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4 years ago

Find the range of the function. f(x) = (x + 5)2 + 8

1 answer:

6 0

Finding the vertex of the parabola
<span>y = (x + 5)^2 + 8 the vertex is at (-5, 8)
its coefficient so the parabola turns upward so the range is [8 , inf]</span>

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two years of local internet service cost $6855, including the installation fee of $85. What is the monthly fee?

Artemon [7]

First subtract the installation price:
6855-85= 6,770

Then divide 6,770 by 24(12 months in 1 yr.):
6770/24= $282.08

Your monthly fee is $282.08

5 0

3 years ago

The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

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4 years ago

PLS HELP 25 POINTS NO CAP PLS BRAINLEIST

Oliga [24]

Answer:

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7 0

3 years ago

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Help pls!! I’ll give Brainlist!! For questions 1-5 determine if the quadrilaterals are parallelograms or not. Beside the picture

tia_tia [17]

Answer:

1. no

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Step-by-step explanation:

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3 years ago

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Of 560 marbles in a bag, 65% are red and the rest are blue. After 28 red marbles are replaced with blue ones, how many blue marb

jonny [76]

Answer: The answer is 400 blue marbles.

Step-by-step explanation: Given that there are 560 marbles in a bag, out of which 65% are red and rest are blue.

So, number of red marbles is

$n_r=65\%\times 560=\dfrac{65}{100}\times 560=364,$

and number of blue marbles is

$n_b=560-364=196.$

Now, if 28 red marbles are replaced by blue marbles, the the new number of red and blue marbles will be

$n_r^\prime=364-28=336~~~\textup{and}~~~n_b^\prime=196+28=224.$

Now, to get 65% of the marbles blue, we need to add some more blue marbles to the bag. Let 'x' number of blue marbles are added to the bag, then

$65\%\times (560+x)=224+x\\\\\Rightarrow \dfrac{65}{100}\times (560+x)=224+x\\\\\Rightarrow 13(560+x)=20(224+x)\\\\\Rightarrow 7280+13x=4480+20x\\\\\Rightarrow 7x=2800\\\\\Rightarrow x=400.$

Thus, 400 blue marbles need to be added to the bag.

5 0

3 years ago

Read 2 more answers