The terms of this sequence increase by the same amount each time _,_,17_,_,29

9, 13, 17, 21, 25, 29

Step-by-step explanation:

Since there is an equal increase of the same amount, the sequence is arithmetic with n th term

Substituting a = 9 and d = 4 into the n th term expression

= 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5

= a + (n - 1)d

where a is the first term and d the common difference

The third term and sixth term are therefore

a + 2d = 17 → (1)

a + 5d = 29 → (2)

Subtract (1) from (2) term by term, eliminating a, that is

3d = 12 ( divide both sides by 3 )

d = 4

Substitute d = 4 into either of the 2 equations and solve for a

Substituting into (1)

a + 2(4) = 17

a + 8 = 17 ( subtract 8 from both sides )

a = 9

Thus the first term is 9 and the common difference d = 4

The sequence of terms is therefore

9, 13, 17, 21, 25, 29

Substituting a = 9 and d = 4 into the n th term expression

= 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3