<img src="https://tex.z-dn.net/?f=%20%5Cbold%7B%2810x%20-%206x%C2%B3%20%2B%208x%C2%B2%29%20-%20%285x%C2%B2%20%2B%2012x%C2%B3%20-

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2 years ago

%204%29%E2%80%8B%7D" id="TexFormula1" title=" \bold{(10x - 6x³ + 8x²) - (5x² + 12x³ - 4)}" alt=" \bold{(10x - 6x³ + 8x²) - (5x² + 12x³ - 4)}" align="absmiddle" class="latex-formula">

Mathematics

2 answers:

Serjik [45]2 years ago

5 0

Answer:

$\boxed{\sf -18x^3+3x^2+10x+4}$

Explanation:

$\rightarrow \sf (10x - 6x^3 + 8x^2) - (5x^2 + 12x^3 - 4)$

distribute

$\rightarrow \sf 10x - 6x^3 + 8x^2 - 5x^2 - 12x^3 + 4$

collect terms

$\rightarrow \sf -6x^3-12x^3+3x^2+10x+4$

add similar terms

$\rightarrow \sf -18x^3+3x^2+10x+4$

barxatty [35]2 years ago

3 0

Answer:

$-18x^3+3x^2+10x+4$

Step-by-step explanation:

Given:

$(10x-6x^3+8x^2)-(5x^2+12x^3-4)$

Apply the rule (a) = a:

$\implies 10x-6x^3+8x^2-(5x^2+12x^3-4)$

$\textsf{Use the distributive law} \quad -(a+b)=-a-b:$

$\implies 10x-6x^3+8x^2-5x^2-12x^3-(-4)$

Apply the rule -(-a) = a:

$\implies 10x-6x^3+8x^2-5x^2-12x^3+4$

Collect like terms:

$\implies -6x^3-12x^3+8x^2-5x^2+10x+4$

Combine like terms:

$\implies -18x^3+3x^2+10x+4$

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choli [55]

Answer:

$29.50

Step-by-step explanation:

The price that Rob paid includes a 15% discount. This means that Rob paid 85% of the original price.

100% - 15% = 85%

Divide the price Rob paid by the percentage the price is of the total.

85% = 0.85

50.15/0.85 = 59

Now, divide the total price by 2 so that you can find the price of one pair of jeans.

59/2 = 29.50

The price of one pair of jeans is $29.50

5 0

3 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably norma

Nataliya [291]

Answer:

The degrees of freedom is 11.

The proportion in a t-distribution less than -1.4 is 0.095.

Step-by-step explanation:

The complete question is:

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the proportion in a t-distribution less than -1.4 if the samples have sizes 1 = 12 and n 2 = 12 . Enter the exact answer for the degrees of freedom and round your answer for the area to three decimal places. degrees of freedom = Enter your answer; degrees of freedom proportion = Enter your answer; proportion

Solution:

The information provided is:

$n_{1}=n_{2}=12\\t-stat=-1.4$