a) The first five terms of the sequence are 2, 12, 72, 432, 2592.
b) The first five terms of the sequence are -1, 2, -4, 8, -16.
c) The first five terms of the sequence are 2, -1, -3, -2, 1.
To find the first five terms of the sequence defined by each of these recurrence relations and initial conditions, we will use the given recurrence relation and initial conditions to find the next terms in the sequence.
a) an = 6an-1, a0 = 2
The first term is given as a0 = 2. We will use the recurrence relation to find the next terms.
a1 = 6a0 = 6(2) = 12
a2 = 6a1 = 6(12) = 72
a3 = 6a2 = 6(72) = 432
a4 = 6a3 = 6(432) = 2592
So, the first five terms of the sequence are 2, 12, 72, 432, 2592.
b) an = −2an-1, a0 = −1
The first term is given as a0 = -1. We will use the recurrence relation to find the next terms.
a1 = -2a0 = -2(-1) = 2
a2 = -2a1 = -2(2) = -4
a3 = -2a2 = -2(-4) = 8
a4 = -2a3 = -2(8) = -16
So, the first five terms of the sequence are -1, 2, -4, 8, -16.
c) an = an-1 – an-2, a0 = 2, a1 = −1
The first two terms are given as a0 = 2 and a1 = -1. We will use the recurrence relation to find the next terms.
a2 = a1 - a0 = -1 - 2 = -3
a3 = a2 - a1 = -3 - (-1) = -2
a4 = a3 - a2 = -2 - (-3) = 1
So, the first five terms of the sequence are 2, -1, -3, -2, 1.
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1- y(y + 5) = 750
2- y^2 – 5y = 750
3- 750 – y(y – 5) = 0
4- y(y – 5) + 750 = 0
5- (y + 25)(y – 30) = 0
2, 4, 8, 12
B
13, 15, 17, 19
C
2, 5, 23, 29
D
3, 17, 29, 81
Answer:
x = 96°
Step-by-step explanation:
96 and x are Alternate exterior angles and are congruent, thus
x = 96°
1 cm, 2 cm, 5 cm
14 cm, 8 cm, 5 cm
6 cm, 2 cm, 7 cm
An equation is formed when two equal expressions. The number of dimes and nickels in Caroline's purse is 12 and 27, respectively.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of dimes in Caroline's purse be represented by x, while the number of nickels is represented by y.
Given that the number of nickels is nine less than three times the number of dimes. Therefore, we can write,
y = 3x - 9
Also, Caroline has a total of $2.55 in her purse. Therefore, we can write,
0.10x + 0.05y = 2.55
Substitute the value of y from the above equation,
0.10x + 0.05(3x - 9) = 2.55
0.10x + 0.15x - 0.45 = 2.55
0.25x = 2.55 + 0.45
0.25x = 3
x = 3/0.25
x = 12
Substitute the value of x in the equation of y,
y = 3x - 9
y = 3(12) - 9
y = 36 - 9
y = 27
Hence, the number of dimes and nickels in Caroline's purse is 12 and 27, respectively.
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A. y=-5/6x+4
B. y=-5/6x-6
C. y=-5/6x-4
D. y=-5/6x+6
Which equation produces a line that is perpendicular to the line represented by the function below?
y=2/5x+9
A. 5x+2y=4
B. 2x-5y=8
C. 5x+2y=-3
D.2x+5y=-7
What is the slope of the line that is parallel to the line represented by the equation below?
4x-5y+-1
A 4/5
B -4/5
C 5/4
D -5/4
Answer:
1. Missing the point - unanswerable
2. A and C
3. A
Step-by-step explanation:
Recall the slope of a line is parallel if the same slope and perpendicular if it is the negative reciprocal.
For number 1, each equation has the same slope as the function and will be parallel. Without the point, you cannot determine which one.
For number 2, find an equation that has slope -5/2. Both A and C have this property when converted to slope intercept form.
5x+2y=4 5x+2y = -3
2y=4-5x 2y= -3-5x
y=2-5/2 x y=-3/2 -5/2 x
For number 3, the slope will be the same as the equation for parallel. Convert the equation 4x-5y=-1 to find the slope.
4x-5y=-1
-5y = -1-4x
y=1/5 + 4/5 x
A is the solution.