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4 years ago

Using substitution or elimination 3y=-1/2x+2. y=-x+9

Mathematics

1 answer:

I am Lyosha [343]4 years ago

4 0

Answer:

(x, y) = (10, - 1)

Step-by-step explanation:

given the 2 equations

3y = - $\frac{1}{2}$ x + 2 → (1)

y = - x + 9 → (2)

substitute y = - x + 9 into (1)

3(- x + 9) = - $\frac{1}{2}$ x + 2

- 3x + 27 = - $\frac{1}{2}$ x + 2

add $\frac{1}{2}$ x to both sides

- $\frac{5}{2}$ x + 27 = 2 ( subtract 27 from both sides )

- $\frac{5}{2}$ x = - 25

multiply both sides by 2 and divide by - 5

x = 10

solution (10, - 1)

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3 years ago

A lightbulb has a power of 60 W and is used for 16 hours. A toaster oven has a power of 1500 W

krek1111 [17]

a. The lightbulb uses the energy of 960 W or 9.60 kW.

Step-by-step explanation:

Step 1:

To determine the energy used by the appliances we need to understand the equation

$power = \frac{energy}{time} .$

To determine the energy used, we multiply the power of the appliance with the amount of time it has been used for.

Step 2:

The lightbulb has a power of 60 W and is used for a period of 16 hours.

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4 years ago

Explain what happens when you have an exponent to the power of another exponent.

jekas [21]

Answer:

The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.

Step-by-step explanation:

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3 years ago

A cardboard box has a square base and an open top. the four sides are made of wood that costs 2 dollars per square foot, while t

serious [3.7K]

Answer:

$300

Step-by-step explanation:

Let x represent the side length of the square base in feet. Then the height of each side is ...

... h = (50 ft³)/(x ft)² = (50/x²) ft

The cost of the sides of the box is then ...

... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x

The cost of the bottom is ...

... (x ft)² × $25/ft² = $25x²

So, the total dollar cost is

... C = 400/x + 25x²

This will be a minimum where its derivative with respect to x is zero.

... 0 = -400/x² +50x

... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50

... x = ∛8 = 2

For this value of x, the minimum cost is ...

... C = 400/2 + 25·2² = 300

The minimum possible cost is $300.

_____

<em>Comments on the problem</em>

1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.

2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.

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4 years ago

Y=2x-4 what is say the y intercept?

Afina-wow [57]

Answer:

-4

Step-by-step explanation:

The number that is by itself is always the y-intercept

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3 years ago