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Mariulka [41]
3 years ago
13

Andrew has six fewer coins than Casey. Bob has two more than twice as many coins as Andrew. Altogether, they have 544 coins. How

many coins does Bob have?
Mathematics
1 answer:
Damm [24]3 years ago
8 0
Assuming: number of coins Andrew has=a, number of coins Bob has=b, number of coins Casey has=c
Andrew has six fewer coins than Casey, so, c-6=a, or a+6=c
Bob has two more than twice as many coins as Andrew, so 2a+2=b
Together, there are 544 coins: a+b+c=544. Rewrite the equation in terms of a: a+(2a+2)+(a+6)=544. Combine like terms: 4a+8=544. Solve the equation: 4a=536, so a=134. If b=2a+2, then b=2(134)+2=268+2=270.
Bob has 270 coins.
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For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Kipish [7]

The numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = <u>67/24</u> on simplification using the BODMAS rule.

In the question, we are asked to simplify the numerical expression:

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3.

To simplify the expression, we will follow the BODMAS rule, where B means Brackets, O means Of, D means Divide, M means Multiplication, A means Addition, and S means Subtraction.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

= 2/3 ÷ 16 + (3/4 + 1/6) ÷ 1/3 {Solving 2⁴ = 16, before proceeding BODMAS}.

= 2/3 ÷ 16 + ((9+2)/12) ÷ 1/3 {Solving Brackets by taking LCM}

= 2/3 ÷ 16 + 11/12 ÷ 1/3 {Simplifying}

= 2/3 * 1/16 + 11/12 * 3/1 {Solving divisions by taking reciprocals}

= 1/24 + 11/4 {Multiplying}

= (1 + 66)/24 {Adding using LCM}

= 67/24 {Simplifying}.

Thus, the numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = <u>67/24</u> on simplification using the BODMAS rule.

Learn more about the simplification of numerical expression at

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The provided question is incomplete. The complete question is:

"Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.

Simplify the numerical expression.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

The expression has a value equal to."

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Hi can someone help me out. This is due by the end of the day.​
solmaris [256]

Answer:

b. Divided

Step-by-step explanation:

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3 years ago
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A) Use the limit definition of derivatives to find f’(x)
Ann [662]
<h3>1)</h3>

\text{Given that,}\\\\f(x) =  \dfrac{ 1}{3x-2}\\\\\text{First principle of derivatives,}\\\\f'(x) = \lim \limits_{h \to 0} \dfrac{f(x+h) - f(x) }{ h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{1}{3(x+h) - 2} - \tfrac 1{3x-2}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0}  \dfrac{\tfrac{1}{3x+3h -2} - \tfrac{1}{3x-2}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{3x-2-3x-3h+2}{(3x+3h-2)(3x-2)}}{h}\\\\\\

       ~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{-3h}{(3x+3h-2)(3x-2)}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{-3h}{h(3x+3h-2)(3x-2)}\\\\\\~~~~~~~~=-3 \lim \limits_{h \to 0} \dfrac{1}{(3x+3h-2)(3x-2)}\\\\\\~~~~~~~~=-3 \cdot \dfrac{1}{(3x+0-2)(3x-2)}\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)(3x-2)}\\\\\\~~~~~~~=-\dfrac{3}{(3x-2)^2}

<h3>2)</h3>

\text{Given that,}~\\\\f(x) = \dfrac{1}{3x-2}\\\\\textbf{Power rule:}\\\\\dfrac{d}{dx}(x^n) = nx^{n-1}\\\\\textbf{Chain rule:}\\\\\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}\\\\\text{Now,}\\\\f'(x) = \dfrac{d}{dx} f(x)\\\\\\~~~~~~~~=\dfrac{d}{dx} \left( \dfrac 1{3x-2} \right)\\\\\\~~~~~~~~=\dfrac{d}{dx} (3x-2)^{-1}\\\\\\~~~~~~~~=-(3x-2)^{-1-1} \cdot \dfrac{d}{dx}(3x-2)\\\\\\~~~~~~~~=-(3x-2)^{-2} \cdot 3\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)^2}

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2 years ago
Which expressions are equivalent to 6 (–x) 2x (–7) 2x? Check all that apply. X x 6 – 7 x 2x 2 x 3 – x 2x – 4 2x x – 1 x 1.
qaws [65]

Equivalent expression is the expression which is equal to the original equation but the way of representation is different. The equivalent expression of the given expression are,

x+x+6-7+x

3-x+2x-4+2x=3x-1

Given information

The given expression in the problem is,

6+(-x)+2x+(-7)+2x

<h3>Equivalent expression</h3>

Equivalent expression is the expression which is equal to the original equation but the way of representation is different.

The given equation is,

6+(-x)+2x+(-7)+2x

As the product of the negative and positive is negative. Thus solve the equation by opening the bracket.

6+(-x)+2x+(-7)+2x=6-x+2x-7+2x\\&#10;6+(-x)+2x+(-7)+2x=-x+2x+2x+6-7\\&#10;6+(-x)+2x+(-7)+2x=3x-1

Check all the option,

  • 1) The expression given in the option 1 is,

x+x+6-7+x

Solve it further,

x+x+6-7+x=x+x+x+6-7\\&#10;x+x+6-7+x=3x-1\\

The result is equal to the result of the given expression. Thus the expression of the option 1 is equivalent to the expression given in the problem.

  • 2) The expression given in the option 2 is,

2x+2+x

Solve it further,

2x+2+x=2x+x+2\\2x+2+x=3x+2

The result is not equal to the result of the given expression. Thus the expression of the option 2 is not equivalent to the expression given in the problem.

  • 3) The expression given in the option 3 is,

3-x+2x-4+2x

Solve it further,

3-x+2x-4+2x=3x-1

The result is equal to the result of the given expression. Thus the expression of the option 3 is equivalent to the expression given in the problem.

  • 4) The expression given in the option 4 is,

x-1

The expression of the option 4 is not equivalent to the expression given in the problem.

  • 5) The expression given in the option 4 is,

x+1

The expression of the option 5 is not equivalent to the expression given in the problem.

Hence the equivalent expression of the given expression are,

x+x+6-7+x

3-x+2x-4+2x=3x-1

Learn more about the equivalent expression here;

brainly.com/question/10628562

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