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3 years ago

Identify the decimal 2.16 as a rational number. A)13/60 B)1.3/60 C)130/6 D)13/6

Mathematics

1 answer:

Tema [17]3 years ago

4 0

Answer:

Step-by-step explanation:

2.16=216/100=54/25

check your statement.

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Which statements about the relationship between the two triangles below are true? Check all that apply.

FinnZ [79.3K]

Answer:

Triangle ACD is similar to triangle RST

Step-by-step explanation:

In triangle ACD

$\angle A=74.9^{\circ}$

$\angle D=60^{\circ}$

In triangle RST

$\angle R=74.9^{\circ}$

$\angle S=45.1^{\circ}$

In triangle ACD

$\angle A+\angle C+\angle D=180^{\circ}$

By triangle angles sum property

Substitute the values

$74.9+60+\angle C=180$

$\angle C=180-(74.9+60)=45.1^{\circ}$

Angle A=Angle R

Angle C=Angle S

Therefore, triangle ACD is similar to triangle RST

Reason:By AA similarity postulate

3 0

3 years ago

Read 2 more answers

1.Which are the equation and solution for the sentence, "Anumber, n, divided by

Assoli18 [71]

Answer:

1) B/ 0.4n = 12; n = 30

2) B/ 125 – x = 58

3) B/ $1.75

Step-by-step explanation:

1) 0.4n = 12

n = 12 ÷ 0.4

n = 30

2) 125 – x = 58

– x = 58 – 125

– x = – 67 ( – & – will get cancelled)

x = 67

a) 125 + x = 58

x = 58 – 125

x = – 67 (pages won't be in negative)

c) 125 ÷ 58 = x

2.15 = x (wrong)

d) 58 – x = 125

– x = 125 – 58

– x = 67

x = 67 ÷ –1

x = – 67 ( pages won't be in negative)

3) 12x = 21

x = 21 ÷ 12

x = 1.75

3 0

3 years ago

Find the derivative.

krek1111 [17]

Answer:

$\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Expanding/Factoring

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \frac{\sqrt{x}}{e^x}$

Step 2: Differentiate

Derivative Rule [Quotient Rule]: $\displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}$
Basic Power Rule: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}$
Exponential Differentiation: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}$
Simplify: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}$
Rewrite: $\displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}$
Factor: $\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$