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4 years ago

Rewrite the polynomial 6x4 − 24x3 + 72x2 by factoring out the GCF

1 answer:

3 0

The trick here is to recognize one or more factors common to each term. For example, 6x4 − 24x3 + 72x2 = x^2(6x^2 - 24x + 72), so x^2 is one common factor. Looking at (6x^2 - 24x + 72), you can easily see that 6 is a common factor, so now we have (6)(x^2)(x^2 - 4x + 12). These last 3 terms do not have a common factor, so the factoring process stops here:

(6)(x^2)(x^2 - 4x + 12)

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A plastic sun visor allows light to pass through but reduces the intensity of the light. the intensity is reduced by 5% if the p

irinina [24]

Answer: The equation is f(x) = $0.95^{x}$ ;

The piece of plastic has to have 10mm of thickness.

Step-by-step explanation: It is known that with 1 mm of thickness, 5% of the intensity is reduced. So, 95% of the light is transmitted.

For each milimetre added, "more" 95% of light is transmitted.

For example, if another milimetre of plastic is added, another 0.95 of light is transmitted:

0.95.0.95 = 0.9025 of light reach the visor

So, the model that relate thickness of plastic and intensity of light is:

f(x) = $0.95^{x}$

in which:

f(x) is the intensity of light;

x is thickness in mm;

Using the equation, the thickness necessary to reduce intensity to 60% is:

f(x) = $0.95^{x}$

0.6 = $0.95^{x}$

log 0.6 = log $0.95^{x}$

x. log (0.95) = log (0.6)

x = $\frac{log 0.6}{log 0.95}$

x = 9.95

x ≈ 10

The thickness necessary to reduce intensity of light to 60% is 10mm.

6 0

3 years ago

Read 2 more answers

Picasso's Phone Shop charges $65.54 for its activation fee plus $13.10 for every gigabyte, g, of data you use over your limit. T

konstantin123 [22]

Answer:

$13.10 represents the rate of change

Step-by-step explanation:

13.1 is the only value in the equation with a variable (g). There is an additional $13.10 charge for every gigabyte used over the limit, and this is the rate of change.

For example, if 5 gigabytes were used over the limit, the charge would be 13.1(5) or $65.50

6 0

2 years ago

7) 72, 43, 15, 66, 32, 72, 52, 19, 28, 81 Mean : Median Mode Range

adell [148]

Mean (Average) 48
Median 47.5
Range 66
Mode 72, appeared 2 times
Geometric Mean 41.680398411848
Largest 81
Smallest 15
Sum 480
Count 10

8 0

3 years ago

Standard form of a point that goes through-2,4 and the slope is -1/7

lesantik [10]

Answer:

Standard form of a line passing through (-2, 4) and having slope of -1/7 is x + 7y = 26

Solution:

Given that we need to determine standard form of a line that goes through (-2 , 4) and slope of the line is -1/7

Standard form of line passing through point ( a , b ) and having slope m is given by

(y – b) = m ( x – a) --------(1)

In our case given point is ( -2 , 4 ) and slope is -1/7 that means

a = -2 , b = 4 , m = -(1/7)

On substituting given value of a , b and m is equation (1) we get

$(y-4)=\left(-\frac{1}{7}\right)(x-(-2))$

$=>(y-4)=\left(-\frac{1}{7}\right)(x+2)$

=> 7( y - 4 ) = -x – 2

=> 7y + x = -2 + 28

=> x + 7y = 26

Hence standard form of a line passing through (-2,4) and having slope of –(1/7) is x + 7y = 26

8 0

3 years ago

Evaluate the series. A)125 B) 38 C) 210 D) 165

Reika [66]

165 is answer we also use a formula
5 ( n/2(2a + ( n-1)d)
in that n=6 ,a=3 , d= 1

4 0

3 years ago

Read 2 more answers