Answer:
y = 3/-1 + 1 or y = -3/1 + 1
Step-by-step explanation:
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
<h3>
Answer: 10^(1/2)</h3>
When we use an exponent of 1/2, it is the same as a square root. The more general rule is
In this case, we plug in x = 10.
The use of a fractional exponent is handy when you want to deal with things like cube roots on a calculator. This is because
![\sqrt[3]{x} = x^{1/3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%20%3D%20x%5E%7B1%2F3%7D)
Many calculators don't have a button labeled ![\sqrt[3]{}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%7D)
but they have the button 
to allow fractional exponents.
The length of the diagonal will be 2.
When a translation is performed on a shaped, it simply moves location. The size and shape of the object do not change. Therefore, the length of AC will remain the same at all times.
Answers:
- x = 10
- angle CAT = 126 degrees
- angle MUD = 54 degrees
=========================================================
Explanation:
∠CAT and ∠MUD are supplementary, which means the angle measures add to 180. They form a straight line.
( m∠CAT ) + ( m∠MUD ) = 180
( 11x+16 ) + ( 4x+14 ) = 180
11x+16 + 4x+14 = 180
(11x+4x) + (16+14) = 180
15x+30 = 180
15x = 180-30
15x = 150
x = 150/15
x = 10
Let's find each angle based on this x value
- m∠CAT=11x+16 = 11*10+16 = 110+16 = 126 degrees
- m∠MUD=4x+14 = 4*10+14 = 40+14 = 54 degrees
Those two angles add to 126+54 = 180 to confirm we do indeed have supplementary angles, and confirm the correct answers.
