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4 years ago

Given y = -7x + 7, the y-intercept is

Mathematics

2 answers:

Sidana [21]4 years ago

5 0

Answer:

The y-intercept is 7

Step-by-step explanation:

y = slope(x) + y-intercept

Ede4ka [16]4 years ago

3 0

The y-intercept is 7

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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

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

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

3 years ago

How many solutions will there be to the following equation?16x^2=100

djverab [1.8K]

Answer:

2 solutions; x=2.5 x=-25

Step-by-step explanation:

16x^2 = 100

x^2 = 100/16

x^2 = 6.25

x = (+-) sqrt 6.25

x = (+-) 2.5

4 0

3 years ago

Laketown had 215 inches of snowfall last year, but only 155 inches this year. What was the percent decrease in snowfall for Lake

skelet666 [1.2K]

Okay, so FIRST you would subtract 215 - 155, which is 60, and THEN divide it by 215, so 60 divided by 215 = 0.27, and rounded that is 0.28, then you move the decimal two places to the right to make it a percentage so your answer would be A., 28%
I hope I helped! =D

8 0

3 years ago

Read 2 more answers

PLEASE HELP. I NEED THIS ASAP.

padilas [110]

Don’t know sorry I need point

6 0

3 years ago

Read 2 more answers

Andrew and Sam start counting from 150 to 200 including. Andrew counts by fives, and Sam counts by threes. What is the ratio of

Agata [3.3K]

Answer: