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2 years ago

SELECT ALL EXPRESSIONS THAT ARE EQUIVALENT TO (2)(-3)(-4)

2 answers:

8 0

In this problem you have: 2(-3)(-4). After doing the math you should get 24. The ones that are equivalent are:
(12)(2) and (-4)(-6)

denis-greek [22]2 years ago

5 0

Answer:

3rd and 4th one.

Step-by-step explanation:

So we can just do this by simplifying each expression

The expression we are comparing the answers to is:

because

(-6) (-4) = 24

So now we just see which ones are equal to 24.

1). -24 (no)

2). -24 (no)

3). 24 (yes)

4). 24 (yes)

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Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1]

Alekssandra [29.7K]

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

<u>Given expression is </u>

$\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }$

can be rewritten as

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

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\$

And

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\$

So, using this identity, we

$\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }$

can be further rewritten as

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}$

$\rm \: = \: \dfrac{4}{25 - 1}$

$\rm \: = \: \dfrac{4}{24}$

$\rm \: = \: \dfrac{1}{6}$

<u>Hence, </u>

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}$

4 0

2 years ago

The local train heading for Westford at 60km/h and the express train heading for Eastford at 80 km/h pass each other at Centervi

Wewaii [24]

Answer:

The maximum distance to the nearest kilometer between Westford and Centerville is 111.43 km.

Step-by-step explanation:

Local train stats:

Rate = 60 km/h

Distance = x km

Time = x/60 hours

Express train stats:

Rate = 80 km/h

Distance = $(195-x)$ km

Time = $(195-x)/80$ hours

Now we will equate both the times.

$x/60 =(195-x)/80$

$x/3= (195-x)/4$

$4x= 585-3x$

$7x= 585$

x = 83.57 km

$195-x=195-83.57= 111.43$ km

Hence, the maximum distance to the nearest kilometer between Westford and Centerville is 111.43 km.

3 0

3 years ago

The dimensions of a right rectangular prism are shown below. 1 in. 1a in. 2 in. in. How many cubes with side lengths of inch are

Dafna1 [17]

First we neeed to find the volume of the rectangular prism

$V=\text{ l}\times w\times h$ $V=1\times1\frac{1}{6}\times2\frac{1}{6}$ $=1\times\frac{7}{6}\times\frac{13}{6}$ $=\frac{91}{36}in^3$

Volume of cube with side lengths 1/6 = 1/6 x 1/6 x 1/6 = 1/216

The number of cubes needed to fill the prism without gaps or overlaps =

$=\frac{91}{36}\text{ divide by }\frac{1}{216}$ $=\frac{91}{36}\times\frac{216}{1}$ $=\frac{19656}{36}$ $=546$

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1 year ago

= Solving a word problem with two unknowns using a linear... A washer and a dryer cost $650 combined. The washer costs $100 less

nikdorinn [45]

Answer:

Washer 225

Dryer 425

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2 years ago

The sum of x and ten is twenty( write the equation

iren [92.7K]

Answer:

2x10=20 X=2

Step-by-step explanation:

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2 years ago

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