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timurjin [86]
3 years ago
8

Consider the geometric sequence 16, 8, a, 2, b, ... (a) Write down the common

Mathematics
1 answer:
Artist 52 [7]3 years ago
3 0

Find the common ratio by dividing.

16 / 8 = 2

8 / a = 2

2 / b = 2

The common ratio is 2.

Since we need to find the values of a and b, use the common ratio to solve for them.

8 / 2 = 4 (a)

2 / 2 = 1 (b)

Now, we know that first 5 terms.

We can solve for the 8th term using the previous terms and the common ratio.

6th term: 1 / 2 = 0.5

7th term: 0.5 / 2 = 0.25

8th term: 0.25 / 2 = 0.125

Part A: 2

Part B: a = 4, b = 1

Part C: 0.125

Best of Luck!

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A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of the house
Nina [5.8K]

Answer:

(15,18)

Step-by-step explanation:

write two equations with the information provided.

2x + 3y = 84

x + 4y = 87

use the property of substitution to answer.

x + 4y = 87,   x = 87 - 4y

2(87 - 4y) + 3y = 84

174 - 8y + 3y = 84

174 - 84 = 8y - 3y

90 = 5y

90/5 = y

y = 18

Add the value of Y to an original equation. Solve for X

2x + 3(18) = 84

2x + 54 = 84

2x = 84 - 54

2x = 30

x = 30/2

x = 15

8 0
3 years ago
The area of circle B is 121 times greater than the area of circle A. The radius of circle B is 44. What is the radius of circle
xxMikexx [17]
<em>Formula:</em>
\bigg( \dfrac{radius_1}{radius_2} \bigg)^2 =  \dfrac{area_1}{area_2}

<em>Plug in the values:</em>
\bigg( \dfrac{r}{44} \bigg)^2 = \dfrac{1}{121}

<em>Simplify LHS:</em>
\dfrac{r^2}{1936}  = \dfrac{1}{121}

<em>Multiply by 1936 on both sides:</em>
r^2  = \dfrac{1936}{121}&#10;

<em>Simplify RHS:</em>
r^2 = 16

<em>Square root both sides:</em>
r = 4

Answer: The radius is 4 units. (Answer B)
5 0
3 years ago
What is a possible solution for x+6≥10
ira [324]

Answer:

4,5,6

Step-by-step explanation:

*The sign of ≥ means that it must be greater or equal to 10 in this case

1). 3 isn't a possible solution due to 9 being less than 10

3+6_10

9_10

9<10

2). 4 is a possible solution due to the sum of 4 and 6 being equal to 10

4+6_10

10_10

10=10

3). 5 is a possible solution due to the sum of 5 and 6 being larger than 10

5+6_10

11_10

11>10

4).6 is a possible solution due to the sum of 6 and 6 being larger than 10

6+6_10

12_10

12>10

Hope this helped! (:

6 0
3 years ago
Mathematicians 4: Who is Who?
larisa86 [58]

Answer:

a. x = -9 or x = -2

b. -5(x - 4)

c. x = -3 or x = 5

d. x = ±7

Step-by-step explanation:

a. First person;

y = x² + 11x + 18

y = x² + 9x + 2x + 18

y = x(x + 9) + 2(x + 9)

y = (x + 9)(x + 2)

y = x = -9 or x = -2

b. Second person;

y = -5x + 20

The common factor is 5.

y = -5(x - 4)

c. Third person;

y = x² - 2x - 15

y = x² - 5x + 3x - 15

y = x(x - 5) + 3(x - 5)

y = (x + 3)(x - 5)

y = x = -3 or x = 5

d. Fourth person;

y = x² - 49

Applying the difference of squares formula;

(a² - b²) = (a - b)(a + b)

y = x² - 49 = x² - 7² = (x - 7)(x + 7)

y = (x - 7)(x + 7)

y = x = ±7

6 0
2 years ago
On a certain hot summer’s day, 372 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for a
Alex73 [517]

Answer:

Step-by-step explanation:

7 0
3 years ago
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