MATHEMATICS MIDDLE SCHOOL

A rectangular prism with a volume of 2 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4 unit cubes does it take to fill the prism

Answers

Answer 1

Answer:

Answer:

128

Step-by-step explanation:

Method A.

The volume of the prism is 2 cubic units.

Each cube has side length of 1/4 unit.

The volume of each cube is (1/4)^3 cubic unit.

The volume of each cube is 1/64 cubic unit.

To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.

(2 cubic units)/(1/64 cubic units) =

= 2/(1/64)

= 2 * 64

= 128

Method B.

Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128

Answer 2

Answer:

Answer:

128 cubes.

Step-by-step explanation:

Volume of each cube = (1/4)^3 = 1/64 cubic units.

Number of cubes that will fill the prism

= 2 / 1/64

= 2*42

= 128 answer

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Find the solution set of this inequality|10x+20| ≤10

Answers

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

$|10x+20|\leq 10$

Firstly, we will find critical values

so, let's assume it is equal

$|10x+20|= 10$

now, we can break absolute sign

For $|10x+20|= -(10x+20)$ :

$-(10x+20)= 10$

we can solve for x

$-10x-20= 10$

Add both sides by 20

$-10x-20+20= 10+20$

$-10x= 30$

Divide both sides by -10

and we get

$x=-3$

For $|10x+20|= (10x+20)$ :

$(10x+20)= 10$

we can solve for x

$10x+20= 10$

Subtract both sides by 20

$10x+20-20= 10-20$

$10x= -10$

Divide both sides by 10

and we get

$x=-1$

so, critical values are

$x=-3$

$x=-1$

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For $(-\infty,-3)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

$|10* -5+20|\leq 10$

$|-50+20|\leq 10$

$30\leq 10$

so, this is FALSE

For $[-3,-1]$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

$|10* -2+20|\leq 10$

$|-20+20|\leq 10$

$0\leq 10$

so, this is TRUE

For $(-1,\infty)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

$|10* 0+20|\leq 10$

$|0+20|\leq 10$

$20\leq 10$

so, this is FALSE

so, solution is

[-3,-1]

PLEASE HELP AND ANSWER RIGHT AWAY! I'M TERRIBLE AT MATH!Jeremy ate 1 1/2 tacos at the birthday party. Cecilia ate 2 1/2 times as much as Jeremy.

How many tacos did Cecilia eat?
Express your answer in simplest form.

Answers

$1 (1)/(2) = (3)/(2)\n\n2 (1)/(2) = (5)/(2)\n\n\n\n(3)/(2) * (5)/(2) = (3* 5)/(2* 2) = \huge{\boxed{(15)/(4)=3(3)/(4)}}$

The width of a rectangle is one half its length. The perimeter of the rectangle is 54 cm. What are the width and length of therectangle?
A. 9 cm; 18 cm
B. 18 cm
C. 18 cm; 36 cm

Answers

Answer:

Length of rectangle = 18 cm

Width of rectangle = 9 cm

Step-by-step explanation:

Let the length of rectangle be x

$\therefore \: width \: (w) = (1)/(2) x \n \n perimeter \: of \: rectangle = 54 \: cm \n \therefore \:2(l + w) = 54 \n \therefore \:(l + w) = (54)/(2) \n \therefore \:l + w= 27 \n \n \therefore \:x + (1)/(2) x = 27 \n \n \therefore \:(3)/(2) x = 27 \n \n \therefore \:x = 27 * (2)/(3) \n \n \therefore \:x = 9 * 2 \n \n \huge \red{ \boxed{\therefore \:x = 18}} \n \n \implies \: (1)/(2) x = (1)/(2) * 18 = 9$

Hence

Length of rectangle = 18 cm

Width of rectangle = 9 cm

Evaluate 6j+23+kl−3, when j=3, k=7, and l=33.

Answers

The answer is 269. Hope this helped!! Could I possibly get brainliest!? :)

the answer is 265 to the question

What value of a makes the equation true?1.7a + 0.3a = 4/5
btw 4/5 is a fraction

A. a= 2 4/5
B. a= 1 3/5
C. a= 2/5
D. a= 1 1/5

Answers

Answer: C) a = 2/5

1.7a+0.3a simplifies to 2.0a or just 2a. We have the equation 2a = 4/5. If we multiply each side by 1/2, then we can isolate 'a' fully to get

2a = 4/5

(1/2)*2a = (4/5)*(1/2)

(2/2)a = (4*1)/(5*2)

1a = 4/10

a = 2/5

Which is true about the degree of the sum and difference of the polynomials 3xy - 2xy4 - 7xy and -8xy + 2x°y4 + xy?O Both the sum and difference have a degree of 6.
O Both the sum and difference have a degree of 7.
The sum has a degree of 6, but the difference has a degree of 7.
The sum has a degree of 7, but the difference has a degree of 6.