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3 years ago

14

Twenty-eight people in student council are running for the offices of president and vice-president. In how many different ways c

an those offices be assigned?
55
378
756

1 answer:

motikmotik3 years ago

5 0

I think the answer is 55

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What is the solution of the system? Use elimination.

sweet [91]

Answer:

The solutions to the system of the equations by the elimination method will be:

$x=2,\:z=-1,\:y=2$

Step-by-step explanation:

Given the system of the equations

$2x\:+\:2y\:+z\:=\:7$

$-x-\:y\:+z\:=\:-5$

$x+3y-4z=12$

solving the system of the equations by the elimination method

$\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}$

$\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10$

$\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}$

$-2x-2y+2z=-10$

$+$

$\underline{2x+2y+z=7}$

$3z=-3$

$\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}$

$2x+6y-8z=24$

$-$

$\underline{2x+2y+z=7}$

$4y-9z=17$

$\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}$

Rearranging the equations

$\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}$

solve $3z=-3$ for z:

$z=-1$

$\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1$

solve $4y-9\left(-1\right)=17$ for y:

$4y-9\left(-1\right)=17$

$4y+9=17$

$4y=8$

$y=2$

$\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2$

solve $2x+2\cdot \:2-1=7$ for x:

$2x+2\cdot \:2-1=7$

$2x+3=7$

$2x=4$

$x=2$

Therefore, the solutions to the system of the equations by the elimination method will be:

$x=2,\:z=-1,\:y=2$

5 0

3 years ago

What is the recursive formula for this geometric sequence<br><br>4,-12,36,-108...

Natalka [10]

$a_{n+1}$ = - 3 $a_{n}$ with $a_{1}$ = 4

To find the next term in the sequence multiply the previous term by - 3

the common ratio r = $\frac{-108}{36}$ = $\frac{36}{-12}$ = - 3

$a_{n+1}$ = $a_{n}$ × r ← recursive formula

7 0

3 years ago

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Classify the following number. Select all that apply.<br>-3 IrrationalRationalIntegerWholeNatural

SOVA2 [1]

-3 is a irrational,integer

8 0

3 years ago

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A car that retails for $14,999 has a sticker on the windshield that says, "$429/mo for 48 months." What interest rate is this ca

kkurt [141]

14,999(1+.o825)^4= 20,595. $429x48 months= 20,592
Interest rate 8 1/4%

Check 20592/14999= 1.37289
Log(1.37289)/ log(1.0825)= 3.99 years

4 0

3 years ago

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Help please quickly thank you so much

STALIN [3.7K]

Answer:

120 deg

Step-by-step explanation:

4 0

3 years ago

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