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Marta_Voda [28]

2 years ago

7

A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the teams change in field posit

ion after the 3 plays.

1 answer:

patriot [66]2 years ago

4 0

Subtract 5 each play so go backwards from zero and you should finish at -15

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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

3 years ago

Y= -8/9 (x+1)+6 <br> convert to standard form

Trava [24]

Answer:

mm

kl l

Step-by-step explanation:

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2 years ago

Give two ways to write each algebraic expression in words. 4+×

KATRIN_1 [288]

Answer:

the sum of 4 and a number

4 plus a number

4 0

3 years ago

A certain arithmetic sequence has the following explicit formula for the nth term: an = 3 + (n - 1)(8) The same sequence has the

zhuklara [117]

From the explicit formula:
an=3+(n-1)8
simplifying this we get:
an=3+8n-8
an=8n-5
thus
the recursive formula is:
an=an-1+
the missing part is the common difference which is 8

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3 years ago

How many lines are symmetry

VladimirAG [237]

Answer:

specify which shape's symmetry do you want

6 0

3 years ago

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