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Home » Subtract 5 from both sides: \(x = 10\). - Parker Core Knowledge

Subtract 5 from both sides: \(x = 10\). - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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Since $36 \equiv 1 \pmod{7}$, its inverse modulo 7 is 1. So:
k \equiv 3 \pmod{7} \Rightarrow k = 7m + 3
Then $n = 36k = 36(7m + 3) = 252m + 108$.
We seek the smallest four-digit value of $n$:
252m + 108 \geq 1000 \Rightarrow 252m \geq 892 \Rightarrow m \geq \lef...
For $m = 4$:
n = 252 \cdot 4 + 108 = 1008 + 108 = 1116
$1116 \div 36 = 31$, so divisible by 36
$1116 \div 7 = 159$ remainder $3$, so satisfies the second condition
Thus, the smallest such number is $\boxed{1116}$.

📝 Recent Posts

The area \(A_1\) of an equilateral triangle with side \(s\) is:
A_1 = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\...
If each side is increased by 2 cm, the new side length is \(8\) cm. Th...
A_2 = \frac{\sqrt{3}}{4} \times 8^2 = \frac{\sqrt{3}}{4} \times 64 = 1...
A_2 - A_1 = 16\sqrt{3} - 9\sqrt{3} = 7\sqrt{3} \text{ square cm}
Thus, the area increases by \(\boxed{7\sqrt{3}}\) square cm.
A rectangle with dimensions 3 cm by 4 cm is inscribed in a circle. Wha...
The diagonal of the rectangle is the diameter of the circle. Using the...
d = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm}
The radius \(r\) of the circle is half of the diameter:

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