Someone please help me out

Write an equation of the line that passes through (2,7) and is parallel to the line shown ( please help !! )

Anna007 [38]

Answer:

$y=2x+3$

Step-by-step explanation:

We will first need to determine the slope of the line shown.

We know that it passes through the two points (-2, -2) and (1, 4).

Thus, we can use the slope formula to find the slope between the two points:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Let (-2, -2) be (x₁, y₁) and let (1, 4) be (x₂, y₂). Substitute:

$\displaystyle m=\frac{4-(-2)}{1-(-2)}=\frac{6}{3}=2$

Hence, the slope of the original line was 2.

Since we want the new line to be parallel, the slope of the new line must also be 2.

We know that the slope is 2 and it passes through the point (2, 7).

So, we can use the point-slope form:

$y-y_1=m(x-x_1)$

We will substitute 2 for m. We will also let (2, 7) be (x₁, y₁). Substitute:

$y-7=2(x-2)$

Solve for y. Distribute the right:

$y-7=2x-4$

Add 7 to both sides. Hence, our equation is:

$y=2x+3$

6 0

2 years ago

What is the lenght of the distance between the chair and the end table ?

pentagon [3]

check the picture below.

8 0

3 years ago

Suppose total benefits and total costs are given by b(y) = 100y − 8y2 and c(y) = 10y2. what is the maximum level of net benefits

olga nikolaevna [1]

Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).

B(y)=b-c
B(y)=100y-18y²

Now that we have a net benefits function we need find it's derivate with respect to y.

$\frac{dB(y)}{dy} =100-36y$

Now we must find at which point this function is equal to zero.

0=100-36y
36y=100
y=2.8

Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.

B(2.8)=100(2.8)-18(2.8)²=138.88≈139.

One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.

3 0

3 years ago

PLS HURRY! WILL MARK BRAINLIEST

defon

Answer:

A=941.33 square inches.

Step-by-step explanation:

The total area of the banner is the sum of the areas of the square and the semicircle (half cricle) The side length of the square is 26 inches and the radius of the semicircle is 13 inches (half of the dimeter) so: A=Asquare+Asemicircle A=(s2)+(12)πr2 A=262+12(3.14)(13)2 A=676+265.33

5 0

2 years ago

Help me substitution method define variables

Rina8888 [55]

$\left \{ {{S=14+L} (I) \atop {S+L=124}(II)} \right.$

Substitute (I) into (II), we have:
 $S+L=124$
$(14+L)+L=124$
$14 + 2L = 124$
$2L = 124 - 14$
$2L = 110$
$L = \frac{110}{2}$
$\boxed{L = 55}$

Replace (II) in (I), we have:
 $S=14+L$
$S = 14+ 55$
$\boxed{S = 69}$

Answer:
each student sell:
Lori = 55 pizzas
Steve = 69 pizzas

7 0

3 years ago