Answer:2x+2
Step-by-step explanation:
Answer:
Ai. Common ratio = 2/3
Aii. First term = 54
B. Sum of the first five terms = 422/3
Step-by-step explanation:
From the question given above, the following data were obtained:
3rd term (T3) = 24
6Th term (T6) = 64/9
First term (a) =?
Common ratio (r) =?
Sum of the first five terms (S5) =?
Ai. Determination of the common ratio (r).
T3 = ar²
T3 = 24
24 = ar²....... (1)
T6 = ar⁵
T6 = 64/9
64/9 = ar⁵......... (2)
The equation are:
24 = ar²....... (1)
64/9 = ar⁵......... (2)
Divide equation 2 by equation 1.
64/9 ÷ 24 = ar⁵ / ar²
64/9 × 1/24 = r³
8/27 = r³
Take the cube root of both side
r = 3√(8/27)
r = 2/3
Thus, the common ratio is 2/3
Aii. Determination of the first term (a).
T3 = ar²
3rd term (T3) = 24
Common ratio (r) = 2/3
First term (a) =?
24 = a(2/3)²
24 = 4a/9
Cross multiply
24 × 9 = 4a
216 = 4a
Divide both side by 4
a = 216/4
a = 54
Thus, the first term (a) is 54
B. Determination of the sum of the first five terms.
Common ratio (r) = 2/3
First term (a) = 54
Number of term (n) = 5
Sum of first five terms (S5) =?
Sn = a[1 –rⁿ] / 1 – r
S5 = 54[1 – (⅔)⁵] / 1 – ⅔
S5 = 54 [1 – 32/243] / ⅓
S5 = 54 (211/243) × 3
S5 = 54 × 211/81
S5 = 6 × 211/9
S5 = 2 × 211/3
S5 = 422/3
Thus, the sum of the first five terms is 422/3
The correct answer is: $20
Explanation:
3 pounds of hamburger is $6.
1 pound of hamburger is 
Now,
10 pounds of hamburger is 
Hence the correct answer is $20.
Answer:
<h2>864 cm²</h2>
Step-by-step explanation:
The formula of a volume of a cube:
<em>s</em> - <em>edge</em>
We have
Substitute:
![s^3=1728\to s=\sqrt[3]{1728}\\\\s=12\ cm[/texbecause[tex]12^3=1728](https://tex.z-dn.net/?f=s%5E3%3D1728%5Cto%20s%3D%5Csqrt%5B3%5D%7B1728%7D%5C%5C%5C%5Cs%3D12%5C%20cm%5B%2Ftex%3C%2Fp%3E%3Cp%3Ebecause%3C%2Fp%3E%3Cp%3E%5Btex%5D12%5E3%3D1728)
The formula of a surface area of a cube:
(6 square faces of a cube)
Substitute:
We know the opposite side (10) and the adjacent side (7), so we can use tangent to find angle B. Since tan = opposite side/adjacent side, we can set up this equation: tan(B) = 10/7. We can get B on its own by making the equation this:
Now, we plug this into our calculator to get:
B = 55°, so angle B is 55°.
Let me know if you need any more help!
