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3 years ago

The quotient of 35 and the quantity of x minus 7

Mathematics

1 answer:

Fantom [35]3 years ago

3 0

The quotient (÷) of 35 and the quantity of x minus 7 (x - 7).

$\frac{35}{x - 7}$

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Need the missing length

Gala2k [10]

Answer:

Step-by-step explanation:

The side to the right is 15. The side to the left is 5. You can subtract these two to find the length.

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3 years ago

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What is the completely factored form of f(x)=x^3-7x^2+2x+4

xxMikexx [17]

$Solution, \mathrm{Factor}\:x^3-7x^2+2x+4:\quad \left(x-1\right)\left(x^2-6x-4\right)$

$Steps:$

$x^3-7x^2+2x+4$

$Use\:the\:rational\:root\:theorem,\\a_0=4,\:\quad a_n=1,\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1},\\\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x-1,\\\left(x-1\right)\frac{x^3-7x^2+2x+4}{x-1}$

$\frac{x^3-7x^2+2x+4}{x-1}$

$\mathrm{Divide}\:\frac{x^3-7x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}x^3-7x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{x^3}{x},\\\mathrm{Quotient}=x^2,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}x^2:\:x^3-x^2,\\\mathrm{Subtract\:}x^3-x^2\mathrm{\:from\:}x^3-7x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-6x^2+2x+4,\\Therefore,\\\frac{x^3-7x^2+2x+4}{x-1}=x^2+\frac{-6x^2+2x+4}{x-1}$

$\mathrm{Divide}\:\frac{-6x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-6x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-6x^2}{x}=-6x,\\\mathrm{Quotient}=-6x,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-6x:\:-6x^2+6x,\\\mathrm{Subtract\:}-6x^2+6x\mathrm{\:from\:}-6x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-4x+4,\\\mathrm{Therefore},\\\frac{-6x^2+2x+4}{x-1}=-6x+\frac{-4x+4}{x-1}$

$\mathrm{Divide}\:\frac{-4x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-4x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-4x}{x}=-4,\\\mathrm{Quotient}=-4,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-4:\:-4x+4,\\\mathrm{Subtract\:}-4x+4\mathrm{\:from\:}-4x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=0,\\\mathrm{Therefore},\\\frac{-4x+4}{x-1}=-4$

$\mathrm{The\:Correct\:Answer\:is\:\left(x-1\right)\left(x^2-6x-4\right)}$

$\mathrm{Hope\:This\:Helps!!!}$

$\mathrm{-Austint1414}$

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3 years ago

Justin has three goldfish and one turtle. Write a fraction to represent the part of his pets that are goldfish.

Troyanec [42]

Answer:

3/4

Step-by-step explanation:

3 goldfish

4 total pets

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3 years ago

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A = 1/2 bh (solve for b)

Vikentia [17]

Answer:

Step-by-step explanation:

if A=1/2 bh

to solve for b

2A=bh

b=2A/h

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2 years ago

Alexis scale drawing represents the longest side of the storage bin as 2 3/4 inches. What is the actual length, in feet, of the

Whitepunk [10]

Answer: The correct answer is C,

5 1/2 feet

Step-by-step explanation:

Alexis' scale drawing represents the longest side of the storage bin as 2 3/4 inches. Converting to improper fraction, it becomes 11/4 inches. This is also 2.75 inches.

The scale used is 1/2 inch = 1 feet. This means that a length of 1 feet of the longest side of the actual storage bin is 1/2 inch on the drawing.

Let the actual length, in feet of the longest side of the storage bin be x feet. Therefore

If 0.5 inch = 1 feet

2.75 inch = x

0.5x = 2.75 × 1

x = 2.75/0.5 = 5.5 feet

6 0

3 years ago