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3 years ago

Can someone help with that?if x+y=2, calculate: P=4x (x-3)+4y(y-3)+8xy

Mathematics

1 answer:

olganol [36]3 years ago

6 0

Answer:

Step-by-step explanation:

P = 4x(x - 3) + 4y(y - 3) + 8xy

= 4x² - 12x + 4y² - 12y + 8xy

= (4x² + 8xy + 4y²) - (12x + 12y)

= 4(x² + 2xy + y²) - 12(x + y)

= 4(x + y)² - 12(x + y)

x+y =2 ⇒ P = 4.2² - 12.2 = 16 - 24 = -8

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50 points!!!

fenix001 [56]

Answer: A

Step-by-step explanation: once you line the numbers up in order from least the greatest, the two middle numbers will be 12. Add 12 + 12 and you get 24. Then divide it by 2 and get 12. That is your median. Your 1st quartile will be 10. Your second quartile will be 15. Your minimum number is 4 and your maximum number is 18.

6 0

2 years ago

Aaron was offered a job that paid a salary of \$57,000$57,000 in its first year. The salary was set to increase by 1% per year e

Jobisdone [24]

Answer:

The total amount received is: $1906650

Step-by-step explanation:

Given

$a = \$57000$ --- initial

$b = 1\%$ --- rate

$n = 29$ --- time

Required

Determine the total amount at the end of 29 years

The given question is an illustration of geometric progression, and we are to solve for the sum of the first n terms

Where $n = 29$

$r = 1 + b$

$r = 1 + 1\%$

Express percentage as decimal

$r = 1 + 0.01$

$r = 1.01$

The required is the calculated using:

$S_n = \frac{a(r^n - 1)}{r - 1}$

So, we have:

$S_n = \frac{57000 * (1.01^{29} - 1)}{1.01 - 1}$

$S_n = \frac{57000 * (1.3345- 1)}{0.01}$

$S_n = \frac{57000 * 0.3345}{0.01}$

$S_n = \frac{19066.5}{0.01}$

$S_n = 1906650$

<em>The total amount received is: $1906650</em>

8 0

3 years ago

Simplify the expression csc(-x)/1+tan^2x)

Charra [1.4K]

Assuming ya meant $\frac{csc(-x)}{1+tan^2(x)}$

to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos

for the pythaogreaon identity
$cos^2(x)+sin^2(x)=1$
divide both sides by $cos^2(x)$
$1+tan^2(x)=sec^2(x)$ since $\frac{sin(x)}{cos(x)}=tan(x)$
subsitute
$\frac{csc(x)}{sec^2(x)}$

recall that $csc(x)=\frac{1}{cos(x)}$
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore $csc(-x)=\frac{1}{cos(-x)}=\frac{1}{cos(x)}=csc(x)$
so we get

$\frac{csc(x)}{sec^2(x)}$
decompose them into $\frac{1}{cos(x)}$ and $\frac{1}{sin^2(x)}$ to get $\frac{\frac{1}{cos(x)}}{\frac{1}{sin^2(x)}}$
multiply by $\frac{sin^2(x)}{sin^2(x)}$ to get
$\frac{sin^2(x)}{cos(x)}$
we can furthur simlify to get
$(\frac{sin(x)}{cos(x)})(sin(x))=tan(x)sin(x)$
the expression simplifies to tan(x)sin(x)

5 0

3 years ago

Read 2 more answers

Find the angle of depression from point A to point C.<br><br> Angle of depression= ?

san4es73 [151]

Check the picture below.