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3 years ago

What is the point-slope form with the slope -6 and the line through (1,-4)?

Mathematics

2 answers:

lakkis [162]3 years ago

8 0

Answer:

y-(-4)=-6(x-1)

its is either (x-1), or (x+1). Im not sure on the last part

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

ladessa [460]3 years ago

4 0

Plug those numbers into y - y1 = a(x - x1)

so you would get y-(-4) = -6(x - 1) (this is your point-slope form)

simplify to get y + 4 = -6x + 6

simplify more to get y = -6x + 2

then 6x + y =2 (this is your standard form)

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A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t

Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be $F=L+2W$ .

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

$LW=80,000...(1)$

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be $C=20L+5(2W)\Rightarrow 20L+10W$ .

From equation (1), we will get:

$L=\frac{80,000}{W}$

Upon substituting this value in cost equation, we will get:

$C=20(\frac{80,000}{W})+10W$

$C=\frac{1600,000}{W}+10W$

$C=1600,000W^{-1}+10W$

To minimize the cost, we need to find critical points of the the derivative of cost function as:

$C'=-1600,000W^{-2}+10$

$-1600,000W^{-2}+10=0$

$-1600,000W^{-2}=-10$

$-\frac{1600,000}{W^2}=-10$

$-10W^2=-1,600,000$

$W^2=160,000$

$\sqrt{W^2}=\pm\sqrt{160,000}$

$W=\pm 400$

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

$C''=-2(-1600,000)W^{-3}$

$C''=3200,000W^{-3}$

$C''=\frac{3200,000}{W^3}$

Now, we will substitute $W=400$ in 2nd derivative as:

$C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05$

Since 2nd derivative is positive at $W=400$ , therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting $W=400$ in $L=\frac{80,000}{W}$ , we will get:

$L=\frac{80,000}{400}\\\\L=200$

Therefore, the side parallel to the river will be 200 feet.

4 0

3 years ago

a fountain in a pond has a pump that recirculates 75 gallons of water in 1/4 of an hour.express this rate as a unit rate in gall

olga55 [171]

So if in 1/4 of an hour 75 gallons are pumped you would multiply 75 by four which will give you 300. This means 300 gallons are pumped in an hour

6 0

3 years ago

In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Ja

kipiarov [429]

Answer:

Step-by-step explanation:

the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.

first lets start with shirts and pants, number of unique combinations are,

(for each shirt there are 4 different pant combinations) = $(3)(4)$

=12

similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.

thus, total number of combinations are=

$(12)(2)(2)$

= 48

8 0

3 years ago

If D is the midpoint of CE, CD= 9x-7, and DE= 3x+17, find CE

tatuchka [14]

Hello!

Since D is the midpoint and the two equations are and both sides of point D the equations equal each other

9x - 7 = 3x + 17

Now you solve it algebraically

Add 7 to both sides

9x = 3x + 24

Subtract 3x from both sides

6x = 24

Divide both sides by 6

x = 4

Now we put this into both equations and add them

9(4) - 7 = 29
3(4) + 17 = 29

29 + 29 = 58

The answer is 58 units

Hope this helps!

3 0

2 years ago

Ross is buying hats for his baseball team. Each package contains 4 hats. Generate the set of ordered pairs for the ratio relatio

Katena32 [7]

He has 13 and 1 graphs

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3 years ago