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3 years ago

7.14 + 33=100 = /100 + 33/100

Mathematics

1 answer:

tatiyna3 years ago

7 0

Answer:

First off 7.14 + 33 ≠ 100,

Step-by-step explanation:

7.14 + 33=100 = /100 + 33/100 i don't know what this means

7.14 + 33 = 100 100/100 = 7.14/100 + 33/100

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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

PLZ HELP!!!!

gizmo_the_mogwai [7]

The answer to the second question is 8/15

3 0

3 years ago

Read 2 more answers

You have a square garden that has an area of 400 square yards what is the length of one side of the garden

sashaice [31]

The area of a square is S^2 with S as one side. To find the length of the side, simply work the formula backwards. The square root of 400 is 20. Hope this helps! :)

5 0

3 years ago

5/8= x + 1/12. What is x

raketka [301]

Answer:

0.54166666666

Step-by-step explanation:

5/8= x + 1/12

-1/12 -1/12

x= 0.54166666666

6 0

3 years ago

Two Fifths of the vegetables in Priya's garden are tomatoes.

IgorLugansk [536]

Let
V-------------> total vegetables in Priya's garden
T------------> total tomatoes in Priya's garden

we know that
T=(2/5)V

Part A) HOW many tomatoes are there I'd Priya's garden has.

1) 20 Vegetables?
T=(2/5)*20----------> 20*2/5---------> 8 tomatoes
the answer Part A1) is 8 tomatoes

2) x Vegetables?
T=(2/5)*x----------> x*2/5---------> (2/5)*x ----------> 0.40*x tomatoes
the answer Part A2) is (0.40)*x tomatoes

Part B) Priya's garden has 6 tomatoes. How many total vegetables are there?

T=(2/5)V-----------> V=5T/2--------> V=(5*6)/2--------> V=15 vegetables

the answer part B) is 15 vegetables

5 0

3 years ago