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ioda
2 years ago
8

PLEASE HELP!! WILL GIVE BRANLIEST

Mathematics
1 answer:
stepladder [879]2 years ago
3 0
The equation for this is ; y=1/2(x+4)^2-1

Explain

we use the vertex form
y=a(x-h)^2+k where the vertex is (h,k)

Select ( -4,-1)


Where h=-4
K=-1


y=a(x-h)^2+k

We get

y=a(x-(-4))^2+ -1

Y= a(x+4)^2+-1

Now replace to 0,7

7=a(0+4)^2-1

7=a(4)^2-1

7=16a-1


So now

7=16a-1
7+1=16a

8=16a
a=8/16
That should 1/2

So y=a(x+4)^2 -1
Should become

Y=1/2(x+4)^2 -1



Do you have any doubts now !
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A fence must be built to enclose a rectangular area of 20,000 ft^2. Fencing material costs $4 per foot for the two sides facing
Marysya12 [62]

The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

  • A fence must be built to enclose a rectangular area of 20,000 ft²
  • Fencing material costs $4 per foot for the two sides facing north and south and ​$8 per foot for the other two sides

We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides  is y feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle = y feet

∵ The rectangular area is 20,000 ft²

- Area of a rectangle = length × width

∴ x × y = 20,000

- Divide both sides by x to find y in terms of x

∴ y=\frac{20,000}{x}

The fence's length is equal to the perimeter of the rectangular area

∵ Perimeter of the rectangle = 2 length + 2 width

∴ Perimeter of the rectangle = 2x + 2y

∵ Fencing material costs $4 per foot for the two sides facing

   North and South

∴ x costs $4 per foot

∵ The cost of the other two sides is $8 per foot

∴ y costs $8 per feet

The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y

∵ The cost of the fence (C) = 4(2x) + 8(2y)

∴ C = 8x + 16y

- Substitute y by its value above

∴ C=8x+16(\frac{20,000}{x})

∴ C=8x+\frac{320,000}{x}

To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x

∵ \frac{320,000}{x} can be written as 320,000x^{-1}

∴ C=8x+320,000x^{-1}

∵ \frac{dC}{dx}=8(1)x^{1-1}+320,000(-1)x^{-1-1}

∴ \frac{dC}{dx}=8-320,000x^{-2}

- Equate \frac{dC}{dx} by zero

∴ 8-320,000x^{-2}=0

∵ -320,000x^{-2}=-\frac{320,000}{x^{2}}

∴ 8-\frac{320,000}{x^{2}}=0

- Subtract 8 from both sides

∴ -\frac{320,000}{x^{2}}=-8

- Multiply both sides by x²

∴ - 320,000 = - 8x²

- Divide both sides by -8

∴ 40,000 = x²

- Take √  for both sides

∴ 200 = x

Substitute x in the equation of C to find the least cost of fence

∵ C=8(200)+\frac{320,000}{(200)}

∴ C = 1600 + 1600

∴ C = 3200

The cost of the least expensive fence is $3200

Learn more:

You can learn more about the differentiation in brainly.com/question/4279146

#LearnwithBrainly

5 0
3 years ago
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JulsSmile [24]

Answer: 30.048

Try a calculator, it can help a lot!

6 0
3 years ago
A triangle has side lengths of (8d – 3) centimeters, (6d + 2) centimeters, and
alisha [4.7K]

The perimeter of a triangle is the sum of its side lengths.

The perimeter of the triangle is: 14d + 7f +7

<u>The sides of the triangle are:</u>

Side 1 = (8d - 3) cm

Side 2 = (6d + 2) cm

Side 3 = (7f + 8) cm

The perimeter (P) is calculated as:

P = Side 1 + Side 2 + Side 3

So, we have:

P = (8d - 3) + (6d + 2) + (7f + 8)

Remove brackets

P = 8d - 3 + 6d + 2 + 7f + 8

Collect like terms

P = 8d  + 6d + 7f - 3 + 2 + 8

P = 14d + 7f +7

Hence, the perimeter of the triangle is: 14d + 7f +7

Read more about perimeters at:

brainly.com/question/6465134

3 0
3 years ago
Jason rolls a fair number cube labeled 1 through 6, and then he flips a coin. What is the probability that he rolls a 3 and flip
qwelly [4]

The answer is 1/12

The chance of getting a 3 on a six-sided dice is 1/6

The possibility of getting heads on a two-sided coin is 1/2

6 multiplied by 2 is 12

1 multiplied by 1 is 1

Hope it helps!

3 0
3 years ago
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I need to solve for x, help please.
BaLLatris [955]

Answer:

x = 52   i hope this helps!   :)

Step-by-step explanation:

so first you gotta realize that every triangle has an interior angle measurement sum of 180 degrees

so we are given 3 angles   74 degrees  x + 2  and x

we now are going to put this into an equation   74 + x + 2 + x = 180

now lets combine like terms to get   76 + 2x = 180

then we are going to subtract the 76 from both sides   2x = 104

now lets divide both sides by 2   x = 52

so x = 52

we can plug in the value of x into both of the other equations to find the angle measurement

52 degrees

52 + 2 = 54 degrees

and then we have 74 degrees

add the 52, 54, and the 74 to make sure it is equal to 180 degrees

106 + 74 = 180

so yes, x does indeed equal 52 degrees

3 0
3 years ago
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