Algebra

Problem 31201

Determine if the lines $-3y=5x+2$ , $10x-6y=-2$ , and $y=-\frac{3}{5}x+1$ are parallel, perpendicular, or neither.

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Problem 31202

Using Rachel's method, what is the third line for $23 \times 17$ ? A. $(2 \times 17)+(3 \times 17)$ B. $(2 \times 1)+(2 \times 7)+(3 \times 1)+(3 \times 7)$ C. $(20 \times 10)+(20 \times 7)+(3 \times 10)+(3 \times 7)$ D. $(2 \times 10)+(2 \times 7)+(3 \times 10)+(3 \times 7)$

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Problem 31203

Identify the property illustrated in each case: a. $(6 \cdot 7) 0=0$ b. $3(5 \cdot 7)=3(7 \cdot 5)$ c. $3(5 \cdot 7)=(5 \cdot 7) 3$ d. $(5+7) 1=5+7$ e. $3(5+7)=3 \cdot 5+3 \cdot 7$ f. $(3+5)(6+7)=(3+5) 6+(3+5) 7$

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Problem 31204

Simplify the expression $5\left(a b^{-1}\right)$ using exponent properties and show only positive exponents.

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Problem 31205

```latex \text{التمرين السادس والخمسون}
\begin{enumerate} \item المتتالية العددية المعرفة بـ: $a_n = 13$ ومن أجل كل عدد طبيعي $n$ \begin{enumerate} \item برهن بالتراجع أنه: من أجل كل عدد طبيعي $n$ , $a_n$ . \item أدرس اتجاه تغير المتتالية $a_n$ واستنتج أنها متقاربة. \end{enumerate} \item المتتالية العددية المعرفة على $\mathbb{N}$ بـ: $u_n = 1 - \frac{1}{n}$ \begin{enumerate} \item أثبت أن المتتالية $u_n$ حسابية وعيّن أساسها وحدها الأول. \end{enumerate} \item اكتب $u_n$ بدلالة $n$ ثم بين أنه من أجل كل عدد طبيعي $n$ , $12 + 1 = u_n$ . واحسب عندئذ $\lim_{n \to \infty} u_n$ . \item بيّن أنّه من أجل كل عدد طبيعي $n$ \end{enumerate}

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Problem 31206

$\frac{1+\frac{6 x}{4-y}}{2 y}=\frac{3 z}{9 y}=\frac{10}{9}$ , then $\frac{3 x+z}{2 y+3 y}=$

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Problem 31207

\$e number which is added to each of the numbers 1,3 and 6 to become in continued proportion is

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Problem 31208

20) Simplify:- $\frac{\left(3^{-2}\right)^{2} \times\left(5^{2}\right)^{-3} \times\left(t^{-3}\right)^{2}}{\left(3^{-2}\right)^{5} \times\left(5^{3}\right)^{-2} \times\left(t^{-4}\right)^{3}}$

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Algebra

Problem 31201

Determine if the lines $-3y=5x+2$ , $10x-6y=-2$ , and $y=-\frac{3}{5}x+1$ are parallel, perpendicular, or neither.

Problem 31202

Using Rachel's method, what is the third line for $23 \times 17$ ? A. $(2 \times 17)+(3 \times 17)$ B. $(2 \times 1)+(2 \times 7)+(3 \times 1)+(3 \times 7)$ C. $(20 \times 10)+(20 \times 7)+(3 \times 10)+(3 \times 7)$ D. $(2 \times 10)+(2 \times 7)+(3 \times 10)+(3 \times 7)$

Problem 31203

Identify the property illustrated in each case: a. $(6 \cdot 7) 0=0$ b. $3(5 \cdot 7)=3(7 \cdot 5)$ c. $3(5 \cdot 7)=(5 \cdot 7) 3$ d. $(5+7) 1=5+7$ e. $3(5+7)=3 \cdot 5+3 \cdot 7$ f. $(3+5)(6+7)=(3+5) 6+(3+5) 7$

Problem 31204

Simplify the expression $5\left(a b^{-1}\right)$ using exponent properties and show only positive exponents.

Problem 31205

Problem 31206

$\frac{1+\frac{6 x}{4-y}}{2 y}=\frac{3 z}{9 y}=\frac{10}{9}$ , then $\frac{3 x+z}{2 y+3 y}=$

Problem 31207

\$e number which is added to each of the numbers 1,3 and 6 to become in continued proportion is

Problem 31208

20) Simplify:- $\frac{\left(3^{-2}\right)^{2} \times\left(5^{2}\right)^{-3} \times\left(t^{-3}\right)^{2}}{\left(3^{-2}\right)^{5} \times\left(5^{3}\right)^{-2} \times\left(t^{-4}\right)^{3}}$

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Algebra

Problem 31201

Determine if the lines −3y=5x+2-3y=5x+2−3y=5x+2, 10x−6y=−210x-6y=-210x−6y=−2, and y=−35x+1y=-\frac{3}{5}x+1y=−53​x+1 are parallel, perpendicular, or neither.

Problem 31202

Problem 31203

Problem 31204

Simplify the expression 5(ab−1)5\left(a b^{-1}\right)5(ab−1) using exponent properties and show only positive exponents.

Problem 31205

Problem 31206

1+6x4−y2y=3z9y=109\frac{1+\frac{6 x}{4-y}}{2 y}=\frac{3 z}{9 y}=\frac{10}{9}2y1+4−y6x​​=9y3z​=910​, then 3x+z2y+3y=\frac{3 x+z}{2 y+3 y}=2y+3y3x+z​=

Problem 31207

\$e number which is added to each of the numbers 1,3 and 6 to become in continued proportion is

Problem 31208

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Determine if the lines $-3y=5x+2$ , $10x-6y=-2$ , and $y=-\frac{3}{5}x+1$ are parallel, perpendicular, or neither.

Simplify the expression $5\left(a b^{-1}\right)$ using exponent properties and show only positive exponents.

$\frac{1+\frac{6 x}{4-y}}{2 y}=\frac{3 z}{9 y}=\frac{10}{9}$ , then $\frac{3 x+z}{2 y+3 y}=$