Given: 3x - 5 = 4 (2x – 15) Prove: x = 11 Statement Reason

Generate the nest three terms of each arithmetic sequence shown below.

o-na [289]

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

A)a1=-2 and d=4

We know that the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{2}=a_{1}+(2-1)d$

$a_{2}=a_{1}+(1)d$

Substituting the given value we get

$a_{2}= -2+(1)4$

$a_{2}= -2+4$

$a_{2}= 2$

------------------------------------------

Similarly

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the given value we get

$a_{3}= -2+(2)4$

$a_{3}= -2+8$

$a_{3}= 6$

-------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the given value we get

$a_{4}= -2+(3)4$

$a_{4}= -2+16$

$a_{4}= 10$

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B $a_n=a_{(n-1)}-8$ with $a_1=10$

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

$a_4= -14$

-------------------------------------------------------------------------------------------

C) $a_1=3, a_2=1$

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

$a_{4}= 3+(3)-2$

$a_{4}= 3-6$

$a_{4}= -3$

----------------------------------------------------------------------------------

$a_{5}=a_{1}+(5-1)d$

$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

4 0

3 years ago

2. measure of an angle that is supplementary to

leonid [27]

Answer: 99°

explanation: first, we need to find angle T. we know that angle T and angle R are vertical angles, which means they’re the same. therefore, we solve the equation for x by doing angle T = angle R:
3x + 36 = 6x - 9
subtract 36 on both sides
3x = 6x - 45
subtract 6 on both sides
-3x = -45
divide both sides by -3
x= 15
then, plug in the value of x in 3x+36 to get angle T:
3(15) + 36= 81°
we found that angle T is 81°.
now, we need to find the supplementary angle of angle T. supplementary angles add up together to have a sum of 180°. to find the supplementary angle, subtract angle T from 180°:
180 - 81 = 99°
there we have the answer!

7 0

3 years ago

What is the mode of the following list of numbers:

Hoochie [10]

Answer: Your answer is 6

5 0

4 years ago

I need helping finding KMC.

NikAS [45]

Hello from MrBillDoesMath!

Answer:

See discussion below. (I think the desired answer is 130)

Discussion:

The problem needs to be clarified to give you a answer. Her'es why:

Argument 1:

When two lines intersect vertical angles are equal. So angle HMC =

angle RMK. That's equivalent to

5M + 15 = 7M +1 => subtract 5M from both sides

5M - 5M + 15 = 7M -5M +1 => subtract 1 from both sides

0 + 15 -1 = 2M + 1 -1 =>

14 = 2M =>

M = 7

As a straight line has 180 degrees

angle RMK + angle KMC = 180 => as angle RMK = 7M + 1

(7M + 1 ) + angle KMC = 180 => as M =7 from above

50 + angle KMC = 180 =>

angle KMC = 180 - 50 = 130.

I think this is the answer they want BUT notice

Argument 2.

Per the diagram, M can be interpreted as either the point of

intersection of the 2 lines or as the angle at the intersection of the two

lines. If the point of intersection were called, say Q, and M reserved

for angles, the problem would be clearer. BUt as I said above I think

they are looking for the answer found in Argument 1 (130 degrees)

Thank you,

MrB

6 0

3 years ago

I just need an answer for number two please?

Nikolay [14]

< DAF and <EAD are supplementary ( both on same straight line FE)

but we are given that <EAD = <BAE ( as AE bisects <BAD)
Therefore <BAE and <DAF are supplementary.

8 0

3 years ago