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yKpoI14uk [10]
3 years ago
9

Which expression is equivalent to (4x^3)(2x)^-4

Mathematics
2 answers:
BabaBlast [244]3 years ago
7 0

Given: The equation (4x^{3})(2x)^{-4}

To Find: The simplified expression

Solution: \frac{1}{4x}

Calculation/Explanation: The equation can be simplified in the follwing way by using the Rules of Exponents.

4x^{3}(2x)^{-4} \\\\= \frac{4x^{3}}{(2x)^{4}} \\\\=\frac{4x^{3}}{16x^{4}}\\\\=\frac{1}{4}x^{3-4} \\\\=\frac{1}{4}x^{-1}\\\\ =\frac{1}{4x}

We have used two <u>Rules of Exponents</u>

  1. For any integer a, x^{-a}= \frac{1}{x^{a}}
  2. And for any integers a, b, x^{a-b}= \frac{x^a}{x^b}
liubo4ka [24]3 years ago
3 0
(4x^3)(2x)^-4=(4x^3)<span> (2^-4)(x^-4)
=(4/16)(x^-1) = 1/4x
The answer is 1/4x</span>
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A line passes through (-2, 3) and has a slope of 0.2. Write an equation of the line.
mars1129 [50]

Answer:

y = 0.2x + 3.4

Step-by-step explanation:

Slope intercept form of line is

y = mx + c

where

m = slope

c is y intercept

given that slope is 0.2 thus, m = 0.2

now equation of line

y = 0.2x + c

now we substitute value of x and y ( (-2, 3) in this equation as given that the given point passes through the line

3 = 0.2*-2 + c

3 = -0.4 + c

c = 3+0.4 = 3.4

put c = 3.4 in equation

y = 0.2x + c

y = 0.2x + 3.4

Thus,

third option , y = 0.2x + 3.4 is the correct answer

3 0
3 years ago
kevin was a product tester at texas instruments. he was dropping calculators from a height of 5 feet on to a concrete surface. h
Shtirlitz [24]

Answer:

80%

Step-by-step explanation:

1 in 5 breaks

1/5 is 20%

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4 0
3 years ago
Which ordered pair is a solution to this equation?
yarga [219]

Let's test each alternative :

2 x - 9 y = 38      ( 7,5 ) :

( 2 * 7 ) -  ( 9 * 5 ) = 38

14 - 45  = 38

-31 ≠ 38   (  wrong )


( 4 , - 1 ) :

( 2 * 4 ) - ( 9 * ( - 1 ) =  38

8 + 9  = 38

17 ≠ 38  ( wrong )

( 3 , - 3 ) :

2 * ( 3 ) - ( 9 * ( - 3 ) = 38

6 + 27 = 38

33 ≠ 38  ( wrong )

( 1 , - 4 ) :

2* ( 1 ) - 9 * ( - 4 ) = 38

2 + 36 = 38

38 = 38    ( Correct alternative )

( 1 , - 4 ) is correct alternative


3 0
3 years ago
An orange grower find that she gets an average yield of 40 bushels per tree when she plants 20 trees on an acre of ground. Each
sdas [7]

Answer:

30 trees/acre

Step-by-step explanation:

Let n = the number of trees added to 1 acre

Let Y(n) = the yield in bushels/acre

Yield in bushels/acre = [bushels/tree] x [trees/acre]

Y(n) = (40-n)*(20+n)

       = 800 - 20n + 40n - n^2

       = n^2 + 20n + 800 ---------------------(1)

The n-value of the vertex ( which is a peak )  is given by the formula:

n(max) = -b/2a

Putting values from equation (1) gives us

n(max) = 10

The grower started with 20 tree/acre and adds 10  more for max yield, so she should plant:  30 trees/acre

and

Maximum yield is 900 bushels/acre.

5 0
4 years ago
Peter's paint company made the same number of gallons of paint on Monday, Tuesday, and Wednesday. On Thursday, they made twice a
umka2103 [35]

Answer:

Peter's company uses on:

Monday = 4 gallons

Tuesday = 4 gallons

Wednesday = 4 gallons

Thursday = 8 gallons

Step-by-step explanation:

If they made a total of 20 gallons over the course of these four days, how many gallons did they make each day? Monday

Let the gallons of paint used be Peter's company on Monday, Tuesday, and Wednesday since it is the same amount be represented by x

On Thursday, they made twice as many as any of the previous days.

= 2x

Hence:

x + x + x + 2x = 20 gallons

5x = 20 gallons

x = 20 gallons/5

x = 4 gallons

Note that:

Thursday = 2x

Hence, = 2 × 4 gallons = 8 gallons

Hence, Peter's company uses on:

Monday = 4 gallons

Tuesday = 4 gallons

Wednesday = 4 gallons

Thursday = 8 gallons

5 0
3 years ago
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