Find the volume of the right triangle retangular prism

Name the property:

Naddik [55]

Answer:

Distributive Property

Step-by-step explanation:

3 0

3 years ago

A geometric sequence has second term 12 and fifth term 324. A) find common ratio b) calculate 10th term c) the kth term is the f

Alborosie

Answer:

a) find common ratio = 3

b) calculate 10th term = 78732

c) k = 7

Step-by-step explanation:

A geometric sequence has second term 12 and fifth term 324.

a) find common ratio

Common ratio = r

Hence

We solve for this below:

r = cube root(fifth term/second term)

r = cube root (324/12)

r = cube root (27)

r = 3

Therefore, the common ratio = 3

b) calculate 10th term

The formula for a geometric sequence is given as:

an = ar^n-1

Where

a = First term

r = Common ratio = 3

n = Nth term = 10

Step 1

We have to find the first term

Common ratio = Second term/First term

Common ratio = 3

Second term = 12

Hence:

3 = 12/x

Cross Multiply

3x = 12

x = 12/3

x = 4

Hence , First term = 4

Step 2

We find the 10th term

an = ar^n-1

a10 = 4 × 3^10 - 1

a10 = 4 × 3⁹

a10 = 4 × 19683

a10 = 78732

Therefore, the 10th term = 78732

c) the kth term is the first term that is greater than 2000. Find the value of K

For kth term,

ak = ar^k-1 >2000

a = 4, r = 3

Hence

4 × 3^k-1 > 2000

We divide both sides by 4

4 × 3^k-1/4 > 2000/4

3^k-1 > 500

We take the logarithm of both sides

log 3^k-1 > log 500

k-1 log 3 > log 500

Divide both sides by log 3

k-1 log 3/log 3 > log 500/log 3

k - 1 > 5.6567800693

k > 5.6567800693 + 1

k > 6.6567800693

k = 7

Therefore, k = 7

6 0

2 years ago

50 POINTS!!!!

mixer [17]

Answer: Option 'B' is correct.

Step-by-step explanation:

since we have given that

Time taken to build a cabinet by Genna = 4 hours.

Time taken to build a cabinet by Claude = 3 hours

Now, time taken by both Genna and Claude to build a cabinet together is to be find.

Work done by Genna is given by

$\frac{1}{4}$

Work done by Claude is given by

$\frac{1}{3}$

According to question,

$\frac{1}{4}+\frac{1}{3}=\frac{1}{x}\\\\\frac{3+4}{12}=\frac{1}{x}\\\\\frac{7}{12}=\frac{1}{x}\\\\x=\frac{12}{7}\\\\x=1\frac{5}{7}\ hours$

Hence, Option 'B' is correct.

7 0

3 years ago

Read 2 more answers

X-(9x-10)+11=12x+3(-2x+ 1/3)

morpeh [17]

X - (9x - 10) + 11 = 12x + 3(-2x + $\frac{1}{3}$ ) equals x = $\frac{10}{7}$ .

First, simplify brackets. / Your problem should look like: x - 9x + 10 + 11 = 12x + 3(-2x + $\frac{1}{3}$ ).
Second, simplify x - 9x + 10 + 11 to -8x + 10 + 11. / Your problem should look like: -8x + 10 + 11 = 12x + 3(-2x + $\frac{1}{3}$ ).
Third, simplify -8x + 10 + 11 to -8x + 21. / Your problem should look like: -8x + 21 = 12x + 3(-2x + $\frac{1}{3}$ ).
Fourth, expand. / Your problem should look like: -8x + 21 = 12x - 6x + 1.
Fifth, simplify 12x - 6x + 1 to 6x + 1./ Your problem should look like: -8x + 21 = 6x + 1.
Sixth, add 8x to both sides. / Your problem should look like: 21 = 6x + 1 + 8x.
Seventh, simplify 6x + 1 + 8x to 14x + 1. / Your problem should look like: 21 = 14x + 1.
Eighth, subtract 1 from both sides. / Your problem should look like: 21 - 1 = 14x.
Ninth, simplify 21 - 1 to 20. / Your problem should look like: 20 = 14x.
Tenth, divide both sides by 14. / Your problem should look like: $\frac{20}{14}$ = x.
Eleventh, simplify $\frac{20}{14}$ to $\frac{ 10}{7}$ . / Your problem should look like: $\frac{10}{7}$ = x.
Twelfth, switch sides. / Your problem should look like: x = $\frac{10}{7}$ which is your answer.

8 0

2 years ago

What is 7 9/13 as an improper fraction

jasenka [17]

7 9/13
= (7×13)+9/13
= 91+9/13
= 98/13 (as an improper fraction).

6 0

3 years ago