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3 years ago

Select all the correct graphs. Choose the graphs that indicate equations with no solution.

Mathematics

1 answer:

Natali [406]3 years ago

3 0

Answer:

The first and last graph.

General Formulas and Concepts:

<u>Algebra I</u>

Solving systems of equations graphically

Step-by-step explanation:

In order for a systems of equations to have a solution set, the 2 graphs must intersect at at least 1 point. Here, we see that graphs 1 and 5 do not intersect each other at all.

Therefore, the rest of the graphs have solutions and #1 and #5 do no have any solutions.

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3 years ago

If xy + y² = 6, then the value of dy/dx at x= -1 is<br>

mylen [45]

Hi there!

$\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}$

$\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}$

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx) + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

-1(y) + y² = 6

-y + y² = 6

y² - y - 6 = 0

(y - 3)(y + 2) = 0

Thus, y = -2 and 3.

We can calculate dy/dx at each point:

At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.

At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.

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3 years ago

An equation and the first step in its solution are shown: Equation: x2 + 8x - 9 = 0

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2 years ago

There were two containers of oil. There was twice as much oil in the second container as in the first one. After using 13 liters

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Answer:

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Step-by-step explanation:

First container = x

Second container has twice as much oil.

Second container = 2x

13 liters of oil was used from first container.

x - 13

7 liters of oil was used from the second container.

2x - 7

Second container has 3 times more oil than the first one.

2x - 7 = 3(x - 13)

x - 7 = 3(x - 13)

x - 7 = 3x - 39

2x = 32

x = 16

First container = 16 liters

second container = 16 x 2 = 32 liters

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3 years ago

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