How would I graph 3x-y=10 and y=x-4

The end points of Line GH are G (10,2) and H(4,8). Find the coordinates of the midpoint M.

nikitadnepr [17]

Answer:

(10-4)/2 , (2-8)/2

6/2 , -6/2

Midpoint = (3,-3)

7 0

2 years ago

If the diagonal of a square is approximately 12.73, what is the length of its sides?

Alja [10]

Answer:

The length of the sides of the square is 9.0015

Step-by-step explanation:

Given

The diagonal of a square = 12.73

Required

The length of its side

Let the length and the diagonal of the square be represented by L and D, respectively.

So that

D = 12.73

The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:

$D^{2} = L^{2} + L^{2}$

Solving further, we have

$D^{2} = 2L^{2}$

Divide both sides by 2

$\frac{D^{2}}{2} = \frac{2L^{2}}{2}$

$\frac{D^{2}}{2} = L^2$

Take Square root of both sides

$\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}$

$\sqrt{\frac{D^{2}}{2}} = L$

Reorder

$L = \sqrt{\frac{D^{2}}{2}}$

Now, the value of L can be calculated by substituting 12.73 for D

$L = \sqrt{\frac{12.73^{2}}{2}}$

$L = \sqrt{\frac{162.0529}{2}}$

$L = \sqrt{{81.02645}$

$L = 9.001469325$

$L = 9.0015$ (Approximated)

Hence, the length of the sides of the square is approximately 9.0015

7 0

3 years ago

I will mark brainiest is my answer is correct? I just got confuse because it saying do not simplify

sasho [114]

Answer:

m^2 +my-my-y^2

Step-by-step explanation:

just dont simplify

6 0

3 years ago

Consider a system with one component that is subject to failure, and suppose that we have 115 copies of the component. Suppose f

castortr0y [4]

Answer:

Step-by-step explanation:

From the given information:

the mean $(\mu) = 115 \times 20$

= 2300

Standard deviation = $20 \times \sqrt{115}$

Standard deviation (SD) = 214.4761

TO find:

a) $P(x > 3500)= P(Z > \dfrac{3500-\mu}{214.4761})$

$P(x > 3500)= P(Z > \dfrac{3500-2300}{214.4761})$

$P(x > 3500)= P(Z > \dfrac{1200}{214.4761})$

$P(x > 3500)= P(Z >5.595)$

From the Z-table, since 5.595 is > 3.999

$P(x > 3500)=1-0.9999$

P(x > 3500) = 0.0001

b)

Here, the replacement time for the mean $(\mu) = \dfrac{0+0.5}{2}$

= 0.25

Replacement time for the Standard deviation $\sigma = \dfrac{0.5-0}{\sqrt{12}}$

$\sigma = 0.1443$

For 115 component, the mean time = (115 × 20)+(114×0.25)

= 2300 + 28.5

= 2328.5

Standard deviation = $\sqrt{(115\times 20^2) +(114\times (0.1443)^2)}$

= $\sqrt{(115\times 400) +(114\times 0.02082249}$

= $\sqrt{(46000) +2.37376386}$

= $\sqrt{(46000) +(2.37376386)}$

= $\sqrt{46002.374}$

= 214.482

Now; the required probability:

$P(x > 4125) = P(Z > \dfrac{4125- 2328.5}{214.482})$

$P(x > 4125) = P(Z > \dfrac{1796.5}{214.482})$

$P(x > 4125) = P(Z >8.376)$

$P(x > 4125) =1- P(Z$

From the Z-table, since 8.376 is > 3.999

P(x > 4125) = 1 - 0.9999

P(x > 4125) = 0.0001

7 0

2 years ago

X^2 - 36 = 0.

strojnjashka [21]

Answer:

(x+6)(x−6)=0

x=-6 or x=6

Step-by-step explanation:

X^2 - 36 = 0

Solve by Square Root

add 36 both sides

x^2−36+36=0+36

x^2=36

square root

x=±√36

x=6 or x=−6

You can do that or for 2nd option

Solve by factoring

x^2-36=0

(x+6)(x−6)=0

Set factors equal to 0

x+6=0 or x−6=0

x=-6 or x=6

PLEASE NOTE: 36 is the square of 6

and

x2 is the square of x1

8 0

3 years ago