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3 years ago

Solve the system of equations using any appropriate method: 5x + 2y = -4 and -x + 2y = 8

Mathematics

1 answer:

Maru [420]3 years ago

4 0

Answer:

Step-by-step explanation:

-x + 2y = 8

5x + 2y = -4

+ x. -2y. -8

6x = -12

÷6. ÷6

x = -2

5(-2) + 2y = -4

-10 + 2y = -4

+10. +10

2y = 6

÷2. ÷2

y = 3

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Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistent

Eddi Din [679]

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

x = 13.96

x = 14

mathew needs to get 14 gallons of gasoline.

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3 years ago

Please Help I Don't Understand.

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BE and CD are parallel, so the triangles ABE and ACD are similar. Then the following relation holds:

AE/AD = AB/AC

10/(10 + 8) = x/(x + 6)

Solve for x :

10 (x + 6) = x (10 + 8)

10x + 60 = 18x

8x = 60

x = 60/8 = 7/5

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2 years ago

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2 years ago

E temperature t of a metal sphere is inversely proportional to the distance from the centre of the sphere (the origin (0, 0, 0))

olasank [31]

(-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

<h3>How to calculate temperature?</h3>

The quantity or amount of radiation contained in material or item, as measured by a temperature or sensed by touch and stated on a numerical scale.

The temperature T of a ball bearing is inverse to the length first from the origin, which we consider to be the center of the ball. The temperature at the exact location

(x, y, z) is a point on the sphere, the temperature at this point is given by

$T(x,y,z)= \dfrac{k}{(x^2 +y^2+z^2)^{1/2}}$

Where k is constant, then we have

T(1, 2, 2) = k/3 = 170

k = 510

$T(x,y,z)= \dfrac{510}{(x^2 +y^2+z^2)^{1/2}}$

Then we have

$\rm \triangledown T = \left ( -\dfrac{510x}{(x^2 +y^2+z^2)^{1/2}}, -\dfrac{510y}{(x^2 +y^2+z^2)^{1/2}}, \dfrac{510z}{(x^2 +y^2+z^2)^{1/2}} \right )\\\\\\\triangledown T (1, 2, 2) = -\dfrac{510}{27} (1, 2, 2) =-\dfrac{170}{9} (1, 2, 2)$

Then the direction will be from (1, 2, 2) to (4, 3, 5) will be (3, 1, 3)

So u = (3/√19, 1/√19, 3/√19)

Then we get

$\rm \triangledown T \cdot u = \dfrac{-170}{9}(1, 2, 2) \cdot \left (\dfrac{3}{\sqrt{19}}, \dfrac{1}{\sqrt{19}}, \dfrac{3}{\sqrt{19}} \right )\\\\\\\triangledown T \cdot u = - \dfrac{170}{9\sqrt{19}} (3 + 2 + 6)\\\\\\\triangledown T \cdot u = -\dfrac{1870}{9\sqrt{19}}$

The direction of the greatest inverse in the temperature is given by any vector parallel to and having the same direction $\triangledown$ T. (-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

More about the temperature link is given below.

brainly.com/question/11464844

#SPJ4

6 0

1 year ago

Graph the function g(x) = 1/3 - 4/3x

True [87]

Solutions

g(x) = $\frac{1}{3}$ - $\frac{4}{3}$ x

 g(x) = - $\frac{4}{3}$ x + $\frac{1}{3}$

x = -5

= g(x) = - $\frac{4}{3}$ × (-5) + $\frac{1}{3}$

= $\frac{20}{3}$ + $\frac{1}{3}$

= $\frac{21}{3}$

= 7

(-5,7)

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x = 7

 = g(x) = - $\frac{4}{3}$ × (7) + $\frac{1}{3}$

= $\frac{-28}{3}$ + $\frac{1}{3}$

= $\frac{-27}{3}$ = -9

(-7,9)

x = (-7,9) y = (-5,7)

6 0

3 years ago