Ask question

Ask question

All categories

anzhelika [568]

3 years ago

14

how many 1/2 foot unit cubes can be added to fill the prism completely use what you know about unit cubes or the side lengths of

prism to show your work or explain your answer

1 answer:

Dima020 [189]3 years ago

4 0

Answer:The volume of the cube is 1/2 x 1/2 x 1/2 = 1/8

2646/(1/8) = 21168

Step-by-step explanation:

You might be interested in

Which is an example of an algebraic expression?

kherson [118]

The best option is A) d - 90.

Expressions has no equal sign nor an inequality symbol. An expression has only standard or normal numbers, with variables and some basic mathematical operations.

4 0

3 years ago

Identify the value of C for completing the square

I am Lyosha [343]

Answer: 64

Step-by-step explanation:

6 0

2 years ago

-3x + 1 + 10x = x + 4<br><br> x = 12<br> x = 18

s344n2d4d5 [400]

-3x + 1 + 10x = x + 4

-3x +10x -x = 4 -1

6x = 3

x = 3/6

3 0

3 years ago

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

Marsha is buying a new cell phone. She has a 45% off coupon from the store. She pays $275 for the cell phone. What is the price

jekas [21]

Answer:

The price of the cell phone without the coupon= $500

Step-by-step explanation:

Step 1: Express discounted amount

The discounted amount can be expressed as a function of the original cost of the phone as follows;

D=r×A

where;

D=discounted amount

r=coupon rate

A=original price of the cell phone before the coupon

In our case;

r=45%=45/100=0.45

A=a

replacing;

Discounted amount=(0.45×a)=0.45 a

Step 2: Amount she pays up

Amount she pays=Original cost of cell phone-discounted amount

where;

Amount she pays= $275

original cost of cell phone=a

discounted amount=0.45 a

replacing;

$275=a-0.45 a

0.55 a=275

a=275/0.55

a=500

The price of the cell phone without the coupon= $500

7 0

3 years ago