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3 years ago

Factor the following expression completely 16x^5-x^3

Mathematics

2 answers:

Gnom [1K]3 years ago

8 0

X^(16x^2-1) factor the expression

The answer to the graph
X^3(4x-1)(4x+1)

Eduardwww [97]3 years ago

7 0

Answer:

x^3(4x + 1)(4x - 1)

Step-by-step explanation:

To start, let's note that to factor something, we need to GCF (Greatest common factor). Notice that we have a 16 and 1 as the coefficients, but because there is a 1, there is a coefficient of 1 in the GCF. Now notice that in x^5 and x^3, the GCF is x^3. So, we get x^3(16x^2 - 1). But, we are not done yet! 16x^2 - 1 is a difference of squares, where a^2 - b^2 = (a + b)(a - b), so a is 4x and b is 1, so we get (4x + 1)(4x - 1), so the final answer is x^3(4x + 1)(4x - 1).

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Directed line segment has endpoints P(– 8, – 4) and Q(4, 12). Determine the point that partitions the directed line segment in a

larisa86 [58]

Answer:

Point (1,8)

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

$[x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}]$

Let us substitute coordinates of point P and Q as:

$x_1=-8$ ,

$y_1=-4$

$x_2=4$

$y_2=12$

$m=3$

$n=1$

$[x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}]$

$[x=\frac{12-8}{4},y=\frac{36-4}{4}]$

$[x=\frac{4}{4},y=\frac{32}{4}]$

$[x=1,y=8]$

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

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2 years ago

CAT FOODA grocery store is selling 6 cans of cat food for $3. Write and solve an equation to find the cost of a can of cat food.

Digiron [165]

Answer:

6 * 3 = 18

Step-by-step explanation:

4 0

2 years ago

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Ivan, a botanist, treated a 2 cm plant with a special growth fertilizer. With this fertilizer,

chubhunter [2.5K]

Answer

poop

jsjeiwowkwkw i siemens iwejwns. die ensue i we diei iyyo i yea ma’am i thank you for picking out the car for me today thank youuu so much for bc thank you for bc hbu had to do my streaks

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3 years ago

A trapezoid has an area of 780 square meters. The height of the trapezoid is 40 meters, and the length of the longer base is tw

o-na [289]

Answer:

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2 years ago

Please help! How on earth do I do this? In the year 2015, Anna bought a new car for $36,000. In 2017, she was told that the valu

Klio2033 [76]

Part A

Purchase Value of Anna's Car in 2015 = $36,000

Depreciated Value of Anna's Car in 2017 = $25,000

We know that the value of the car is depreciating linearly.

From the above data, we can see that the value of the car has reduced by $36,000-$25,000 = $11,000 over 2 years.

⇒ Per year the value has been depreciated by $\frac{11000}{2}$

⇒ Per year the value has been depreciated by $5,500

So if the value of a car in 2015 is V₀ then value of the car after t years can be determined by the below function:

V (t) = V₀ - (t*5,500), where t indicates the years passed since 2015

OR V (t) = 36,000 - (t*5,500), where t indicates the years passed since 2015

Part B

Suggested value of Anna's car for trade in option in 2018 = $15,000

In 2018, 3 years would have been passed since 2015. Using the value of t = 3 in the function determined in Part A:

V(3) = V₀ - (3*5,500)

⇒ V(3) = 36,000 - (16,500)

⇒ V(3) = $19,000

From the above calculations, we can see that the value of the car in 2018 should be $19,000, however the suggested value for trade in is indicated as $15,000 which is lower than what the value of the car should be. Hence, basis linear depreciation, the $15,000 value is not fair for the car in 2018.

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3 years ago