The answer is true. It does increase
Firstly let’s make the -2 2/3 easier
-2*2/3= -4/3
Then we will move all the numbers to one side and keep the x on the other side. Remember when u move a negative from one side of the equal sign it changes to positive and if u move a positive it changes to a negative.
X= -4/3+15-7
=-4/3+8
=-4/3+24/3 (To add fractions the denominator has to be the same, and 24/3 is the same as 8)
X=20/3
Hopefully this helps
Answer:
C. B = (19)(14)
Step-by-step explanation:
Given:
length (l) = 19 in.
width (w) = 14 in.
height (h) = 11 in.
Formula for volume of the rectangular prism = Bh
Base area (B) = l*w
Base area (B) = (19)(14) in.²
Formula for finding base area: B = (19)(14)
Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
The slopes of two parallel lines must be identical.
We have slope
, so the slope for the parallel line be the same.
Now, to find an equation that also passes through the given point, we use slope-point form,
, where our point
is substituted for
.
Now, we convert to slope-intercept form as such.
And we are done. :) We can verify graphically that these are indeed parallel lines. See attached.
