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:
The pieces are 55 inches, 55 inches and 46 inches long
Step-by-step explanation:
A 13ft board is to be cut into three pieces consisting of two equal length ones. The third one is 9in shorter than each of the other two.
Let us first convert the length of the board to inches:
1 ft = 12 inches
13 ft = 12 * 13 = 156 inches
Let the length of each of the other two pieces be x.
Therefore, the length of the third piece is (x - 9)
Therefore, the sum of the lengths of the three pieces is equal to 156 inches. This means that:
x + x + (x - 9) = 156
x + x + x - 9 = 156
=> 3x = 156 + 9
3x = 165
x = 165 / 3 = 55 inches
Each of the first two pieces are 55 inches long.
The length of the third piece will be:
55 - 9 = 46 inches
The pieces are 55 inches, 55 inches and 46 inches long.
Step-by-step explanation:
Replace x and y.
Solve for y.
Square both sides.
This is the inverse function or you can also say
Point, line, and plane are the
undefined expression that relinquish the starting location for geometry. When
we define words, we ordinarily use simpler words, and these simpler words are
in turn defined using yet simpler words. This procedure must eventually abort;
at some stage, the definition must use a word whose meaning is accepted as
intuitively clear. Because that meaning is accepted without definition, we
refer to these words as undefined terms. These terms will be used in defining
other terms. Although these expressions are not formally defined, a brief
intuitive dialogue is needed.
A point is the most fundamental
object in geometry. It is represented by a dot and named by a capital letter. A
point constitute position only.
A line (straight line) can be
thought of as a connected set of infinitely many points. It extends infinitely
far in two opposite directions. A line has boundless length, zero width, and
zero height. Any two points on the line name it. The symbol ↔ written on top of
two letters is used to denote that line.
<span>A plane may be contemplating as
an infinite set of points creating a connected flat surface extending
infinitely far in all directions. It is usually represented in drawings by a
four‐sided figure. A single capital letter is used to designate a plane.</span>
12=8 18=12 24=16 (find 2/3 of each one)
So 8, 12 and 16
