Answer:
.
Step-by-step explanation:
Distance formula : Distance between points (a,b) and (c,d) is given by :-
![D=\sqrt{(d-b)^2+(b-a)^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%28d-b%29%5E2%2B%28b-a%29%5E2%7D)
Distance between points
.
![D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%282%5Csqrt%7B3%7D-%28-%5Csqrt%7B12%7D%29%29%5E2%2B%28-%5Csqrt%7B32%7D-%28-4%5Csqrt%7B2%7D%29%29%7D%5C%5C%5C%5C%3D%5Csqrt%7B%282%5Csqrt%7B3%7D%2B%5Csqrt%7B2%5Ctimes2%5Ctimes3%7D%29%5E2%2B%28-%5Csqrt%7B4%5Ctimes4%5Ctimes2%7D%2B4%5Csqrt%7B2%7D%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7B%282%5Csqrt%7B3%7D-%5Csqrt%7B2%5E2%5Ctimes3%7D%29%5E2%2B%28-%5Csqrt%7B4%5E2%5Ctimes2%7D%2B4%5Csqrt%7B2%7D%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7B%282%5Csqrt%7B3%7D%2B2%5Csqrt%7B3%7D%29%5E2%2B%28-4%5Csqrt%7B2%7D%2B4%5Csqrt%7B2%7D%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7B%284%5Csqrt%7B3%7D%29%5E2%2B0%7D%5C%5C%5C%5C%3D4%5Csqrt%7B3%7D%5Ctext%7B%20units%7D)
Hence, the correct option is
.
1.) 4 - t = 3(t - 1) - 5
4 - t = 3t - 3 - 5
4 - t = 3t - 8
3t + t = 4 + 8
4t = 12
t = 12/4 = 3
2.) 8x - 2(x + 1) = 2(3x - 1)
8x - 2x - 2 = 6x - 2
6x - 2 = 6x - 2
0 = 0
solution is identity.
3.) 3(c - 2) = 2(c - 6)
3c - 6 = 2c - 12
3c - 2c = -12 + 6
c = -6
4.) 0.5(m + 4) = 3(m - 1)
0.5m + 2 = 3m - 3
3m - 0.5m = 2 + 3
2.5m = 5
m = 5/2.5 = 2
m = 2
Answer:
![35 {z}^{6} {d}^{11}](https://tex.z-dn.net/?f=35%20%7Bz%7D%5E%7B6%7D%20%7Bd%7D%5E%7B11%7D%20)
Step-by-step explanation:
Assuming you are supposed to simplify:
![7 {z}^{2} \times 5 {z}^{4} \times {d}^{3} \times {d}^{8}](https://tex.z-dn.net/?f=7%20%7Bz%7D%5E%7B2%7D%20%20%5Ctimes%205%20%7Bz%7D%5E%7B4%7D%20%20%5Ctimes%20%20%7Bd%7D%5E%7B3%7D%20%20%5Ctimes%20%20%7Bd%7D%5E%7B8%7D%20)
Then we need to apply the product rule of indices.
![{a}^{m} \times {a}^{n} = {a}^{m + n}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7Bm%7D%20%20%5Ctimes%20%20%7Ba%7D%5E%7Bn%7D%20%20%3D%20%20%7Ba%7D%5E%7Bm%20%2B%20n%7D%20)
So we multiply to get:
![35 {z}^{2 + 4} \times {d}^{3 + 8}](https://tex.z-dn.net/?f=35%20%7Bz%7D%5E%7B2%20%2B%204%7D%20%20%5Ctimes%20%20%7Bd%7D%5E%7B3%20%2B%208%7D%20)
We now simplify the exponents to get:
![35 {z}^{6} \times {d}^{11}](https://tex.z-dn.net/?f=35%20%7Bz%7D%5E%7B6%7D%20%20%5Ctimes%20%20%7Bd%7D%5E%7B11%7D%20)
Therefore the required product is
![35 {z}^{6} {d}^{11}](https://tex.z-dn.net/?f=35%20%7Bz%7D%5E%7B6%7D%20%7Bd%7D%5E%7B11%7D%20)
The possibile answer is 10 ÷ 6 = 1.6
Answer:
It's C) 53
Step-by-step explanation: