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3 years ago

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Miyo works for an ice cream vendor. She receives $25 for taking

1 answer:

Natasha2012 [34]3 years ago

5 0

I don’t get the rest

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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

A seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus. How many yards will she need to make costume

Step2247 [10]

Answer:

100 yards

Step-by-step explanation:

It takes 4 yards of fabric to make a costume for one student. She needs to make costumes for every student in chorus, so you just multiply this number by 25 and get 100 yards.

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3 years ago

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Jaime graphed the quadratic y=-2x^2-12x+3. The equation of the line of symmetry of the function is x=-3 What is the vertex of th

miv72 [106K]

Vertex is (-3 , 21 ) you can put <span>y=-2x^2-12x+3 in google and you will see the function</span>

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3 years ago

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An electrician charges a set fee for every house call and then charges an hourly ratedepending on how long the job takes. The to

Luda [366]

We have the equation:

$C(t)=65+60t$

Given the slope-intercept formula for the equation of the line, we have the following:

$\begin{gathered} y=mx+b \\ m\colon\text{ slope} \\ If\text{ C=65+60t} \\ \Rightarrow slope\text{ = 60} \end{gathered}$

Now, since we have that t is the number of hours the electrician spends working, the slope of the function represents the hourly rate charged.

8 0

1 year ago

What’s The coefficient in the expression 7x+ 14

nydimaria [60]

Answer:

7 is the coefficient.

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3 years ago