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2 years ago

Solve the equations. 2x+4y+3x=6 5x+8y+6z=4 4x+5y+2z=6

Mathematics

1 answer:

Art [367]2 years ago

3 0

Answer:

b. (x, y, z) = (-8, 10, -6)

Step-by-step explanation:

The easiest way to do this one is to try the answers to see which works.

2(-8) +4(10) +3(-6) = -16 +40 -18 = 6

5(-8) +8(10) +6(-6) = -40 +80 -36 = 4

4(-8) +5(10) +2(-6) = -32 +50 -12 = 6

The answers of choice B work in the given equations.

___

In case you don't have answers to select from, you generally solve this sort of problem using elimination. You can also use Cramer's rule, a graphing calculator, an on-line equation solving tool, or any of a variety of other methods.

Here, we can find the variable x by subtracting twice the first equation from the second:

(5x +8y +6z) -2(2x +4y +3z) = (4) -2(6)

x = -8

This is sufficient to identify the correct answer choice.

We can substitute this into the last two equations to get ...

-40 +8y +6z = 4 . . . . 8y +6z = 44

-32 +5y +2z = 6 . . . . 5y +2z = 38

Subtracting the first of these from 3 times the second gives ...

3(5y +2z) -(8y +6z) = 3(38) -(44)

7y = 70 . . . . . . . simplify

y = 10 . . . . . . . . divide by 7

Substituting this into the second of the above equations, we have ...

5(10) +2z = 38

25 +z = 19 . . . . . . divide by 2

z = -6 . . . . . . . . . . subtract 25

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The choice of the combinations to use to eliminate variables can be ad hoc (as here), or it can be made according to some rules (as in Gaussian elimination).

My personal choice for solving systems like this is to use the matrix functions of a graphing calculator.

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Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? acute, because 62 + 102 < 122 acute

maw [93]

The Pythagoras theorem states that
the sum of squares of the shorter sides (legs) of a right triangle equals the square of the third side.

A corollary from the same theorem helps us solve this problem:
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Conversely, if the sum of the squares of the shorter sides of a triangle is less than the square of the third side, the triangle is obtuse. .....(case 2)

Here we have
6^2+10^2 = 36+100=136 <12^2=144
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2 years ago

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8. The ratio of students in Arts, Science and Commerce Faculties is 5: 4: 3. If the number

N76 [4]

Answer:

Arts=295, Commerce=177

Step-by-step explanation:

That the three subjects have a common ratio implies that there is some common factor between them that relates to the actual number of students in each area, so 5:4:3 means 5x:4x:3x for some value of x

We know that there are 236 science students, so 4x = 236 or x = 59

so the number of arts students is 5(59) and the number of commerce students is 3(59)

Arts = 5*59 = 295

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1 year ago

A large city in the ancient world was square-shaped. measured in miles, its area numerically exceeded its perimeter by about 132

melisa1 [442]

Area = perimeter + 132.

Let each side of the city be x miles long, then:-

x^2 = 4x + 132
x^2 - 4x - 132 = 0

x = [-(-4) +/- sqrt((-4)^2 - 4 * 1 *-132)] / 2

x = 13.66, -9.66 We ignore the negative

So the city has dimension of 13.66 * 13.66

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2 years ago

In the diagram, DC is 10 units and BC is 6 units. Line l is a perpendicular bisector of line segment A C. It intersects line seg

Orlov [11]

Answer:

12 units

Step-by-step explanation:

Point B is the midpoint of AC, and it is 6 units from C. Therefore A must be 12 units from C.

AC = 12 units

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2 years ago

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PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of z

dimaraw [331]

1) $\frac{v(8)-v(0)}{8 - 0} = \frac{10-18}{8} = -1\frac{m}{s}$ .
2) $v(5) = 5^2-9*5+18 = 25-45+18 = -2\frac{m}{s}$ .
3) The particle is moving right when the velocity function is positive: $0\ \textless \ t\ \textless \ 3$ or $6\ \textless \ t\ \textless \ 8$ .
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