All categories

3 years ago

Find the distance between this pair of parallel lines. These equations are in slope- intercept form.

Mathematics

1 answer:

garri49 [273]3 years ago

8 0

Distance is -2 my dude

You might be interested in

F(x)=2x^2+1 using the derivate definition

morpeh [17]

$\bf \stackrel{\textit{de} \textit{finition of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}}\\\\
-------------------------------\\\\
f(x)=2x^2+1\implies \lim\limits_{h\to 0}~\cfrac{[2(x+h)^2+1]~~-~~[2x^2+1]}{h}
\\\\\\
\lim\limits_{h\to 0}~\cfrac{[2(x^2+2xh+h^2)+1]~~-~~[2x^2+1]}{h}
\\\\\\
\lim\limits_{h\to 0}~\cfrac{[2x^2+4xh+2h^2+1]~~-~~[2x^2+1]}{h}$

$\bf \lim\limits_{h\to 0}~\cfrac{\underline{2x^2}+4xh+2h^2\underline{+1}~~~~\underline{-2x^2-1}}{h}\implies \lim\limits_{h\to 0}~\cfrac{4xh+2h^2}{h}
\\\\\\
\lim\limits_{h\to 0}~\cfrac{2\underline{h}(2x+h)}{\underline{h}}\implies \lim\limits_{h\to 0}~2(2x+h)\implies \lim\limits_{h\to 0}~2(2x+0)\implies 4x$

3 0

4 years ago

Part 2: Identify the vertex, focus, and directrix of each. Then sketch the graph.

Andre45 [30]

Answer: $\bold{1.\quad \text{Vertex}}:(-3,-6)\qquad \text{Focus}:\bigg(-3,-\dfrac{17}{4}\bigg)\qquad \text{Directrix}:y=-\dfrac{19}{4}$

2. Vertex: (-5, 4) Focus: (-6, 4) Directrix: x = -4

<u>Step-by-step explanation:</u>

The vertex form of a parabola is y = a(x - h)² + k or x = a(y - k)² + h

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet \quad a=\dfrac{1}{4p}$

1) y = (x + 3)² - 6 → a = 1 (h, k) = (-3, -6)

$a=\dfrac{1}{4p}\qquad \rightarrow \qquad 1=\dfrac{1}{4p} \qquad \rightarrow \qquad p=\dfrac{1}{4}\\\\\text{Focus = Vertex + p}\\\\.\qquad =\dfrac{-18}{4}+\dfrac{1}{4}\\\\.\qquad = -\dfrac{17}{4}\qquad \rightarrow \qquad \text{Focus}=\bigg(-3,-\dfrac{17}{4}\bigg)\\\\\\\text{Directrix: y = Vertex - p}\\\\.\qquad \quad y=\dfrac{-18}{4}-\dfrac{1}{4}\\\\.\qquad \quad y= -\dfrac{19}{4}$

****************************************************************************************

$2.\quad x=-\dfrac{1}{4}(y-4)^2-5\qquad \rightarrow \quad a=\dfrac{1}{4}\qquad (h, k)=(-5,4)$

$a=\dfrac{1}{4p}\qquad \rightarrow \qquad -\dfrac{1}{4}=\dfrac{1}{4p} \qquad \rightarrow \qquad p=-1\\\\\text{Focus = Vertex + p}\\\\.\qquad =-5+\ -1\\\\.\qquad = -6\qquad \rightarrow \qquad \text{Focus}=(-6,4)\\\\\\\text{Directrix: y = Vertex - p}\\\\.\qquad \quad y=-5+\ -1\\\\.\qquad \quad y= -4$

7 0

4 years ago

Autumn creates bracelets as a hobby and is planning to start selling them online for $10 per bracelet. Autumn has already sold 5

Slav-nsk [51]

Answer:

(24*10)+50=290

Step-by-step explanation:

7 0

3 years ago

8.) Out of 600 employees, only 270 are happy with their pay. What percent is this? (Please show your work.) *

Gnom [1K]

For this case we can raise a rule of three:

600 employees -------------> 100%

270 employees -------------> x

Where the variable "x" represents the percentage of employees who are satisfied with their salary. So, we have:

$x = \frac {270 * 100} {600}\\x = 45$

Thus, 45% of employees are satisfied with their salary.

Answer:

45%

5 0

4 years ago

Read 2 more answers

PLSSSSSS HELPPPPPPP FAST WILL GIVE BRAINLIEST

labwork [276]

Answer:

540

Step-by-step explanation:

This is a linear equation y=18x. I got this equation by dividing all of the y values by the x value and finding that 18 was the common answer. Then I plugged in 30 for x and solve for y.

7 0

3 years ago