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Bezzdna [24]
3 years ago
12

You are putting together your first post-graduation budget. Your take-home or net pay will

Mathematics
1 answer:
DanielleElmas [232]3 years ago
7 0

Answer:

B) you have a deficit of 175

Step-by-step explanation:

Add up all of your costs per month and subtract that from your net pay.

ie: 2500-2675=-175

Since the answer is negative, and you don't make the extra $175 dollars needed to cover all your costs, it is a deficit.

If you made $2675 a month and your total expenses were 2500, then you would have a surplus of $175. Because it is money that you still have and don't need to use for anything specific.

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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
3 years ago
The equation shows the relationship between x and y:
wlad13 [49]

Answer: -7

Step-by-step explanation:

The equation is in slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept

Therefore, the m value is -7 and it is the slope

4 0
2 years ago
What is the simplified form of the quantity of x plus 6, all over the quantity of x plus 4 + the quantity of x minus 3, all over
11Alexandr11 [23.1K]

Answer:

<u>(x² + 4x + 6)/ 3x + 12</u>

<u>This is the most simplified form</u>

Step-by-step explanation:

Let's simplify the expression:

(x + 6)/(x + 4) + (x - 3)/3

Least Common Denominator : 3 * (x + 4)

[3 * (x + 6) + (x - 3) (x + 4)]/ 3 * (x + 4)

Solving parentheses:

[3x + 18 + x² - 3x + 4x - 12]/ 3 * (x + 4)

Like terms:

<u>(x² + 4x + 6)/ 3x + 12</u>

<u>This is the most simplified form</u>

6 0
4 years ago
Angle of rotation(including direction of rotation)
arlik [135]
What is the question
7 0
3 years ago
(1 point) Your velocity is given by v(t)=2t2+8 in m/sec, with t in seconds. Estimate the distance, s, traveled between t=0 and t
yKpoI14uk [10]

Answer:

The estimated distance is 405 meter.

Step-by-step explanation:

Given : Your velocity is given by v(t)=2t^2+8 in m/sec, with t in seconds.

To find : Estimate the distance, s, traveled between t=0 and t=8 ?

Solution :

We have to integrate the function from 0 to 8 to get the distance.

Integrate v(t)=2t^2+8 w.r.t  t,

\int\limits^8_0 {2t^2+8} \, dt

We know, \int\limits {x} \, dx=\frac{x^2}{2}

=[\frac{2t^3}{3}+8t]^8_0

=(\frac{2(8)^3}{3}+8(8))-(\frac{2(0)^3}{3}+8(0))

=(\frac{1024}{3}+64)-(\frac{0}{3}+8(0))

=\frac{1024+192}{3}

=\frac{1216}{3}

=405.33

The estimated distance is 405 meter.

5 0
4 years ago
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