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AnnyKZ [126]
3 years ago
11

Match the inequality with its line graph.

Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

The answer to your question is below

Step-by-step explanation:

A) 2x > -6

   x > -6/2

   x > -3

   It must be a graph with an open circle starting at -3 and then to the right.

   It is the first graph.

B) x - 4 < -7

   x < -7 + 4

  x < -3

  The graph must be an open circle starting at -3 and pointing to the left.

  it is the second graph.

C) 6 + x ≤ 3

    x ≤ -6 + 3

    x ≤ -3

   The graph must be a closed circle starting at -3 and pointing to the left.

   it is the forth graph.

D) -x - 5 ≤ -2

    -x ≤ -2 + 5

   - x ≤ 3

     x ≥ -3

    The graph must be a closed circle starting at -3 and pointing to the right.

    It is the third graph.

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To check the decay rate, we need to check the variation in y-axis.

Since our interval is

-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}

To compare the decay rates we need to check the variation on the y-axis of both functions.

\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}

Now, we calculate their ratio to find how they compare:

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This tell us that the exponential function decays at three-fourths the rate of the quadratic function.

And this is the fourth option.

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1 year ago
VXYZ is a rectangle with a length of 20cm and a width of 12 cm. The length of the rectangle is increased by 30%. The width of th
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Step-by-step explanation:

the area is

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increasing the length by 30% means multiplying the original length by 1.3.

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Thus, pattern n consists of

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