All categories

3 years ago

How to put -7/9 and -4/9 and 1/9 and 1/2 on a number line from least to greatest

Mathematics

2 answers:

Dmitry_Shevchenko [17]3 years ago

5 0

Answer:

-7/9, -4/9, 1/9, 1/2

There's no change as this list is already from smallest to largest

==========================================================

Explanation:

We can get each denominator to 18 as this is the LCD (lowest common denominator)

-7/9 = -14/18 ... multiply top and bottom by 2

-4/9 = -8/18 ... multiply top and bottom by 2

1/9 = 2/18 ... multiply top and bottom by 2

1/2 = 9/18 ... multiply top and bottom by 9

We now have to sort this list {-14/18, -8/18, 2/18, 9/18}

Which is the same as sorting {-14, -8, 2, 9} since we can focus solely on the numerators. This only applies when the denominators are the same.

The list {-14, -8, 2, 9} is already sorted from smallest to largest. Think of a number line. We would have -14 as the left most value, then -8 is next, followed by 2 and then 9.

So the original list of fractions {-7/9, -4/9, 1/9, 1/2} is already sorted from smallest to largest.

--------------

An alternative is to use your calculator to see that

-7/9 = -0.78 approximately

-4/9 = -0.44 approximately

1/9 = 0.11 approximately

1/2 = 0.50

The order from least to greatest is

-0.78, -0.44, 0.11, 0.50

The -0.78 is smaller than -0.44 since its further away from 0

So the order would be

-7/9, -4/9, 1/9, 1/2

and there's no change from the original order your teacher gave you.

WARRIOR [948]3 years ago

4 0

Step-by-step explanation:

Take the LCM of the denominators:

=> LCM = 18

=> -7/9 x 2/2 = -14/18

=> -4/9 x 2/2 = -8/18

=> 1/9 x 2/2 = 2/18

=> 1/2 x 9/9 = 9/18

When the number is negative, the greater the number, the smaller it is.

So, -14 is smaller than -8.

< = smaller than

=> -14/18 < -8/18 < 2/18 < 9/18

=> -7/9 < -4/9 < 1/9 < 1/2

You might be interested in

The sum of 5 consecutive numbers is -5. What is the largest out of the numbers?

xxTIMURxx [149]

We can say that x is the largest number.

So the sum is x + (x - 1) + (x - 2) + (x - 3) + (x - 4) = -5

Now solve for x:

x + x + x + x + x - 1 - 2 - 3 - 4 = -5

5x - 10 = -5

5x = 5

x = 1

So the largest number is 1.

Check: 1 + 0 + -1 + -2 + -3 = -2 + -3 = -5 so 1 is correct.

3 0

3 years ago

How does the value of log Subscript 2 Baseline 100 compare with the value of Log Subscript 6 Baseline 20?.

attashe74 [19]

You can use the change of base formula to get

$\log_2(100) = \frac{\log(100)}{\log(2)} \approx 6.643856$

and also

$\log_6(20) = \frac{\log(20)}{\log(6)} \approx 1.671950$

In general, the change of base formula is

$\log_b(x) = \frac{\log(x)}{\log(b)}$

8 0

2 years ago

(6.253•10^-2)(7.112x10^3) in scientific notation

zlopas [31]

Answer:

4.4471336 * 10^2.

Step-by-step explanation:

(6.253•10^-2)(7.112x10^3)

= 6.253*7.112 * 10^-2*10^3

= 44.471336 * 10^1

= 4.4471336 * 10^2.

7 0

3 years ago

What is the value of x, if the area of ΔABC is 12√3 square cm.

lana [24]

Answer:

What is the value of x, if the area of ΔABC is 12√3 square cm ...

Step-by-step explanation:

maybe this link helps you

6 0

3 years ago

A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru

Viktor [21]

Answer:

1) $S = 2\cdot w\cdot l - 8\cdot x^{2}$ , 2) The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$ , 3) $S = 176\,in^{2}$ , 4) $x \approx 4.528\,in$ , 5) $S = 164.830\,in^{2}$

Step-by-step explanation:

1) The function of the box is:

$S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)$

$S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w$

$S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x$

$S = 2\cdot w\cdot l - 8\cdot x^{2}$

2) The maximum cutout is:

$2\cdot w \cdot l - 8\cdot x^{2} = 0$

$w\cdot l - 4\cdot x^{2} = 0$

$4\cdot x^{2} = w\cdot l$

$x = \frac{\sqrt{w\cdot l}}{2}$

The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$

3) The surface area when a 1'' x 1'' square is cut out is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}$

$S = 176\,in^{2}$

4) The size is found by solving the following second-order polynomial:

$20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}$

$20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}$

$8\cdot x^{2} - 164\,in^{2} = 0$

$x \approx 4.528\,in$

5) The equation of the box volume is:

$V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x$

$V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x$

$V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}$

$V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}$

$V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}$

The first derivative of the function is:

$V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}$

The critical points are determined by equalizing the derivative to zero:

$12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0$

$x_{1} \approx 4.952\,in$

$x_{2}\approx 1.548\,in$

The second derivative is found afterwards:

$V'' = 24\cdot x - 78\,in$

After evaluating each critical point, it follows that $x_{1}$ is an absolute minimum and $x_{2}$ is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

$x \approx 1.548\,in$

The surface area of the box is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}$

$S = 164.830\,in^{2}$

4 0

2 years ago