Answer:
4 units
Step-by-step explanation:
volume of cube = 64 cubic units

The given polygons are similar
Step-by-step explanation:
By observing the given diagrams, we can see that the respective angles are congruent.
Two shapes are said to be similar if they have same shapes or one shape is created by uniformly increasing or decreasing the side of other.
For this purpose we find the scale factor of greater to smaller image, if the scale factor is same for each side then the two shapes are similar
So,
The scale factor is:

We can see that the scale factor is same for all sides.
Hence,
The given polygons are similar
Keywords: Polygons, similarity
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Answer 1:
It is given that the positive 2 digit number is 'x' with tens digit 't' and units digit 'u'.
So the two digit number x is expressed as,


The two digit number 'y' is obtained by reversing the digits of x.
So, 

Now, the value of x-y is expressed as:




So,
is equivalent to (x-y).
Answer 2:
It is given that the sum of infinite geometric series with first term 'a' and common ratio r<1 = 
Since, the sum of the given infinite geometric series = 200
Therefore,
Since, r=0.15 (given)



a=170
The nth term of geometric series is given by
.
So, second term of the series =
= ar
Second term = 
= 25.5
So, the second term of the geometric series is 25.5
Step-by-step explanation:
6x + 12y = 7
12y = -6x + 7
y = -6/12 + 7
y = -1/2 + 7
the slope of the equation is -1/2
Answer:
The first term is 3. The common difference is 2.
Step-by-step explanation:
The first term is x.
The common difference is d.
The second term is x + d.
3rd term: x + 2d
4th term: x + 3d
7th term: x + 6d
"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"
x + 3d = 3 * x Eq. 1
"the seventh term exceeds twice the third term by 1"
x + 6d = 2(x + 2d) + 1 Eq. 2
Simplify Eq. 1:
2x = 3d
Simplify Eq. 2:
x + 6d = 2x + 4d + 1
x = 2d - 1
Multiply both sides of the last equation by 2.
2x = 4d - 2
2x = 3d (simplified Eq. 1)
Since 2x = 2x, then the right sides are equal.
3d = 4d - 2
d = 2
2x = 3d
2x = 3(2)
2x = 6
x = 3
Answer: The first term is 3. The common difference is 2.