x + 7 $\leq$ 10x - 3

7 + 3 $\leq$ 10x - 5x

10 $\leq$ 5x

2 $\leq$ x

x $\geq$ 2

8 0

3 years ago