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3 years ago

Find the missing side of each triangle. Leave your answers in simplest radical form.

Mathematics

1 answer:

jeka57 [31]3 years ago

3 0

Answer:

x = 2 $\sqrt{34}$

Step-by-step explanation:

Using Pythagoras identity in the right triangle

x² = 10² + 6² = 100 + 36 = 136 ( take the square root of both sides )

x = $\sqrt{136}$ = $\sqrt{4(34)}$ = 2 $\sqrt{34}$

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Rachael wants to receive monthly payments of $2,775 for 20 years. How much does she have to invest now in an annuity that offers

adoni [48]

Answer:

$387,336.64 1

Step-by-step explanation:

The computation of the amount invested now is shown below:

Here we use the present value formula i.e. to be shown in the spreadsheet

Given that,

Future value = $0

Rate of interest = 6% ÷ 12 months = 0.5%

NPER = 20 years × 12 months = 240 months

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= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the present value is $387,336.64 1

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4 years ago

Jaren is the manager of a department store. The morning of a big holiday sale, when Jaren opened the door, 12 customers were wai

shtirl [24]

Answer:

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Step-by-step explanation:

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3 years ago

In rectangle ABCD, point L lies on diagonal

iVinArrow [24]

Answer:

ab/(a+b)

Step-by-step explanation:

Without loss of generality, we can put point C at the origin and define line BD by the equation ...

x/a +y/b = 1

Points (x, y) fall on the line BD, and we have point L where x=y. That value of x, the square's side length, will satisfy ...

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The length of the side of the square is ab/(a+b).

5 0

3 years ago

What is the derivative of 1/square root 4x.

Bumek [7]

Answer:

$\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Exponential Properties

Exponential Property [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Property [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

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

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]$

Step 2: Differentiate

Simplify: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'$
Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'$
Derivative Rule [Basic Power Rule]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)$
Simplify: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}$