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3 years ago

8

the watch bee would like to buy costs $10 less then 2 times the amount she has saved the watch costs $50. how much money does be

e have saved?

1 answer:

Aleksandr-060686 [28]3 years ago

6 0

Answer:

20$

Step-by-step explanation:

50 - (2x - 10) = x

50 + 10 = x + 2x

60 = 3x

60/3 = x

20 = x

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How many of the positive divisors of 2160 are multiples of 3?

TEA [102]

30 of the divisors are multiples of 3

The factors of 2160 are 1, 2160, 2, 1080, 3, 720, 4, 540, 5, 432, 6, 360, 8, 270, 9, 240, 10, 216, 12, 180, 15, 154, 16, 135, 18, 120, 20, 108, 24, 90, 27, 80, 30, 72, 36, 60, 40, 54, 45, 48
These are all divisors of 2160 but only 30 are multiples of 3.
The ones that are NOT are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

You can also do this using prime factors 2x2x2x2x3x3x3x5 = 2160 but it is harder to explain.

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3 years ago

geometry question(s) on triangle similarity, please help, i’d really appreciate it! image is included.

Sergio [31]

1. D. The triangles have two given sides with an included angle, so the postulate would be SAS.

2. A. The triangles have three given sides, so the postulate would be SSS.

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4 years ago

What is 10% of 800Hhhhhhhhhhhh

Bogdan [553]

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3 years ago

The problem is attached, thanks.

NeX [460]

Answer:

$\displaystyle \frac{dy}{dx} \bigg| \limit_{(1, 4)} = 2$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

<u>Algebra I</u>

Coordinates (x, y)
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative of a constant is 0

Implicit Differentiation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

$\displaystyle \sqrt{x} - \sqrt{y} = -1$

Point (1, 4)

<u>Step 2: Differentiate</u>

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle x^{\frac{1}{2}} - y^{\frac{1}{2}} = -1$
[Implicit Differentiation] Basic Power Rule: $\displaystyle \frac{1}{2}x^{\frac{1}{2} - 1} - \frac{1}{2}y^{\frac{1}{2} - 1}\frac{dy}{dx} = 0$
[Implicit Differentiation] Simplify Exponents: $\displaystyle \frac{1}{2}x^{\frac{-1}{2}} - \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Isolate <em>y</em> terms: $\displaystyle -\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = \frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Simplify: $\displaystyle \frac{dy}{dx} = \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}$

<u>Step 3: Evaluate</u>

Substitute in point [Derivative]: $\displaystyle \frac{dy}{dx} = \frac{(4)^{\frac{1}{2}}}{(1)^{\frac{1}{2}}}$
Exponents: $\displaystyle \frac{dy}{dx} = \frac{2}{1}$
Division: $\displaystyle \frac{dy}{dx} = 2$

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

Unit: Implicit Differentiation

Book: College Calculus 10e

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3 years ago

Find the point at which the line with parametric equations x = 2 3t, y =-4t, z =5 t intersects the plane 4x 5y -2z=18

sashaice [31]

It looks like you have

$\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}$

Substituting these in to the plane equation, we have

$4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2$

When $t=-2$ , we get the point

$\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}$

4 0

2 years ago