All categories

3 years ago

13y-2x=3 slope intercept

Mathematics

1 answer:

Fiesta28 [93]3 years ago

8 0

Answer:

World shown below!

Step-by-step explanation:

Slope-intercept form: y = mx + b

13y - 2x = 3

Add 2x to both sides;

13y = 2x + 3

Divide both sides by 13;

$y = \frac{2}{13}x+\frac{3}{13}$

You might be interested in

17x2 - 5x + 10x - 8x2

USPshnik [31]

Answer:

9x2+5x

Step-by-step explanation:

combine like terms

4 0

3 years ago

Can someone explain interval notations? Also, How do you figure them out?

sergeinik [125]

A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included.

For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8.

8 0

2 years ago

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

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

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

2 years ago

Caroline, Krutika and Natasha share some sweets in the ratio 1:2:4. Caroline gets 14 sweets.

lisov135 [29]

Answer:

98 sweets

Step-by-step explanation:

Caroline got 14 sweets, ratio for her was 1.

Krutika had twice the bigger ratio than her, which means you have to multipy Carolines' sweets by 2. -> 14*2= 28

And do the same thing for Natasha which gives us the result of 56. 14*4= 56

And finally, you add all of those together and get 14+28+56=98.

Hope I helped! :)

5 0

2 years ago

Could someone please help me with this question? 15 points.

polet [3.4K]

1a) f(x) = I x+2 I. This is a piece-wise graph ( V form)
x = 0 →f(x) =2 (intercept y-axis)
x = -2→f(x) = 0 (intercept x-axis)
x = -3→f(x) = 1 (don't forget this is in absolute numbers)
x = -4→f(x) = 2 (don't forget this is in absolute numbers)
Now you can graph the V graph

1b) Translation: x to shift (-3) units and y remains the same, then
f(x-3) = I x - 3 + 2 I = I x-1 I
the V graph will shift one unit to the right, keeping the same y. Proof:
f(x) = I x-1 I . Intercept x-axis when I x-1 I = 0, so x= 1

8 0

3 years ago