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3 years ago

Find the eighth term of a geometric sequence for which a,3 = 35 and r= 7.

Mathematics

1 answer:

Alenkinab [10]3 years ago

8 0

Answer:

588245.

Step-by-step explanation:

nth term = an = a1 r^(n-1) where a1 = the first term

a3 = 35 = a1 7^(3 - 1)

35 = a1* 49

a1 = 35/49 = 5/7

So the 8th term = (5/7)* (7)^7

= 588245

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allochka39001 [22]

Part A

Converse = "If corresponding angles are equal, then two lines are parallel"
Result = True

Explanation:

Refer to the converse of the corresponding angles theorem. The original version is stated as part A, and the converse is marked in bold above.

Conditional statements are of the form "if this, then that". Symbolically we can use the template "If P, then Q". The P and Q are placeholders for logical statements.

The converse of "if P, then Q" is "If Q, then P". We swap the positions of P and Q. Do not negate either piece.

========================================================

Part B

Converse = "If angle C is 70 degrees, then the sum of angles A and B is 110 degrees"
Result = True

Explanation:

Recall that for any triangle, the three interior or inside angles always add to 180 degrees. In short: A+B+C = 180. If C = 70, then A+B = 180-C leads to A+B = 180-70 and A+B = 110. This process can be reversed.

========================================================

Part C

Converse = "If two lines are not parallel, then alternate interior angles k and s are not equal"
Result = True

Explanation:

For more information, check out the converse of the alternate interior angles theorem. The regular version of the theorem is "If two lines are parallel, then the alternate interior angles are congruent".

The converse of this theorem flips things to say: "If alternate interior angles are congruent, then the lines are parallel".

========================================================

Part D

Converse = "If John loses his money, then he throws coins in the fountain"
Result = False

Explanation:

Throwing coins in a fountain is one way to lose money, but there are other ways. He could drop a coin somewhere, or leave the coin somewhere he forgot.

In other words, just because he lost his money does not mean he threw a coin in the fountain.

8 0

2 years ago

Need help please worth 50 points

Law Incorporation [45]

Here's how you simplify those. The rule for raising an exponent to an exponent is that you multiply them. The rule for dividing exponents with the same base is that you subtract the denomonator from the numerator. So let's simplify the first one, which is actually the most confusing.
$( \frac{ p^{5} }{ p^{-3} q^{-4} } )^{ \frac{1}{4} }$
Multiplying the exponents you get:
$( \frac{ p^{ \frac{5}{4} } }{ p^{- \frac{3}{4} } q^{-1} })$
Subtracting the denominator from the numerator between the common base of p you get this:
$\frac{ p^{ \frac{5}{4}- (-\frac{3}{4}) } }{ q^{-1} }$
Doing that math gives you
$\frac{ p^{2} }{ \frac{1}{q} }$ which equals $\frac{ p^{2} }{1} * \frac{q}{1}$ which is $p^{2}q$ , or the third one down.

The next one:
$( \frac{ p^{2} q^{7} }{ q^{4} } )^{ \frac{1}{2} }$
simplifies to:
$\frac{p* q^{ \frac{7}{2} } }{ q^{2} }$
and subtracting the power of the denominator from the power of the numerator gives you:
$p q^{ \frac{3}{2} }$ , which is the last choice.
$( p^{6}q \frac{3}{2})^{ \frac{1}{3} }$
simplifies to:
$( p^{6* \frac{1}{3} } )( q^{ \frac{3}{2}* \frac{1}{3} })$
which simplifies very nicely to:
$p^{2}q^{ \frac{1}{2} }$ , which is the first choice. The other one is found by process of elimination!

8 0

4 years ago

A plan traveled for a total of 2,773 miles over the course of 8 hours. Heading south, the plan traveled at an average speed of 3

AlexFokin [52]

Answer:

5 hours

Step-by-step explanation:

Let s and w represent hours spent traveling south and west, respectively. The problem statement tells us ...

s + w = 8 . . . . . . total trip time

344s + 351w = 2773 . . . . total mileage (using d = s·t)

By Cramer's rule, we can find the value of s as ...

s = (1(2773) -351(8))/(1(344) -351(1)) = -35/-7 = 5

The plane was heading south for 5 hours.

_____

Comment on Cramer's rule

For the equations ...

ax +by = c

dx +ey = f

The solution for x can be found to be ...

x = (bf-ec)/(bd-ea)

Similarly, the solution for y is ...

y = (cd-fa)/(bd-ea)

5 0

3 years ago

Ivanna is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a num

saul85 [17]

Answer:

The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.

I guess that we want to find the expected value in one spin:

number 1: wins $1

number 2: wins $3

number 3: wins $5

number 4: wins $7

number 5: losses $8

number 6: loses $8

The expected value can be calculated as:

Ev = ∑xₙpₙ

where xₙ is the event and pₙ is the probability.

We know that the probability for all the events is 1/6, so we have:

Ev = ($1 + $3 + $5 + $7 - $8 - $8)*(1/6) = $0

So the expected value of this game is $0, wich implies that is a fair game.

8 0

3 years ago

Which of the following is true about the relationship between the slopes of the lines whose equations are 8x - 9y = 5 and 9x - 8

AlexFokin [52]

The answer is they are reciprocal.

(1) Express both equations in the slope-intercept form: y = mx + b, where m is slope:
 8x - 9y = 5
9y = 8x - 5
y = 8/9x - 5/9
m1 = 8/9

9x - 8y = 1
8y = 9x - 1
y = 9/8x - 1/8
m2 = 9/8

So, m1 = 8/9 and m2 = 9/8. They are reciprocal

3 0

3 years ago

Read 2 more answers

Find the eighth term of a geometric sequence for which a,3 = 35 and r= 7.​

Find the eighth term of a geometric sequence for which a,3 = 35 and r= 7.