How can you use base ten blocks to find 2.16 divided by 3

Answers

Answer 1

Answer: For this question, let's move the decimal number 2 spaces to the right. 2.16-->216You need 21 ten rods and 6 cubes. Why: I wouldn't do 2 hundred flats because 2 isn't divisible by 3.Put the ten rods into 3 equal group, then do the same with the cubes.You should end up with 7 in each group since 21 divided by 3 is 7.You should also end up with 2 cubes in each group.So in one group you have 72. Now move the decimal back to where it came from, 2 spaces to the left. Now you have 0.72.

Answer 2

Answer:

Final answer:

Using base ten blocks to divide 2.16 by 3 involves representing 2.16 with the blocks, then dividing them into three equal groups. The result is 0.72.

Explanation:

To use base ten blocks to find 2.16 divided by 3, we first represent the number 2.16 using base ten blocks. This can include two 1-blocks, one 1/10-block (which represents 0.1), and six 1/100-blocks (which represent 0.1 each). Then we divide these blocks evenly among three groups, as we're dividing by 3.

Each group would end up with 0.72, as we would distribute the 1-blocks, the 1/10-block, and the 1/100-blocks evenly among the 3 groups. Therefore, 2.16 divided by 3 is 0.72 when using base ten blocks.

Learn more about Division using base ten blocks here:

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A. Show that the ratios 10/20 and 30/60 form a proportion by finding a common multiplier.B. Show that the ratios in part (A) are equal by writing them in simplest form.

Answers

Answer:

$\text{(A) Hence, The ratio }(10)/(20)\text{ form a proportion by common multiplier 3 to get }(30)/(60)$

$\text{(B) Hence, Both ratio are equal to }(1)/(2)\text{ in simplest form. }$

Step-by-step explanation:

(A) We need to show both fraction of same proportion.

Ratio 1: $(10)/(20)$

If we multiply by 3 at numerator and denominator

$\RIghtarrow (10* 3)/(20* 3)$

$\RIghtarrow (30)/(60)$

$\RIghtarrow (30)/(60) \text{ is equivalent ratio of second one }\frec{30}{60}$

$\text{Hence, The ratio }(10)/(20)\text{ form a proportion by common multiplier 3 to get }(30)/(60)$

(B) Now we simplify both ration into simplest form

$\Rightarrow (10/ 10)/(20/ 10)=(1)/(2)$

$\Rightarrow (30/ 30)/(60/ 30)=(1)/(2)$

$\Rightarrow (1)/(2)=(1)/(2)$

$\text{Hence, Both ratio are equal to }(1)/(2)\text{ in simplest form. }$

Need help ASAP1) A new truck that sells for $42,000 depreciates 11% each year. write a function that models the value of the truck. Find the value of the truck after 8 years. Round to the nearest dollar.

2) Earl mows lawns one weekend. He earns $15 for each lawn that he mows. He spends $50 on gas and other supplies. What function equation represents Earl's profit from mowing x lawns?

A)f(x)=50x-15
B)f(x)=50x+15
C)f(x)=15x-50
D)f(x)=15+50

3) find the common geometric series.
-2,-4,-8,-16.....

Answers

Answer:

$\boxed{1) V = 40 000(0.89)^(n), \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_(n) = -2^(n)}$

Step-by-step explanation:

1) Depreciation

The formula for the value V of an asset after depreciation by an annual percentage rate is

V = P(1 - r)ⁿ

where

P = present value

r = annual percentage rate

n = number of years

Data:

V = 40 000

r = 11 % = 0.11

n = 8 yr

Calculations:

(a) Function model

V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ

The function model is $\boxed{ V= 40 000(0.89)^(n) }$

(b) Future value

V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746

In eight years, the truck will be worth $\boxed{ \text{\$15 476}}.$

2) Profit function

Income from 1 lawn = $15

Income from x lawns = 15x

Less gas and supplies = -50

Net income = 15x – 50

The function is $\boxed{f(x) = 15x - 50}$ .

3) Geometric series

(a) Calculate the common ratio

a₁ = -2

a₂ = -4

a₃ = -8

a₄ = =16

The ratios of consecutive pairs are

a₄/a₃ = -16/(-8) = 2

a₃/a₂ = -8/(-4) = 2

a₂/a₁ = -4/(-2) = 2

All adjacent pairs have the same common ratio r = 2.

(b) Write the formula for the series

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

If a₁ = -2, the formula for the series is

aₙ = -2(2)ⁿ⁻¹ = -2ⁿ

The formula for the series is $\boxed{a_(n) = -2^(n)}$ .

What is 7 - (4 2/3) = to ?

Answers

Answer: 2.33333333333

Step-by-step explanation:

Answer:

6.34

Step-by-step explanation:

(4 2/3)= 0.66

7-0.66= 6.34

Jessica was solving an equation. After she finished simplifying, her result was 0=2. This result confused her. Explain to Jessica what her result means. Explain your reasoning thoroughly.

Answers

It means that the equations are not true. The straight lines are always parallel to the X-axis in all cases Therefore, the line doesn't cut the X-axis. This means that: there is no solution to the equation

Jessica's result means that any value of x (or any variable she used) would not be a solution to the equation. When something like 0 = 2 comes up, they answer is no solution.

For Your Information:

If you get 2=2 or 0=0 or anything like that, the solutions are all real numbers. Any value of x (or any variable used) will be a solution to the equation.

Please comment to let me know you understand. I hope this was helpful!

Two cars start from the same place driving at the same rate, one heading north and the other heading east. After two hours the car heading north has traveled 150 miles and the car heading east has traveled 100 miles. How far apart are the cars at this time?

Answers

Answer:

180.2776 miles

Step-by-step explanation:

Given that two cars start from the same place.

One car is heading towards north and another east.

that means the two cars travel path make 90 degrees at the origin.

Imagine the triangle with one vertex at the starting place right angled at 90 and other two vertices are the locations of the two cars.

We find this triangle has legs of 150 miles and 100 miles respectively.

The distance between the two cars = length of the hypotenuse of the right triangle with legs 150 and 100 miles

= √(150^2)+100^2 (Using Pythagorean theorem)

= √32500

= 180.2776 miles

Answer:

they are 250 miles apart

|150|+|-100|=250

one side of the square is 10 units. which is greater, the number of square units for the area of the square or the number of units for the perimeter? explain.

Answers

It is the area because the perimeter is 10+10+10+10=40 but the area is 10*10=100.

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