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3 years ago

Select the three statements that represents a unit rate.

Mathematics

1 answer:

tino4ka555 [31]3 years ago

7 0

Answer:

6 chairs per table

6 stickers per page

25 miles per hour

Step-by-step explanation:

Each one of these three answers has a ratio of x:1

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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

Pls helpppppppppl!!!!

Troyanec [42]

Answer:

I dont really understand it but I think it's the first one cuz that's the only one that makes sense to me hope it helped tho:))))))))

8 0

3 years ago

Read 2 more answers

Drag the point around to graph more horizontal lines. What is the general equation of a horizontalline?

svetlana [45]

A horizontal line is one for which the value of y is the same for the entire length of the line. Therefore this type of line can be expressed as below:

$y=c$

Where "c" is a constant that changes the position of the line on the coordinate plane. If c is equal to 2, then we have a constant line that crosses the y-axis at the position 2 for example.

7 0

2 years ago

Buy recycling 1 ton of paper 6953 gallons of water are saved how many gallons are water are saved by recycling 4 tons of paper

9966 [12]

27812 gals because you would have to multiply 6953 and 4

8 0

3 years ago

A ladder 20 feet long leans against a building forming and angle of 46 degrees with the level ground. To the nearest foot how fa

sleet_krkn [62]

Answer:

The distance of the foot of the ladder to the building is 14 ft.

Step-by-step explanation:

The length of ladder = 20 ft

Angle formed by ladder with level ground, θ = 46

We are required to find out the distance of the foot of the ladder from the building

The above question can be found out by using trigonometric relations as follows;

$Cos\theta = \frac{Adjacent\, side \, to\, angle}{Hypothenus\, side \, of\, triangle}$

The adjacent side of the right triangle formed by the ladder the building and the ground is the distance of the foot of the ladder from the building

The hypotenuse side is the length of the ladder = 20 ft

Therefore;

Adjacent side of triangle = Hypotenuse × cosθ

∴ Distance of the foot of the ladder from the building = Hypotenuse × cosθ

Distance of the foot of the ladder from the building = 20 ft × cos(56)

Distance of the foot of the ladder from the building = 13.893 ft

To the nearest foot, the distance of the foot of the ladder to the building = 14 ft.

7 0

3 years ago