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3 years ago

Factor the following expression: x2 + 7x - 30.

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

4 0

Answer:

(x-3)(x+10)

Step-by-step explanation:

larisa86 [58]3 years ago

4 0

X2+7x-30. Factor the following expression

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A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three s

makvit [3.9K]

Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

Area of Rectangular garden = $Length \times Breadth = xy$

We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft

So, cost of brick along length x = 20 x

On the other three sides by a metal fence costing $10/ft.

So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

Substitute the value of y from A

Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

$f'(x)=-\frac{2440}{x^2}+30$

Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

4 0

3 years ago

SOLVE THOSE TWO PROBLEMS PLEASEEE I REALLY NEED HELP

BabaBlast [244]

Answer:

I and G

Step-by-step explanation:

3 0

3 years ago

Help I will be marking brainliest!!!

guajiro [1.7K]

A. 45

B. 43

D. 90

#CarryOnLearning.

3 0

3 years ago

81 is 37.5% of what number?

laila [671]

Hi,

81 is 37.5% of 216.

"1. We assume, that the number 37.5 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 37.5, so we can write it down as 100%=37.5.

4. We know, that x% equals 81 of the output value, so we can write it down as x%=81.

5. Now we have two simple equations:

1) 100%=37.5

2) x%=81

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=37.5/81

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 81 is what percent of 37.5

100%/x%=37.5/81

(100/x)*x=(37.5/81)*x - we multiply both sides of the equation by x

100=0.46296296296296*x - we divide both sides of the equation by (0.46296296296296) to get x

100/0.46296296296296=x

216=x

x=216 "

Have a great day!

3 0

3 years ago

Vx4=4 what is the answer

Volgvan

Step-by-step explanation:

v=4÷4

v=1 Ans

Do by transposition

hope it helps

8 0

3 years ago