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4 years ago

Can someone please please please help me it’s ergent

Mathematics

2 answers:

JulsSmile [24]4 years ago

7 0

Answer:

D 192

Step-by-step explanation:

used: new: total

4: 1 : 5

We have 240 stamps

240/5 = 48

Multiply each number by 48

used: new: total

4*48: 1*48 : 5*48

192 : 48 : 240

There are 192 used stamps and 48 new stamps in his collections

yuradex [85]4 years ago

4 0

Answer:

192 used stamps.

Step-by-step explanation:

Since the ratio is 4 used stamps for every new stamp, you can count that as 5 stamps total. Then divide 240 by 5 to get 48. Then multiply that by 4 to get 192.

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Step-by-step explanation:

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3 years ago

Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why th

Veseljchak [2.6K]

If the coefficient matrix has a pivot in each column, it means that it is shaped like this:

$A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]$

So, the correspondant system

$Ax = b$

will look like this:

$\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right]$

This turn into the following system of equations:

$\begin{cases}a_{1,1}x_1+a_{1,2}x_2+a_{1,3}x_3+a_{1,4}x_4=b_1\\a_{2,2}x_2+a_{2,3}x_3+a_{2,4}x_4=b_2\\a_{3,3}x_3+a_{3,4}x_4=b_3\\a_{4,4}x_4=b_4\end{cases}$

The last equation is solvable for $x_4$ : we easily have

$x_4=\dfrac{b_4}{a_{4,4}}$

Once the value for $x_4$ is known, we can solve the third equation for $x_3$ :

$x_3 = \dfrac{b_3-a_{3,4}x_4}{a_{3,3}}$

(recall that $x_4$ is now known)

The pattern should be clear: you can use the last equation to solve for $x_4$ . Once it is known, the third equation involves the only variable $x_3$ . Once

4 0

4 years ago

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y=4x^2+5x-1

Ivanshal [37]

Answer:

Axis of symmetry: $x=-\frac{5}{8}$

Vertex: $(-\frac{5}{8},-2\frac{9}{16})$

Step-by-step explanation:

The given quadratic equation is

$y=4x^2+5x-1$

By comparing to the general quadratic function; $y=ax^2+bx+c$

We have a=4,b=5,c=-1

The equation of the axis of symmetry is given by the formula;

$x=-\frac{b}{2a}$

We got this formula by completing the square on the general quadratic function.

We substitute a=4 and b=5 to obtain;

$x=-\frac{5}{2(4)}$

$x=-\frac{5}{8}$
is the axis of symmetry.

To find the y-value of the vertex, we put $x=-\frac{5}{8}$ into the function to obtain;

$y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1$

$y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1$

$y=-\frac{41}{16}$

The vertex of the given function is $(-\frac{5}{8},-2\frac{9}{16})$

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4 years ago