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4 years ago

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tim and his brother are building towers out of blocks. Tim is using blue blocks that are 6 cm tall and his brother is using gree

n blocks that are 8 cm tall. They both made towers the same height. What is the shortest possible height of the tower? how many of each color block did they use

1 answer:

Karolina [17]4 years ago

7 0

The shortest possible height of tower is 24 cm.

Tim used 4 blue blocks and his brother used 3 green blocks.

Step-by-step explanation:

Given,

Height of blue block = 6 cm

Height of green block = 8 cm

We will take least common multiple to find the shortest possible height.

6 = 2*3

8 = 2*2*2

LCM = 2*2*2*3 = 24 cm

The shortest possible height of tower is 24 cm.

Number of blue blocks used = $\frac{24}{6} = 4$

Number of green blocks used = $\frac{24}{8} = 3$

Tim used 4 blue blocks and his brother used 3 green blocks.

Keywords: LCM, multiplication

Learn more about multiplication at:

#LearnwithBrainly

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Lucy took out a $15,000 to buy her new car. The bank charged her 8% simple interest rate for the term of 5 years. What is the en

MA_775_DIABLO [31]

Answer:

<h2>$21000</h2>

Step-by-step explanation:

This problem is on simple interest calcultion

A=P(1+r*n)

where

A=accumulated amount (final)

P= principal amount (initial), $15,000

r=interest written as decimal, 8% = 8/100= 0.08

n=number of years, 5years

Substituting into the expression we have

A=15000(1+0.08*5)

A= 15000(1+0.4)

A=15000(1.4)

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3 years ago

In 2008, the price of gasoline was $2.79 per gallon. In 2009, the price of gasoline was

ikadub [295]

Answer:

36%

Step-by-step explanation:

line up $ and % data like this:

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cross multiply

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divide both sides by 2.79

X= 3.79*100 / 2.79 ≈ 136%

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3 years ago

What is the answer to -5 ( 4w +12) =15 make sure you write the answer as a decimal

seropon [69]

Answer:

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Step-by-step explanation:

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8 0

4 years ago

Read 2 more answers

Rationalise the denominator of:<br>1/(√3 + √5 - √2)

Paul [167]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} }$

can be re-arranged as

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} - \sqrt{2} + \sqrt{5} }$

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} }$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \dfrac{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

So, using this, we get

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5}) }^{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{5 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{ - ( - \sqrt{3} + \sqrt{2} + \sqrt{5}) }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}}$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\rm \: = \: \dfrac{- \sqrt{18} + \sqrt{12} + \sqrt{30}}{2 \times 6}$

$\rm \: = \: \dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}$

$\rm \: = \: \dfrac{- 3\sqrt{2} + 2 \sqrt{3} + \sqrt{30}}{12}$

Hence,

$\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} } =\dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}}}$

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<h3><u>More Identities to </u><u>know:</u></h3>

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6 0

3 years ago

Which expressions are equivalent to the one below? Check all that apply. 21^x/3^x

satela [25.4K]

Answer:

<em>options: A,C,E </em>are correct.

Step-by-step explanation:

We have to find the expression equivalent to the expression:

$\dfrac{21^x}{3^x}$

we know that: $21^x=(3\times7)^x\\\\21^x=3^x\times7^x$

Hence,

$\dfrac{21^x}{3^x}=\dfrac{3^x\times7^x}{3^x}=7^x$ -----(1)

A) $(\dfrac{21}{3})^x= 7^x$ (same as(1))

Hence, option A is correct.

B) 7 ; which is a different expression from (1)

Option B is incorrect.

C) $7^x$ (Same as (1))

Option C is correct.

D) $(21-3)^x=18^x$ which is a different expression from (1)

Hence, option D is incorrect.

E) $\dfrac{7^x\times3^x}{3^x}=7^x$ ; which is same as (1)

Hence, Option E is correct.

F) $3^x$ ; which is not same as expression (1)

Hence, option F is incorrect.

5 0

4 years ago

Read 2 more answers