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3 years ago

10

The length of a rectangle is 1 ft less than twice the width, and the area of the rectangle is 21 ft2 . Find the dimensions of th

e rectangle.

1 answer:

tatuchka [14]3 years ago

8 0

We normally think of 3x7, but the "7" is one more than 2 widths ... double the 3 and halve the 7 ==> 6 by 3.5 works ...

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X^2 + 18x + c = 25 +c

svet-max [94.6K]

Rearrange to: x^2 + 18x - 25 = 0
Then factorise (I like to do it by completing the square):
(x + 9)^2 -81 -25 = 0
(x + 9)^2 = 106
x + 9 = sqrt(106)
The sol'ns are:
x = -9 + and - sqrt(106)

7 0

3 years ago

3) How many<br>colognes may be packed in a carton measuring 72 cm by 45 cm by 36 cm?

hichkok12 [17]

Is there anymore info

8 0

2 years ago

Find the indicated limit, if it exists. limit of f of x as x approaches 0 where f of x equals 5x minus 8 when x is less than 0 a

vlabodo [156]

The limit does not exist. Why? Because the left hand limit DOES NOT equal the right hand limit. Let’s double check:

We could use -0.000001 to represent the left hand limit. This is less than 0. We plug in 5x - 8

5(-0.000001) - 8
-0.000005 - 8
-8.000005
If we would continue the limit (extend the zeros to infinity), we would get exactly
-8
That is our left hand limit.

Our right hand limit will be represented by 0.000001. This is greater than 0. We plug in abs(-4 - x)

abs(-4 - (0.000001))
abs(-4.000001)
4.000001
If we would continue the limit (extend the zeros to infinity), we would get exactly
4

4 does not equal -8, therefore

The limit does not exist

4 0

2 years ago

Allen's daily regular wage is P1,420. This coming Christmas, his boss is asking him to work for 14 hours. How much is his DAILY

VMariaS [17]

Using proportions, it is found that his DAILY RATE on that particular day is of Php 2,420 .

This question is solved by proportions, using a <em>rule of three.</em>

In a regular 8-hour day, Allen earns Php 1420. How much will he earn on a 14 hour day?

The <em>rule of three</em> is:

8 hours - Php 1420

14 hours - x

Applying cross multiplication:

$8x = 1420 \times 14$

$x = \frac{1420 \times 14}{8}$

$x = 2485$

The closest option is Php 2,420.

A similar problem is given at brainly.com/question/24372153

7 0

2 years ago

An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn

Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43 inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24, this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative value ( -49.7) so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0

2 years ago