All categories

3 years ago

What is the equation of the line that passes through the point (-5,5)and has a slope of -1

Mathematics

1 answer:

erastova [34]3 years ago

3 0

Answer:

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = -1

(-5, 5) ⇒ x₀ = -5, y₀ = 5

The point-slope form of the equation:

y - 5 = -1(x + 5)

So:

y - 5 = -x - 5 {add 5 to both sides}

y = -x ← the slope-intercept form of the equation

You might be interested in

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 monument casts a 40-foot shadow. Adam is 6 feet tall and casts a 5-foot shadow. How tall is the monument

Stolb23 [73]

This is a proportion problem. Let the monument me x feet tall.
40/x=5/6
Cross multiply:
240=5x
x=48 ft.
So the monument is 48 ft tall,

4 0

3 years ago

Read 2 more answers

Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t2 - 28t + 60, where t is the

8_murik_8 [283]

So, h(t) is how far is Daniel's head from the surface of the water, namely the surface itself is when the height is nill, so his head is at the surface and the height of it is just 0, thus h(t) = 0. Namely, what is "t" when h(t) is 0?

$\bf h(t)=-8t^2-28t+60\implies \stackrel{h(t)}{0}=-8t^2-28t+60
\\\\\\
0=-2t^2-7t+15\implies 2t^2+7t-15=0\implies (2t+3)(t-5)=0
\\\\\\
\begin{cases}
2t+3=0\implies 2t=-3\implies &t=-\frac{3}{2}\\\\
t-5=0\implies &\boxed{t=5}
\end{cases}$

clearly the seconds cannot be a negative unit, so is not -3/2.

6 0

3 years ago

charlene has eight more dollars than Megan. Together they have $86.00. Which equiation can be used to determine the amount of mo

Paul [167]

Answer:

Megan has 35.00 dollars.

Step-by-step explanation:

Divide 86.00 by 2 which equals 43.00. Next, minus 8 from the 43.00 and you will get what Megan has. Megan has 35.00 dollars.

I hope this helps!

8 0

2 years ago

The length of a page in a yearbook is 7 inches. The top margin is 1/2 inch, and the bottom margin in 3/4 inch. What is the lengt

Andrei [34K]

Can you be more specific?

7 0

3 years ago