PLEASE HELP ME AND EXPLAIN.

The geography of New England made success of

creativ13 [48]

Hills, mountains and rivers.

3 0

3 years ago

Does the given equation of line form parallel lines or not

malfutka [58]

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2$

$k:x+4y=10\ \ \ |-x\\\\4y=-x+10\ \ \ \ |:4\\\\y=-\dfrac{1}{4}x+\dfrac{10}{4}\to m_1=-\dfrac{1}{4}\\\\l:3x-2y=5\ \ \ \ |-3x\\\\-2y=-3x+5\ \ \ \ |:(-2)\\\\y=\dfrac{3}{2}x-\dfrac{5}{2}\to m_2=\dfrac{3}{2}$

$m_1\neq m_2\to\text{ no parallel}\\\\m_1\cdot m_2=-\dfrac{1}{4}\cdot\dfrac{3}{2}\neq-1\to\text{ no perpendicular}$

Answer: NOT PARALLEL

5 0

3 years ago

Click the picture :)

yarga [219]

Functions are used to represent equations and graphs

The superhero will be able to leap over the building
The support should be placed 48 feet from the edge
Joe will not be able to stand up in the igloo
Joe will be able to lay down in the igloo

<h3>Question 13: How to determine if the superhero will make it to the building</h3>

The function is given as:

$f(x) = -16x^2 + 200x$

Differentiate the function

$f'(x) = -32x + 200$

Set to 0

$-32x + 200 =0$

So, we have:

$-32x =-200$

Solve for x

$x =6.25$

Calculate f(6.25)

$f(x) = -16x^2 + 200x$

$f(6.25) = -16 * 6.25^2 + 200 * 6.25$

$f(6.25) = 625$

The above means that, the superhero reached a height of 625 feet.

625 is greater than 612.

Hence, the superhero will be able to leap over the building

<h3>Question 14: How to determine the distance from the edge</h3>

The function is given as:

$f(x) = -0.03x^2 + 2.4x$

Differentiate

$f'(x) = -0.06x + 2.4$

Set to 0

$-0.06x + 2.4 = 0$

Subtract 2.4 from both sides

$-0.06x = -2.4$

Solve for x

$x = 40$

Calculate f(40)

$f(x) = -0.03x^2 + 2.4x$

$f(40) = -0.03*40^2 + 2.4*40$

$f(40) = 48$

This means that, the support should be placed 48 feet from the edge

<h3>Question 15: Will Joe be able to stand up?</h3>

In (14), the maximum height is 48 feet.

Joe's height (70 feet) is greater than 48.

This means that, Joe will not be able to stand up in the igloo

<h3>Question 15: Will Joe be able to lay down?</h3>

In (14), the midpoint is 40 feet.

This means that the length of the igloo is 80 feet (i.e. 2 * 40 feet)

Joe's height (70 feet) is less than 80.

This means that, Joe will be able to lay down in the igloo

Read more about quadratic functions at:

brainly.com/question/8952707

7 0

2 years ago

Which order pair satisfies 3x-y=8 and x+y=2

GrogVix [38]

Answer:

(2.5, -1/2)

Step-by-step explanation:

Solve the system by substitution 3x-y=8 and x+y=2

lets look at x + y =2

rewrite it as x = 2 - y

so now x is 2- y so we can substitute it in

3(2-y) -y = 8 this is the equation rewritten with x as 2-y, now solve for y

6 -3y - y =8

-6 -6

-4y = 2

/-4 /-4

y = -1/2

so now remember x = 2 - y

use our new y

x = 2 - (-1/2)

x = 2 + 1/2

x = 2 and 1/5 or 2.5

7 0

3 years ago

A game room has a perimeter of 70 ft. The length is 5 more than twice the width. How many feet squared of new carpeting should b

Shkiper50 [21]

Answer:

<em>A = 250 square ft</em>

Step-by-step explanation:

<u>Equations</u>

Let's call:

x = width of the game room

The length is 5 more than twice the width, thus:

2x+5 = length of the game room

The perimeter of a rectangle is twice the sum of the width and the length:

P = 2( x + 2x + 5 )

And the perimeter is 70 ft:

2( x + 2x + 5 ) = 70

Operating:

2( 3x + 5 ) = 70

Dividing by 2:

3x + 5 = 35

Subtracting 5:

3x = 30

Dividing by 3:

x = 30 / 3

x = 10

The width is 10 ft and the length is 2(10)+5=25 ft

The area of the game room is:

A = 10 ft * 25 ft

A = 250 square ft

4 0

3 years ago