All categories

2 years ago

Which of the following represents a valid first step to solving this system of equations using the substitution method?

Mathematics

1 answer:

Phoenix [80]2 years ago

7 0

Answer:

2(2y - 1) - y = 7

Step-by-step explanation:

I guess the 2 equations are

2x - y = 7

x = 2y - 1

substitution message that you use one equation to express one variable by the other, and then you use that in the other equation to get one equation for one variable. then you solve for that, and use that result in the first equation to since for the second variable.

the equations are already defined that way, that the second equation directly defines x as an excision of y.

so, this needs to be used then in the first equation.

and that makes

2(2y - 1) - y = 7

the correct first step.

You might be interested in

Guys help me with this quick pls

Virty [35]

Answer:

$117 = 66 + \beta \\ \beta = 51$

6 0

3 years ago

Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v

k0ka [10]

I'll use subscript notation for brevity, i.e. $\frac{\partial f}{\partial x}=f_x$ .

By the chain rule,

$z_u=z_xx_u+z_yy_u$

$z_v=z_xx_v+z_yy_v$

$z_w=z_xx_w+z_yy_w$

We have

$z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}$

and

$\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}$

When $u=1,v=1,w=0$ , we have

$\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}$

and the partial derivatives take on values of

$\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}$

So we end up with

$\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}$

3 0

3 years ago

Lane is ten times Mel's age. if the difference in their age is 27, how old is Mel?

Digiron [165]

If one number is ten times the other one, then the big wide open space
between them with the wind blowing through it is the other nine times it.

The 27 years is 9 times Mel's age.

Mel is 27/9 =<em> 3 years old</em>.

Lane is (3 + 27) = 30 years old.

Lane is (30/3) = 10 times Mel's age.
The difference is (30 - 3) = 27 years.

3 0

4 years ago

Find the area of triangle ABC to the nearest tenth. Inabc, a=11 c=11 b=100°.

lys-0071 [83]

Answer:

59.6 square units

Step-by-step explanation:

The area is given by the formula ...

area = (1/2)ac·sin(B)

Fill in the given numbers and do the arithmetic.

area = (1/2)(11)(11)(sin(100°)) ≈ 59.6 . . . . square units

7 0

4 years ago

What is the value of x to the nearest tenth?

lorasvet [3.4K]

Answer:

X = 26.3

Step-by-step explanation:

7 0

4 years ago