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3 years ago

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. 2, 9, 16, 23

2 answers:

5 0

This is an arithmetic sequence which means all of these terms are all the same distance from one another.
an=a1+d(n-1)
an=2+7(n-1)
an=2+7n-7
Answer: an=7n-5

musickatia [10]3 years ago

3 0

It increases by 7 and it's arithmetic progression:
Where d = 7
a = 2

and the formula will be

$a_{n}$ = a + d (n-1) = 2 + 7*(n-1)

Where n starts from 1 and continues to the infinity

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Fill in the blanks to complete this proof of theorem 2-3.

Basile [38]

Answer:

Therefore.

angle 1 is congruent to angle 3 ...Proved

The proof with steps are below with Fill in the blanks

Step-by-step explanation:

Complementary Angles:

Two angles are Complementary when they add up to 90 degrees.

Example 40° and 50° are Complementary Angles.

If 'x' and 'y' are Complementary Angles the we have

$x+y=90\°$

Here,

Given:

angle 1 and angle 2 are complementary

angle 3 and angle 2 are complementary

To Prove:

angle 1 is congruent to angle 3

Proof:

Step 1:

angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is Given.

Step 2:

By the definition of complementary angles,

m of angle 1 + m of angle 2 = _90°__ and m of angle 3 + m of angle 2 = _90°_.

Step 3:

Transitive Property of Equality.

Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality.

Step 4:

Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get

$m\angle 1 +m\angle 2-m\angle 2=m\angle 3+m\angle 2-m\angle 2$

$m\angle 1=m\angle 3$

m of angle 1 = _measure of angle_3_.

Step 5:

Angles with the same measure are _Congruent__,

Step 6:

so angle 1 is congruent to angle 3.

Therefore.

angle 1 is congruent to angle 3 ...Proved

6 0

3 years ago

The number m and 5/8 are additive inverses.

Nonamiya [84]

Conveniently, your number line has 8 divisions in each unit interval, so finding 5/8 is a matter of counting 5 divisions.

The additive inverse of a number has the opposite sign from the number, so m = -5/8. The sum of a number and its additive inverse is zero. (That is the definition of additive inverse.)

5 0

3 years ago

Read 2 more answers

Factor each expression completely6x^2+x-2

Citrus2011 [14]

$6x^2+x-2$

first , set the function equal to zero

$6x^2+x-2=0$

now we can use this expression to factor

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

where a is 6, b is 1 and c -2

so, replacing

$\begin{gathered} \frac{-(1)\pm\sqrt[]{1^2-4(6)(-2)}}{2(6)} \\ \\ \frac{-1\pm\sqrt[]{1+48}}{12} \\ \\ \frac{-1\pm\sqrt[]{49}}{12} \\ \\ x=\frac{-1\pm7}{12} \end{gathered}$

x has two values