I think of a number, add 7 to it and double the result is 40. Find the number. 2. change 124 six to binary base. 3. Find the Area of the shaded part. 4. Simplify: 4x-3q+6x+5q-1. IF Set R has 127 proper subsets. Find the Number in set R

• Nambari, $x$.
• Ongeza 7: $x + 7$.
• Fanya matokeo mara mbili: $2(x + 7)$.
• Matokeo ni 40: $2(x + 7) = 40$.

Gawanya pande zote mbili kwa 2:

Jibu la mwisho:

2. Change $124_{\text{six}}$ to binary base.

Kwanza, tutabadilisha nambari kutoka base 6 kwenda base 10, kisha kutoka base 10 kwenda binary (base 2).

Tutagawanya 52 kwa 2 mara kwa mara na kurekodi salio.

• $52 \div 2 = 26$ salio 0
• $26 \div 2 = 13$ salio 0
• $13 \div 2 = 6$ salio 1
• $6 \div 2 = 3$ salio 0
• $3 \div 2 = 1$ salio 1
• $1 \div 2 = 0$ salio 1

Soma salio kutoka chini kwenda juu.

Jibu la mwisho:

3. Find the Area of the shaded part.

Kielelezo kinaonyesha mraba na duara ndani yake. Sehemu iliyotiwa kivuli ni eneo la mraba ukitoa eneo la duara.
Kutoka kwenye mchoro, upande wa mraba ni 21 cm, na hii pia ni kipenyo cha duara.

Upande wa mraba ($s$) = 21 cm.
Kipenyo cha duara ($d$) = 21 cm.
Radiasi ya duara ($r$) = $\frac{d}{2} = \frac{21}{2}$ cm.

Tumia $\pi \approx \frac{22}{7}$.

Jibu la mwisho:

4. Simplify: $4x - 3q + 6x + 5q$

Ili kurahisisha usemi huu, unganisha vigezo vinavyofanana.

Jibu la mwisho:

5. IF Set R has 127 proper subsets. Find the Number in set R.

Idadi ya proper subsets (vijisehemu halisi) ya seti yenye $n$ vipengele hutolewa na formula $2^n - 1$.

Tunajua kuwa $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, $2^4 = 16$, $2^5 = 32$, $2^6 = 64$, $2^7 = 128$.
Hivyo, $2^n = 2^7$.

Jibu la mwisho: