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3 years ago

Find the quotient 81/93 divided by 31/45 divided by 76/96

Mathematics

2 answers:

Cloud [144]3 years ago

7 0

The answer: 1,5968
81/93= 0,87
31/45= 0,68888888
76/96= 0,7916

snow_tiger [21]3 years ago

3 0

(81/93)/(31/45)/(76/96)
(81/93)*(45/31)*(96/76)
(81*45*96)/(93*31*76)
349920/219108
29160/18259
That should be the quotient.

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Write an equation for the graph of each line.

emmasim [6.3K]

Answer:

5. y = 2x + 4

6. y = (-1/2)x - 2

Step-by-step explanation:

5. We want to find the slope-intercept form of this, which is y = mx + b, where m is the slope and b is the y-intercept.

Slope is change in y divided by change in x. Here, let's take two random points: (-2, 0) and (0, 4). Then we have:

m = (4 - 0) / (0 - (-2)) = 4 / 2 = 2

The slope is thus 2.

The y-intercept is where the line crosses the y-axis. We see it does so at the point (0, 4), so b = 4.

Our equation is thus: y = 2x + 4.

6. Again, let's find the slope. Pick any two points: (-4, 0) and (0, -2). The slope will be:

m = (-2 - 0) / (0 - (-4)) = -2 / 4 = -1/2

Now, look at the point (0, -2); that's where the line crosses the y-axis, so the y-intercept is b = -2.

Thus, the equation is: y = (-1/2)x - 2.

3 0

3 years ago

Read 2 more answers

Melanie has a piece of cloth 12 and 1/3 yards long. How many 3/4 yard-long pieces can be cut from the cloth?

Harrizon [31]

This is a division problem. First, get 12 1/3 into fraction form instead of mixed number form to make your life easier;
$12 \frac{1}{3} = \frac{36}{3} + \frac{1}{3} = \frac{37}{3} 
$
Now, divide the two fractions. Since this is fraction division, the reciprocal is flipped and the two fractions multiplied.
$\frac{37}{3} * \frac{4}{3} = \frac{148}{9} = 16 \frac{4}{9} 
$
The answer from the fraction division is 16 and four-ninths, but because you need a whole number as an answer,
the answer is 16 pieces.

8 0

3 years ago

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A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let x be the width and y the length of the rectangular field.

Let C the total cost of the rectangular field.

The side made of heavy duty material of length of x costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are x, y, y. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$