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2 years ago

How do you do 4(x-3) you have to use distributive property to remove the parentheses..

Mathematics

1 answer:

Oksana_A [137]2 years ago

5 0

Answer:

4x -12

Step-by-step explanation:

Your question answers itself: you use the distributive property to remove the parentheses.

4(x -3) = 4(x) +4(-3) = 4x -12

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If the domain of the square root function f(x) is x less-than-or-equal-to 7, which statement must be true?

Damm [24]

Answer:

The x-term inside the radical has a negative coefficient.

Step-by-step explanation:

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2 years ago

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Explanation please will give brainliest.

Sonja [21]

Answer:

$AC = 28$

Step-by-step explanation:

Given

$AB = 16$

$BC = 12$

Required

Determine AC

Since A, B and C are collinear, then:

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So, we have:

$AC = 16 + 12$

$AC = 28$

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2 years ago

Can u help me do this

chubhunter [2.5K]

There will be 2 books left over if he fills each box.
7 · 4 = 28
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2 years ago

Is the result of Double 5 and add 1 the same as the result of Add 1 to 5; then double the result?

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2 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

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

The least cost of fencing for the rancher is $1200

Here’s the diagram:

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2 years ago