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3 years ago

What is the simplified form of 7(5x-6)

Mathematics

2 answers:

Likurg_2 [28]3 years ago

7 0

7(5x-6)

Distribute ....

7 * 5x = 35x

7 * 6 = 42

35x - 42 is the answer

valina [46]3 years ago

3 0

35x-30.....................

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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

What is the store paid $75 for a clarinet and sold it for $100 did the store mark up the price by 30% what the answer

nevsk [136]

Answer:

Mark up = 33.33%

Step-by-step explanation:

Given that:

buying price = $75

selling price = $100

First we will find the difference between two prices:

Difference = 100 - 75 = $25

We will find now that 25 is what percent of 75 so:

=25/75* 100

= 0.333333 * 100

= 33.33%

So the store marked the price by 33.33% instead of 30%

i hope it will help you!

3 0

3 years ago

77 is 0.7% of what number?

olga nikolaevna [1]

Answer:

0.7% of 77 = 0.54 0.7%

Step-by-step explanation:

hope this helps

7 0

4 years ago

What is the probability that a randomly number from 20 to 30 is divisible by 3 and then divisible by 12 after replacing first

tester [92]

Probability of divisibility by3=4/11
probability of divisibility by 12 =1/11
probability of divisibility by 12 and 3=4/11×1/11
answer is 4/121

7 0

3 years ago

What is four over five divided by two

Anastaziya [24]

This is going to be 4 remainders one.

4 0

4 years ago