A line passes through the point (10, -1) and has a slope of 3/2 .

The general term of an arithmetic sequence is tn = 32 + 3n, where n ∈N and n ≥ 1. The sequence is A) 32, 35, 38, 41, 44, 47,...

den301095 [7]

Answer:

35,38,41,44,47,50,....

Step-by-step explanation:

n ∈N means that n is an element of Natural numbers

Natural numbers are whole non-negative numbers

n ≥ 1, means that n = 1, 2, 3, 4, 5, 6,........

tn = 32 + 3n

the first term t1 = 32 + 3(1)

32 + 3 = 35

the second term t2 = 32 + 3(2)

32 + 6 = 38

the third term t3 = 32 + 3(3)

32 + 9 = 41

5 0

4 years ago

What is the sum or difference of 1/6 plus 1/6

Sever21 [200]

2/6 because you just add the top number but not the bottom.

4 0

3 years ago

Read 2 more answers

Solve each inequality for x. (Enter your answers using interval notation.)

olganol [36]

Answer:

(a) ln(x) = 0

Then 0 < x < 1

(b) e^x > 2

Then ln2 < x < ∞

(a) ln(3x - 17) = 5

x = 55.1377197

ln(a + b) + ln(a - b) - 5ln(c)

= ln[(a² - b²)/c^5]

Step-by-step explanation:

First Part.

(a) ln(x) < 0

=> x < e^(0)

x < 1 ....................................(1)

But the logarithm of 0 is 1, and the logarithm of negative numbers are undefined, we can exclude the values of x ≤ 0.

In fact the values of x that satisfy this inequalities are between 0 and 1.

Therefore, we write:

0 < x < 1

(b) e^x > 2

This means x > ln2

and must be finite.

We write as:

ln2 < x < ∞

Second Part.

(a) ln(3x - 17) = 5

3x - 17 = e^5

3x = 17 + e^5

x = (1/3)(17 + e^5)

= 55.1377197

Third Part.

We need to write

ln(a + b) + ln(a - b) - 5ln(c)

as a single logarithm.

ln(a + b) + ln(a - b) - 5ln(c)

= ln(a + b) + ln(a - b) - ln(c^5)

= ln[(a + b)(a - b)/(c^5)]

= ln[(a² - b²)/c^5]

3 0

3 years ago

3. Represents the sets with a Venn diagram: U = {1,2,3,4,5,6,7,8,9, 10, 11, 12} A = {1,2,3,4,6, 12} B = {1,2,4,8}

damaskus [11]

Answer:

See explanation and picture attached

Step-by-step explanation:

A set can be described by<em> listing all of its elements</em>.

For example, A = { 2, 4, 6, 8}, which we read as

“A is the set whose elements are 2, 4, 6 and 8”.

The four elements of the set are separated by commas, and the list is enclosed between curly brackets.

A <em>set can also be described by writing a description of its elements</em> between curly brackets.

Thus the set A above can also be written as

A = { even natural numbers less than 9 }, which we read as

“A is the set of even natural numbers less than 9”.

A set can also be described graphically by using Venn diagrams, which are simply circle shaped drawings showing the elements inside.

In our case U={1,2,3,4,5,6,7,8,9,10,11,12} A={1,2,3,4,6,12} B={1,2,4,8}

See picture attached for the answer.

8 0

3 years ago

A rectangle with a length of x+5 has a perimeter of 4x+14 a. Write an equation for the width of a rectangle in terms of x b. Sup

EastWind [94]

Answer:

B : Length is 12, Width is 9

D: Area is 108

Step-by-step explanation:

Finding x:

Since the Perimeter is 42, subtract 14 from 42 to get 28. Then divide that by 4 to get 7. x = 7. Since x = 7 then 7 + 5 = 12. So the length is 12.

Figuring out the width:

When we find the perimeter we add all the sides, so 12 + 12 = 24 and 42 - 24 = 18. Divide 18 by 2 to get 9 and then add 12 + 12 + 9 + 9 just to check your answer

Since the you know the legnht and width, you now have to multiply them to fine the area. 12 x 9 = 108

3 0

3 years ago