All categories

2 years ago

Which of these is a correct identity? x + 4x = 5x 6x = 18 2x + 1 = 7 7x + 9 = x

Mathematics

1 answer:

dolphi86 [110]2 years ago

7 0

Answer:

x + 4x = 5x

Step-by-step explanation:

An identity is a mathematical equation that is always true (here - for all possible x's).

a). x + 4x = 5x; this is true, because for any possible x

x+4x = (1 + 4)x = 5x; there's not much to add.

b). 6x=18; evaluates to

x = 3; so it only works for one x, not all possible xs.

c). 2x + 1 = 7

2x = 6

x = 3; so it only forks for one x

d). 7x + 9 = x

6x + 9 = 0; we could compute the exact x it works for from here, but suffice to say this doesn't work for x = 0.

You might be interested in

Use Lagrange multipliers to find the maximum and minimum values of

marusya05 [52]

The Lagrangian is

$L(x,y,\lambda)=x+8y+\lambda(x^2+y^2-4)$

It has critical points where the first order derivatives vanish:

$L_x=1+2\lambda x=0\implies\lambda=-\dfrac1{2x}$

$L_y=8+2\lambda y=0\implies\lambda=-\dfrac4y$

$L_\lambda=x^2+y^2-4=0$

From the first two equations we get

$-\dfrac1{2x}=-\dfrac4y\implies y=8x$

Then

$x^2+y^2=65x^2=4\implies x=\pm\dfrac2{\sqrt{65}}\implies y=\pm\dfrac{16}{\sqrt{65}}$

At these critical points, we have

$f\left(\dfrac2{\sqrt{65}},\dfrac{16}{\sqrt{65}}\right)=2\sqrt{65}\approx16.125$ (maximum)

$f\left(-\dfrac2{\sqrt{65}},-\dfrac{16}{\sqrt{65}}\right)=-2\sqrt{65}\approx-16.125$ (minimum)

5 0

3 years ago

X + y = k

liraira [26]

Hello,
Adding the 2 equations,
x+y+x-y=k+k ==>2x=2k==>x=k
if x=k, y=k-k=0
solution is (k,0)

7 0

2 years ago

Read 2 more answers

Makayla is teaching Rodney how to construct a square inscribed in a circle.

Yuliya22 [10]

Answer:

Step-by-step explanation:

6 0

3 years ago

What is 32/23 as a decimal rounded to the nearest hundredth<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B32%7D%7B23%7D%20"

Softa [21]

Answer:

1.39

Step-by-step explanation

32/23 = 1.39130434783

round: 1.39

7 0

3 years ago

Two angles in a triangle have measures of 25° and 55°.

rosijanka [135]

Answer:

B) 100

Step-by-step explanation:

All 3 interior angles of a triangle add up to 180 so:

x + 25 + 55 = 180

x + 80 = 180

x = 180 - 80

x = 100

4 0

3 years ago