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4 years ago

Simplify the expression to a polynomial in standard form:

Mathematics

1 answer:

maksim [4K]4 years ago

4 0

Answer:

$(144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2)$

Step-by-step explanation:

To better understand the question we need to properly format the expression

$(4x^2+x-1)(-3x^2-3x-3)(4x^2+x-1)(-3x^2-3x-3)$

as we can see we have three brackets, we can proceed by first opening the first two brackets, we have.

$(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\$

we then continue by collecting like terms

$=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)$

we then solve for the remaining two brackets

$(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\$

we then continue by collecting like terms

$=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)$

from the two brackets we obtained $(-12x^4-15x^3-12x^2+3)$ each, we now have to multiply both terms together and solve we have

$(-12x^4-15x^3-12x^2+3)(-12x^4-15x^3-12x^2+3)\\=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\$

collecting and summing all like terms we have

$=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\=144x^8+180x^7+180x^7+144x^6+255x^6+180x^5+180x^5-36x^4+144x^4-36x^4-45x^3-45x^3-36x^2-36x^2\\\\\=144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2$

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Can someone please answer this for me I'm begging

GrogVix [38]

If the length of JK is 16.4 miles, it will be diameter of this circle, the radius will be JK/2 = 8.2 miles

As we know the length of circle is 2π*r in this case r = 8.2

The arc JM is 1/4 length of the whole circle so arc JM = (2π*8.2)*(1/4) = 2π*8.2/4 = π*8.2/2 = π*4.1

if we assume that π=3.14 the answer will be 3.14 * 4.1 = 12.874.... And as the answer needs to be rounded to the nearest tenth it will be 12.874≈12.9

So the answer will be 12.9

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4 years ago

A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Kar

ch4aika [34]

Answer:

We conclude that the mean waiting time is less than 10 minutes.

Step-by-step explanation:

We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.

Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes.

Let $\mu$ = mean waiting time for bus number 14.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 10 minutes {means that the mean waiting time is more than or equal to 10 minutes}

Alternate Hypothesis, $H_A$ : $\mu$ < 10 minutes {means that the mean waiting time is less than 10 minutes}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean waiting time = 7.8 minutes

s = sample standard deviation = 2.5 minutes

n = sample of different occasions = 18

So, test statistics = $\frac{7.8-10}{\frac{2.5}{\sqrt{18} } }$ ~ $t_1_7$

= -3.734

The value of t test statistics is -3.734.

Now, at 0.01 significance level the t table gives critical value of -2.567 for left-tailed test.

Since our test statistic is less than the critical value of t as -3.734 < -2.567, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean waiting time is less than 10 minutes.

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4 years ago

There are 9 more pencils than pens in a container. There are 25 writing utensils in the container. How many pens are there in th

SCORPION-xisa [38]

Answer:

Step-by-step explanation:

n=pens

n+9=25

solve for n

n=16

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3 years ago

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Test 21,753 for divisibility by 2, 3, 5, 9, and 10.

geniusboy [140]

Answer:

21,753 is divisible by 3 and 9

Step-by-step explanation:

A number is divisible by 2 if last digit of a number is 0, 2, 4 ,6 ,8

A number is divisible by 3 if sum of digits is divisible by 3.

A number is divisible by 5 if last digit of a number is 0 or 5

A number is divisible by 9 if sum of digits is divisible by 9

A number is divisible by 10 if last digit is 0.

So, according to these rules option (a) 3 ,9 is correct

Therefore , 21,753 is divisible by 3 and 9.

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3 years ago

Please help me thank you

S_A_V [24]

Question 1:

We have a 45-45-90 right triangle with the hypotenuse being the length from one corner to the opposite corner.

Multiply 30 ft with the square root of 2 and use a calculator to help give you numerical value to get your answer.

$30 \sqrt{2} \approx 42$

Your answer is the second choice.

Question 2:

The equilateral triangle can be divided into 2 30-60-90 triangles with the longer leg being the altitude. To get half of the side length of the right triangle, divide the altitude by the square root of 3.

$\dfrac{15}{ \sqrt{3} }=\dfrac{15 \sqrt{3} }{3}=5 \sqrt{3}$

The full side length is double of that, which is $10 \sqrt {3}$ .

Multiply that by 3 to get the full perimeter.
$10 \sqrt{3}*3=30 \sqrt{3}$

Your answer is the third choice. Hope this helps! :)

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4 years ago

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