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3 years ago

10

Find the 11th term of the sequence 11, 19, 27, 35

1 answer:

iragen [17]3 years ago

7 0

Answer:

91

Step-by-step explanation:

Each term is 8 more than the last, so you can write the terms of the sequence until you get there:

11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91

__

Or, you can use the formula for the general term of an arithmetic sequence. You have first term a1=11 and common difference d=8.

an = a1 +d(n -1)

a11 = 11 + 8(11 -1) = 11 + 80

a11 = 91

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Solve the following system of equation

krok68 [10]

Answer:

x = 6 , y = -4 , Z = -1

Step-by-step explanation:

Solve the following system:

{2 x + 3 y - Z = 1 | (equation 1)

3 x + y + 2 Z = 12 | (equation 2)

-3 + x + 2 y = -5 | (equation 3)

Express the system in standard form:

{2 x + 3 y - Z = 1 | (equation 1)

3 x + y + 2 Z = 12 | (equation 2)

x + 2 y+0 Z = -2 | (equation 3)

Swap equation 1 with equation 2:

{3 x + y + 2 Z = 12 | (equation 1)

2 x + 3 y - Z = 1 | (equation 2)

x + 2 y+0 Z = -2 | (equation 3)

Subtract 2/3 × (equation 1) from equation 2:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+(7 y)/3 - (7 Z)/3 = -7 | (equation 2)

x + 2 y+0 Z = -2 | (equation 3)

Multiply equation 2 by 3/7:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+y - Z = -3 | (equation 2)

x + 2 y+0 Z = -2 | (equation 3)

Subtract 1/3 × (equation 1) from equation 3:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+y - Z = -3 | (equation 2)

0 x+(5 y)/3 - (2 Z)/3 = -6 | (equation 3)

Multiply equation 3 by 3:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+y - Z = -3 | (equation 2)

0 x+5 y - 2 Z = -18 | (equation 3)

Swap equation 2 with equation 3:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+5 y - 2 Z = -18 | (equation 2)

0 x+y - Z = -3 | (equation 3)

Subtract 1/5 × (equation 2) from equation 3:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+5 y - 2 Z = -18 | (equation 2)

0 x+0 y - (3 Z)/5 = 3/5 | (equation 3)

Multiply equation 3 by 5/3:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+5 y - 2 Z = -18 | (equation 2)

0 x+0 y - Z = 1 | (equation 3)

Multiply equation 3 by -1:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+5 y - 2 Z = -18 | (equation 2)

0 x+0 y+Z = -1 | (equation 3)

Add 2 × (equation 3) to equation 2:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+5 y+0 Z = -20 | (equation 2)

0 x+0 y+Z = -1 | (equation 3)

Divide equation 2 by 5:

{3 x + y + 2 Z = 12 | (equation 1)

0 x+y+0 Z = -4 | (equation 2)

0 x+0 y+Z = -1 | (equation 3)

Subtract equation 2 from equation 1:

{3 x + 0 y+2 Z = 16 | (equation 1)

0 x+y+0 Z = -4 | (equation 2)

0 x+0 y+Z = -1 | (equation 3)

Subtract 2 × (equation 3) from equation 1:

{3 x+0 y+0 Z = 18 | (equation 1)

0 x+y+0 Z = -4 | (equation 2)

0 x+0 y+Z = -1 | (equation 3)

Divide equation 1 by 3:

{x+0 y+0 Z = 6 | (equation 1)

0 x+y+0 Z = -4 | (equation 2)

0 x+0 y+Z = -1 | (equation 3)

Collect results:

Answer: {x = 6 , y = -4 , Z = -1

6 0

3 years ago

Find the following values from the information given<br> cot(theta°); tan(theta°) = −0.0005

Greeley [361]

Answer:

cot(θ°) = 2000 radians

Step-by-step explanation:

Data provided in the question:

The value of tan(θ°) = −0.0005

To solve:

cot(θ°)

Now,

we know the relation between cot and tan function as:

cot(θ°) = $\frac{1}{\tan\theta}$

therefore on substituting the value of theta in the above relation, we can find the value of cot(θ°)

Thus,

cot(θ°) = $\frac{1}{-0.0005}$

or

cot(θ°) = 2000

5 0

2 years ago

2. Ingrid Sering sells two types of garden fountains on a straight commission basis. On one fountain that sells for $869, she ge

spin [16.1K]

Answer:

$9,102

Step-by-step explanation:

Ingrid Sering sells two types of garden fountains on a straight commission basis. On one fountain that sells for $869, she gets a commission of $174. On the other fountain that sells for $1,260, she gets $252.During a 3-month selling season, Ingrid sold 19 of the lower-priced fountains and 23 of the higher-priced fountains. What were her total commissions for three months

From the question above, we have the following information:

On one fountain that sells for $869 = she gets a commission of $174( the lower-priced fountains)

On the other fountain that sells for $1,260 = she gets $252 ( the higher-priced fountains)

Ingrid sold 19 of the lower-priced fountains)

1 fountain sold = $174 of commission

19 fountains sold =

$174 × 19

= $3,306

She also sold 23 of the higher-priced fountains)

1 higher priced fountains = $252

23 higher priced fountains =

$252 × 23

= $5,796

Hence, the Total commission Ingrid made = Total commission on Lower priced fountains + Total commission on Higher priced fountains

= $3,306 + $5,796

= $9,102

Therefore, the total commission Ingrid made = $9,102

3 0

3 years ago

In order to join a yoga class, you pay a $100 annual fee plus an additional $5 for each class you go to. What is the average cos

babunello [35]

Answer:

200$

Step-by-step explanation:

5x20=100 plus 100 from annual

7 0

3 years ago

2^x times 1/32=32<br> Show work please<br> Will give Brainliest answer

NARA [144]

Answer:

hmmm tough question

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers