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3 years ago

6

Kim has small wooden cube shaped blocks. To make the next size cube, she needs 8 blocks. Write a sequence to show the number of

blocks needed for each increasingly larger cube. Include at least 6 terms in the sequence.

1 answer:

ipn [44]3 years ago

5 0

The situation describes a geometric sequence with first term as 1, and the common ratio of 8.

1st term = 1
2nd term = 1 x 8 = 8
3rd term = 8 x 8 = 64
4th term = 64 x 8 = 512
5th term = 512 x 8 = 4,096
6th term = 4,096 x 8 = 32,768

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A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take

Allisa [31]

Answer:

1/30 of a ton

Step-by-step explanation:

Write this as an expression:

1/3 of a ton and 1/2 of a ton were taken to the site.

4/5 of a ton were remove from the site.

Amount of a ton at the site = $\frac{1}{3}+ \frac{1}{2}- \frac{4}{5}$

Solve the equation by finding <u>common denominators</u> (when the bottom numbers are the same).

$(\frac{1}{3}+ \frac{1}{2})- \frac{4}{5}$ Focus on the first part. The least common multiple (LCM) of 3 and 2 is "6", which will become the denominator.

For <u>1/3 to become ?/6</u>, multiply top and bottom by 2.

For <u>1/2 to become ?/6</u>, multiply top and bottom by 3.

$(\frac{2}{6}+ \frac{3}{6})- \frac{4}{5}$

Now we can add the numerators together over the same denominator.

$\frac{5}{6}- \frac{4}{5}$

Do the same thing as before and change the denominators. The LCM of 6 and 5 is "30".

For <u>5/6 to become ?/30</u>, multiply top and bottom by 5.

For <u>4/5 to become ?/30</u>, multiply top and bottom by 6.

$\frac{25}{30}- \frac{24}{30}$

Subtract the numerators:

$\frac{1}{30}$ Answer in tons

Therefore there was 1/30 of a ton of rock left at the construction site.

7 0

3 years ago

Read 2 more answers

You have been averaging 55 sales per day. Per our new policy, everyone needs to increase his or her sales per day by 10% in the

Mariulka [41]

To find your new number of sales per month, you will need to find the number of sales you have per month (based on 30 days per month).

55 x 20 = 1650 sales.

Than, you will need to calculate what 10% of this is and add it to your original sales number.

0.1 (10%) x 1650 = 165

1650 + 165 = 1815

You will need approximately 1815 sales based on the 30 day month.

8 0

3 years ago

Nine increased by the product of a number and 2 is less than or equal to 27.

Naily [24]

Answer:

x≤9

Step-by-step explanation:

9+2x≤27

1) Subtract both sides by 9:

2x≤18

2) Divide both sides by 2:

x≤9

8 0

4 years ago

I don't know how many thousandths go in 5,000 ones

Verizon [17]

5,000,000 is the answer.
5,000÷0.001=5,000,000

7 0

3 years ago

(½) (6x + 3) = 7 – (3x + 1)

erastovalidia [21]

$\tt Step-by-step~explanation:$

To solve for x, we have to remember to isolate the variable.

$\tt Step~1:$

For 1/2, we can make that 0.5, since their values are equivalent. Our equation:

$\tt (0.5)(6x+3)=7-(3x+1)$

Let's distribute the 0.5 first.

$\tt 0.5*6x=3x\\0.5*3=1.5$

$\tt Step~2:$

Now, let's simplify the right side of the equation. We have to distribute the negative to 3x and 1.

$\tt -1*3x=-3x\\-1*1=-1$

Then, we simplify the entire expression.

$\tt 7-3x-1=-3x+6$

$\tt Step~3:$

Our equation now:

$\tt 3x+1.5=-3x+6$

Let's add 3x to the right and 3x to the left to simplify the -3x on the right side of the equation.

$\tt 3x(+3x)+1.5=-3x (3x)+6\\6x+1.5=6$

$\tt Step~4:$

Let's do the same thing we did in Step 3 to 1.5. Subtract 1.5 on both sides of the equation.

$\tt 6x+1.5(-1.5)=6(-1.5)\\6x=4.5$

$\tt Step~5:$

Finally, we divide both sides by 6 to isolate x.

$\tt \frac{6x}{6} =x\\\frac{4.5}{6}= 0.75~or~\frac{3}{4}$

$\large\boxed{\tt Our~final~answer:~x=0.75~(or~\frac{3}{4})}$

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3 years ago