The question is Mrs.Elliot's room area (including the storage area)= ???

X-2y=18 2x+y=6 parallel perpendicular or neither

sergey [27]

<h3>Therefore they are perpendicular.</h3>

Step-by-step explanation:

A equation of line is

y =mx +c

Here the slope of the line is m.

Given equations are

x - 2y = 18

⇔-2y = -x +18

$\Leftrightarrow y =\frac{1}{2} x -9$ ............(1)

and 2x + y = 6

⇔y = -2x +6 ............(2)

Therefore the slope of equation (1) is $(m_1)$ = $\frac{1}{2}$

Therefore the slope of equation (2) is $(m_2)$ = -2

If two lines are perpendicular, when we multiply their slope we get -1.

therefore,

$m_1. m_2$ = $\frac{1}{2}$ . (-2) = -1

Therefore they are perpendicular.

4 0

3 years ago

Solve 11x + 2 = 68.

lys-0071 [83]

11x+2=68
-2 -2

11x=66
/11 /11

X=6

4 0

3 years ago

Read 2 more answers

F(x) = e^-x . Find the equation of the tangent to f(x) at x=-1

natima [27]

Answer:

The equation of the tangent line is given by the following equation:

$\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)$

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

$\displaystylef(x) = e^{-x} \\x = -1$

Step 2: Differentiate

[Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
$\displaystyle f'(x) = e^{-x}(-x)'$
[Derivative] Rewrite [Derivative Rule - Multiplied Constant]:
$\displaystyle f'(x) = -e^{-x}(x)'$
[Derivative] Apply Derivative Rule [Derivative Rule - Basic Power Rule]:
$\displaystyle f'(x) = -e^{-x}$

Step 3: Find Tangent Slope

[Derivative] Substitute in x = 1:
$\displaystyle f'(1) = -e^{-1}$
Rewrite:
$\displaystyle f'(1) = \frac{-1}{e}$

∴ the slope of the tangent line is equal to $\displaystyle \frac{-1}{e}$ .

Step 4: Find Equation

[Function] Substitute in x = 1:
$\displaystyle f(1) = e^{-1}$
Rewrite:
$\displaystyle f(1) = \frac{1}{e}$

∴ our point is equal to $\displaystyle \bigg( 1, \frac{1}{e} \bigg)$ .

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

$\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }$

∴ we have our final answer.

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Learn more about derivatives: brainly.com/question/27163229

Learn more about calculus: brainly.com/question/23558817

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

3 0

2 years ago

A circular mirror has the diameter of 12 inches. what is the area in square inches?

nika2105 [10]

Hello!

To find the area of a circle you do $\pi r^{2}$

Where r stands for radius.

The radius is just half the diameter

So you put that into a calculator and get 113.1 $in^{2}$

Hope this helps!

5 0

3 years ago

The number of men in a tour group is 15 times the number of women. If there are 48 people in the group, how many are men?

Nata [24]

M + w = 48
m = 15w

15w + w = 48
16w = 48
w = 48/16
w = 3

m = 15w
m = 15(3)
m = 45 <==== there r 45 men

8 0

3 years ago