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Ivanshal [37]
3 years ago
12

Ericka and her friend are going to reshelf library books. Sherri will reshelf 50% and Ericka will reshelf 2/5 of the books. If t

here are 80 books to reshelf, how many will be left?
Mathematics
1 answer:
ipn [44]3 years ago
5 0
Ok so we start with 80 books and remove 50% so 40
2/5 of 40 is 16
16 books
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Jackson used the process of completing the square to solve the equation 2x2−12x=−6.
Nikolay [14]

Answer:

x=3-\sqrt{6},x=3+\sqrt{6}

Step-by-step explanation:

we are given equation as

2x^2-12x=-6

Since, we have to solve it by using complete square

so, firstly we will complete square

and then we can solve for x

step-1:

Factor 2 from both sides

2(x^2-6x)=-3\times 2

step-2:

Simplify it

x^2-6x=-3

step-3:

Add both sides 3^2

x^2-6x+3^2=-3+3^2

now, we can complete square

(x-3)^2=6

step-4:

Take sqrt both sides

(x-3)=-\sqrt{6},(x-3)=\sqrt{6}

step-5:

Add both sides by 3

we get

x=3-\sqrt{6},x=3+\sqrt{6}


3 0
3 years ago
What is the length of side a?
Bad White [126]

\huge \bf༆ Answer ༄

According to given figure, The Triangle BDC is a right angled Triangle (Angle D = 90°)

So, we can apply Pythagoras theorem to find the Side a (Hypotenuse)

Now, let's solve ~

  • \sf \: BD {}^{2}   + CD {}^{2} =   BC {}^{2}

  • \sf4 {}^{2}  +  {3}^{2}  =  {a}^{2}

  • \sf16 + 9 =  {a}^{2}

  • \sf \: a {}^{2}  = 25

  • \sf \: a =  \sqrt{25}

  • \sf \: a  = 5 \: units

Therefore, Length of side a is 5 units ~

6 0
2 years ago
The curve
kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)
  • Functions
  • Function Notation
  • Terms/Coefficients
  • Anything to the 0th power is 1
  • Exponential Rule [Rewrite]:                                                                              \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Rule [Root Rewrite]:                                                                     \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle y = \sqrt{x - 3}<u />

<u />\displaystyle y' = \frac{1}{2}<u />

<u />

<u>Step 2: Differentiate</u>

  1. [Function] Rewrite [Exponential Rule - Root Rewrite]:                                   \displaystyle y = (x - 3)^{\frac{1}{2}}
  2. Chain Rule:                                                                                                        \displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]
  3. Basic Power Rule:                                                                                             \displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)
  4. Simplify:                                                                                                             \displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1
  5. Multiply:                                                                                                             \displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}
  6. [Derivative] Rewrite [Exponential Rule - Rewrite]:                                          \displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}
  7. [Derivative] Rewrite [Exponential Rule - Root Rewrite]:                                 \displaystyle y' = \frac{1}{2\sqrt{x - 3}}

<u>Step 3: Solve</u>

<em>Find coordinates</em>

<em />

<em>x-coordinate</em>

  1. Substitute in <em>y'</em> [Derivative]:                                                                             \displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}
  2. [Multiplication Property of Equality] Multiply 2 on both sides:                      \displaystyle 1 = \frac{1}{\sqrt{x - 3}}
  3. [Multiplication Property of Equality] Multiply √(x - 3) on both sides:            \displaystyle \sqrt{x - 3} = 1
  4. [Equality Property] Square both sides:                                                           \displaystyle x - 3 = 1
  5. [Addition Property of Equality] Add 3 on both sides:                                    \displaystyle x = 4

<em>y-coordinate</em>

  1. Substitute in <em>x</em> [Function]:                                                                                \displaystyle y = \sqrt{4 - 3}
  2. [√Radical] Subtract:                                                                                          \displaystyle y = \sqrt{1}
  3. [√Radical] Evaluate:                                                                                         \displaystyle y = 1

∴ Coordinates of Point N is (4, 1).

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

Unit: Derivatives

Book: College Calculus 10e

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8 1/3 - 4 3/4 I will reward brainlyest
nasty-shy [4]

Answer:

The answer is 3 7/12 Hope this helps :)

Step-by-step explanation:

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Mike and Beth are saving money to go to Disneyworld. They need at least $1975 in order to go. Mike mows yards and Beth will wash
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