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3 years ago

In 2013, Mary worked for Company A. Her salary for the year was $18 750.

Mathematics

1 answer:

Nataly [62]3 years ago

5 0

Answer:

the answer is $2

Step-by-step explanation:

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What is the area of figure shown below!??

Novosadov [1.4K]

Answer:26

Step-by-step explanation:

Add them all up

8 0

3 years ago

Use Cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17

V125BC [204]

Looks like the system is

x + 4y - z = -14

5x + 6y + 3z = 4

-2x + 7y + 2z = -17

or in matrix form,

$\mathbf{Ax} = \mathbf b \iff \begin{bmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -14 \\ 4 \\ -17 \end{bmatrix}$

Cramer's rule says that

$x_i = \dfrac{\det \mathbf A_i}{\det \mathbf A}$

where $x_i$ is the solution for i-th variable, and $\mathbf A_i$ is a modified version of $\mathbf A$ with its i-th column replaced by $\mathbf b$ .

We have 4 determinants to compute. I'll show the work for det(A) using a cofactor expansion along the first row.

$\det \mathbf A = \begin{vmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{vmatrix}$

$\det \mathbf A = \begin{vmatrix} 6 & 3 \\ 7 & 2 \end{vmatrix} - 4 \begin{vmatrix} 5 & 3 \\ -2 & 2 \end{vmatrix} - \begin{vmatrix} 5 & 6 \\ -2 & 7 \end{vmatrix}$

$\det \mathbf A = ((6\times2)-(3\times7)) - 4((5\times2)-(3\times(-2)) - ((5\times7)-(6\times(-2)))$

$\det\mathbf A = 12 - 21 - 40 - 24 - 35 - 12 = -120$

The modified matrices and their determinants are

$\mathbf A_1 = \begin{bmatrix} -14 & 4 & -1 \\ 4 & 6 & 3 \\ -17 & 7 & 2\end{bmatrix} \implies \det\mathbf A_1 = -240$

$\mathbf A_2 = \begin{bmatrix} 1 & -14 & -1 \\ 5 & 4 & 3 \\ -2 & -17 & 2 \end{bmatrix} \implies \det\mathbf A_2 = 360$

$\mathbf A_3 = \begin{bmatrix} 1 & 4 & -14 \\ 5 & 6 & 4 \\ -2 & 7 & -17 \end{bmatrix} \implies \det\mathbf A_3 = -480$

Then by Cramer's rule, the solution to the system is

$x = \dfrac{-240}{-120} \implies \boxed{x = 2}$

$y = \dfrac{360}{-120} \implies \boxed{y = -3}$

$z = \dfrac{-480}{-120} \implies \boxed{z = 4}$

5 0

2 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B60%7D%20%2F%5Csqrt%7B5%7D%20%28in%20radical%20form%29" id="TexFormula1" title="\sqrt

FinnZ [79.3K]

$2\sqrt{3}$

------------------------

Steps:

1st write out equation

$\frac{\sqrt{60}}{\sqrt{5}} \\$

Second write the conjugant and multiply it.

$\frac{\sqrt{60}}{\sqrt{5}} * \frac{\sqrt{5} }{\sqrt{5} }$

After multiplying you should get,

$\frac{10\sqrt{3}}{5}$

now after simplifying you should get

$2\sqrt{3}$

3 0

3 years ago

On another day, Martin bought 123

MArishka [77]

123 I think but let me know if it's right

3 0

3 years ago

Read 2 more answers

Sena determines the remainder of 4x32−14x16+2x3−8x−1, using the remainder theorem. How does she proceed to the correct answer? D

Flauer [41]

Answer: x = 1 and -16

Explanation:

(4x^32 - 14x^16 + 2x^3 - 8)/x - 1

x - 1 = 0
x = 1

f(x) = 4x^32 - 14x^16 + 2x^3 - 8
f(1) = 4(1)^32 - 14(1)^16 + 2(1)^3 - 8
f(1) = 4 - 14 + 2 - 8
f(1) = -10 - 6
f(1) = -16

Therefore, the remainder is -16

4 0

3 years ago