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3 years ago

3x + y - z= -6 2x - y + 2z = 8 4x + y - 3z = -21

Mathematics

1 answer:

Flauer [41]3 years ago

8 0

Answer:

x=-1

y=4

z=7

Step-by-step explanation:

3x + y - z= -6(1)

2x - y + 2z = 8(2)

4x + y - 3z = -21(3)

(1)+(2): 5x+z=2(4)

(2)+(3): 6x-z=-13(5)

(4)+(5): 11x=-11

x=-1

so z=2-5x=7

y=-6-3x+z=4

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1000 households were surveyed. 275 households own a desktop computer, 455 households own a DVD player, 405 households own two ca

icang [17]

Answer:

Step-by-step explanation:

From the given information,

Suppose

X represents the Desktop computer

Y represents the DVD Player

Z represents the Two Cars

Given that:

n(X)=275

n(Y)=455

n(Z)=405

n(XUY)=145

n(YUZ)=195

n(XUZ)=110

n((XUYUZ))=265

n(X ∩ Y ∩ Z) = 1000-265

n(X ∩ Y ∩ Z) = 735

n(X ∪ Y) = n(X)+n(Y)−n(X ∩ Y)

145 = 275+455 - n(X ∩ Y)

n(X ∩ Y) = 585

n(Y ∪ Z) = n(Y) + n(Z) − n(Y ∩ Z)

195 = 455+405-n(Y ∩ Z)

n(Y ∩ Z) = 665

n(X ∪ Z) = n(X) + n(Z) − n(X ∩ Z)

110 = 275+405-n(X ∩ Z)

n(X ∩ Z) = 570

a. n(X ∪ Y ∪ Z) = n(X) + n(Y) + n(Z) − n(X ∩ Y) − n(Y ∩ Z) − n(X ∩ Z) + n(X ∩ Y ∩ Z)

n(X ∪ Y ∪ Z) = 275+455+405-585-665-570+735

n(X ∪ Y ∪ Z) = 50

c. n(X ∪ Y ∪ C') = n(X ∪ Y)-n(X ∪ Y ∪ Z)

n(X ∪ Y ∪ C') = 145-50

n(X ∪ Y ∪ C') = 95

6 0

3 years ago

Cual es la magnitud de la aceleración angular de una llanta de un automóvil que adquiere una velocidad angular de 350 rad/s en 2

drek231 [11]

Respuesta:

175 rad / s²

Explicación paso a paso:

Dado que :

Velocidad angular final = 350 rad / s

Tiempo empleado = 2 segundos

La aceleración angular, a =?

Recordar ; la aceleración angular es igual a la carga en velocidad angular con el tiempo

(velocidad final - Velocidad inicial) / tiempo empleado

Velocidad inicial = 0 rad / s

Aceleración angular = (350 - 0) / 2 = 350/2

= 175 rad / s²

3 0

3 years ago

It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Clau

Gnom [1K]

Answer: 50 miles per hour

Step-by-step explanation:

Find out the length of the normal route.

Distance = Speed * time

= 48 * 40/60

= 32 miles

The detour is 8 miles longer so the length is;

= 32 + 8

= 40 miles

What speed should he travel at to make it in 48 minutes. Remember speed is in miles per <u>hours</u>.

Speed = Distance/ time

= 40 / (48/60)

= 50 miles per hour

7 0

3 years ago

Read 2 more answers

Find the unknown sizes of angles:

pav-90 [236]

First we find X:
3x+x=180
4x=180
x=180/4
x=45.

3x=135

135+y=180
y=180-135
y=45

45+z=180
z=180-45
z=135

In conclusion, x=45, 3x=135, y=45 and z =135

Also note that the opposite angles are equal so you can just find 3x and that will be equal to z and x will be equal to y.

Hope this helped

7 0

3 years ago

Read 2 more answers

The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by R(x) = 0

STatiana [176]

Answer:

The marginal-revenue equation is $R'(x)=0.1226x+1.1584$ .

The marginal revenue for the production of 200,000,000 bushels is $R'(x)=1.4036$ .

The marginal revenue for the production of 650,000,000 bushels is $R'(x)=9.1274$ .

Step-by-step explanation:

The derivative $R'(x)$ of the revenue function is called the marginal revenue function and is the rate of change of revenue with respect to the number of units sold.

We know the revenue function, $R(x) = 0.0613x^{2} +1.1584x+2.4813$ . Therefore, the marginal revenue function is

$R'(x)=\frac{d}{dx}R(x) = \frac{d}{dx}(0.0613x^{2} +1.1584x+2.4813)\\\\=\frac{d}{dx}\left(0.0613x^2\right)+\frac{d}{dx}\left(1.1584x\right)+\frac{d}{dx}\left(2.4813\right)\\\\R'(x)=0.1226x+1.1584$

To find the marginal revenue for the production of:

200,000,000 bushels we use x = 2, since x is in units of hundreds of million of dollars.

$R'(x)=0.1226\cdot \:2+1.1584\\\\R'(x)=0.2452+1.1584\\\\R'(x)=1.4036$

650,000,000 bushels we use x = 65, since x is in units of hundreds of million of dollars.

$R'(x)=0.1226\cdot \:65+1.1584\\\\R'(x)=7.969+1.1584\\\\R'(x)=9.1274$

3 0

3 years ago