Mid-Chapter Check

Mathematics

1 answer:

Nostrana [21]3 years ago

4 0

An equation: 2x=3
an expression: 2x+5

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The factorization of 8x3 -125 is (2x-5)(jx2 +kx+25)

lbvjy [14]

$\bf ~\hspace{10em}\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 8x^3-125~~ \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3\\ 125=5\cdot 5\cdot 5\\ \qquad 5^3 \end{cases}\implies 2^3x^3-5^3\implies (2x)^3-5^3 \\[2em] [2x-5][(2x)^2+(2x)(5)+5^2]\implies (2x-5)(\stackrel{\stackrel{j}{\downarrow }}{4}x^2+\stackrel{\stackrel{k}{\downarrow }}{10}x+25)$

3 0

3 years ago

Sawyer is ordering sets of guitar strings and bags of picks for his guitar. A new set of strings costs $12 and a new bag of pick

quester [9]

Answer: The equation is 16g+6 ,lmk if you need the answer :)

Step-by-step explanation:

4 0

3 years ago

Rewrite! Write an new and equivalent equation that is easier to solve

Marysya12 [62]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - an equation in a standard form

To do - simplify the equation so as to obtain an easier one

Since the equation provided isn't in it's general form , let's first convert it ~

General form of a Linear equation -

$\bold{ax + b = 0}$

The equation after getting converted will be as follows ~

$- 7 + ( \frac{4x + 2}{2} ) = 8 \\ \\ \implies \: \frac{ - 14 + 4x + 2}{2} = 8 \\ \\ \implies \: - 14 + 4x + 2 = 16 \\ \\ \implies \: 4x = 16 + 14 - 2 \\ \\ \implies \: 4x = 28 \\ \\\bold{ General \: form \: \dashrightarrow \: 4x - 28 = 0}$