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3 years ago

Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle.

Mathematics

1 answer:

jenyasd209 [6]3 years ago

7 0

Answer:

The angles are 165 and 15

Step-by-step explanation:

Supplementary angles whose sum is 180°

Let A and B be the two supplementary angles.

Let A be the larger angle and B the smaller angle.

From the question, we were told that the large angle (A) is 15 more than 10 times the smaller angle ie

A = 15 + 10B

We can solve for the value of A and B by doing the following:

A + B = 180

But A = 15 + 10B

15 + 10B + B = 180

Collect like terms

10B + B = 180 — 15

11B = 165

Divide both side by the coefficient of B i.e 11

B = 165/11

B = 15

A = 15 + 10B

A = 15 + 10(15)

A = 15 + 150

A = 165

The angles are 165 and 15

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1) The square ABCD was dilated to form square A'B'C'D' using a scale factor of 1/2

2) The pair of polygons is not similar because their corresponding sides are not proportionals.

Step-by-step explanation:

1) Scale factor: f=?

f=Final dimension / Initial dimension

f=A'B'/AB=B'C'/BC=C'D'/CD=A'D'/AD

f=2/4

Simplifying the fraction dividing the numerator and denominator by 2:

f= (2/2) / (4/2)

f=1/2

2) Let's check the proportion between their corresponding sides:

AM/A'M'=(11 ft)/(9.4 ft)=1.17

HT/H'T'=(11 ft)/(9.4 ft)=1.17

HM/H'M'=(10 ft)/(8.4 ft)=1.19

AT/A'T'=(10 ft)/(8.4 ft)=1.19

AM/A'M'=HT/H'T'=1.17 but different to 1.19=HM/H'M'=AT/A'T'

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Answer:

$\displaystyle \frac{dy}{dx} = \frac{-(2x - 3)(6x - 43)}{(3x + 4)^4}$

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra II

Natural logarithms ln and Euler's number e
Logarithmic Property [Dividing]: $\displaystyle log(\frac{a}{b}) = log(a) - log(b)$
Logarithmic Property [Exponential]: $\displaystyle log(a^b) = b \cdot log(a)$

Calculus

Differentiation

Derivatives
Derivative Notation
Implicit Differentiation

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

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \frac{(2x - 3)^2}{(3x + 4)^3}$

Step 2: Rewrite

[Equality Property] ln both sides: $\displaystyle lny = ln \bigg[ \frac{(2x - 3)^2}{(3x + 4)^3} \bigg]$
Expand [Logarithmic Property - Dividing]: $\displaystyle lny = ln(2x - 3)^2 - ln(3x + 4)^3$
Simplify [Logarithmic Property - Exponential]: $\displaystyle lny = 2ln(2x - 3) - 3ln(3x + 4)$

Step 3: Differentiate

Implicit Differentiation: $\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ 2ln(2x - 3) - 3ln(3x + 4) \bigg]$
Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle \frac{1}{y} \ \frac{dy}{dx} = 2 \bigg( \frac{1}{2x - 3} \bigg)\frac{dy}{dx}[2x - 3] - 3 \bigg( \frac{1}{3x + 4} \bigg) \frac{dy}{dx}[3x + 4]$
Basic Power Rule: $\displaystyle \frac{1}{y} \ \frac{dy}{dx} = 4 \bigg( \frac{1}{2x - 3} \bigg) - 9 \bigg( \frac{1}{3x + 4} \bigg)$
Simplify: $\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{4}{2x - 3} - \frac{9}{3x + 4}$
Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = y \bigg( \frac{4}{2x - 3} - \frac{9}{3x + 4} \bigg)$
Substitute in y [Derivative]: $\displaystyle \frac{dy}{dx} = \frac{(2x - 3)^2}{(3x + 4)^3} \bigg( \frac{4}{2x - 3} - \frac{9}{3x + 4} \bigg)$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{(2x - 3)^2}{(3x + 4)^3} \bigg[ \frac{4(3x + 4) - 9(2x - 3)}{(2x - 3)(3x +4)} \bigg]$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-(2x - 3)(6x - 43)}{(3x + 4)^4}$