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2 years ago

Find the value of x and m∠HKL.

Mathematics

1 answer:

frosja888 [35]2 years ago

5 0

Answer:

x = 25 degrees ∠HKL = 102 degrees

Step-by-step explanation:

The whole thing equals 180, since it is a straight angle

The value of HKL is 180 - 78 = 102

So that means 4x + 2 = 102

Subtract 2 from both sides:

4x = 100

Divide both sides by 4:

x = 25

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2 years ago

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Use the exterior angle theorem to find the value of x in the triangle below.

Arisa [49]

Answer:

Option A

Step-by-step explanation:

By using the definition of an exterior angle of a triangle,

"Measure of the exterior angle of a triangle is equal to the sum of measures of the opposite interior angles"

m∠STP = m∠SWT + m∠STW

Substitute the measures of the angles from the picture attached,

15x = (7x + 1) + (7x + 6)

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3 years ago

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

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

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
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[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

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Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
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2 years ago

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gregori [183]

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