A geometric sequence is a sequence in which there is a common ratio between any two consecutive terms. In this case if X:Y:Z are in the ratio of 2:7:8 the multiplying by a constant k, we have X=2k, Y= 7k and Z=8k.
Then if X, Y-12, Z form a Geometric sequence, it means X/Y-12=Y-12/Z which is the same as 2k/7k-12=7k-12/8k if we cross multply, we get
16k²= 49k²-168k +144
33k²-168k+144 =0 solving for k
k = 4 or 1.091 if we take the whole number to find the values of X,Y and z,
X= 8, Y= 28 and Z=32
Answer:
(-5,-14)
Step-by-step explanation:
To find the solution of the system of two equations
equate right sides of these two equations:
Rewrite terms with x into the left side and without x into the right side:
![4x-2x=-4-6\\ \\2x=-10\ [\text{divide by 2}]\\ \\x=-5](https://tex.z-dn.net/?f=4x-2x%3D-4-6%5C%5C%20%5C%5C2x%3D-10%5C%20%5B%5Ctext%7Bdivide%20by%202%7D%5D%5C%5C%20%5C%5Cx%3D-5)
Substitute x=-5 into the first equation:
The solution is (-5,-14)
Step-by-step explanation:
6k + 12 + 9=9
6k + 12 = 9 - 9
6k + 12 = 0
12 = -6k
12/-6 = -6k/-6
2/-1 = k
k = -2
Answer:
15 feet
Step-by-step explanation:
Since this is a square the sides are of the same length.
Now the side multiplied by itself gives 225. Hence the length of the side is a number which multiplied by itself gives 225. It is easy to see that 15 × 15 = 225. Therefore the side is 15 feet long.
