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Ipatiy [6.2K]
4 years ago
8

PLEASE HELP NOW!!!!! The inequality –3^x + 5 > –4 can be broken into two related inequalities. Review the graphs of the two r

elated inequalities.
On a coordinate plane, a dotted line is at y = 4. Everything above the line is shaded. A dotted curved line approaches y = 5 in quadrant 2 and then curves down through (0, 4) and (1, 2). Everything below and to the left of the curve is shaded.

Which set shows the solution to –3x + 5 > –4?

(–∞, 2)
(–4, ∞)
(–4, 5)
(2, ∞)

Mathematics
2 answers:
Aneli [31]4 years ago
6 0

Answer: A

Step-by-step explanation:

Got it right on Edge

galben [10]4 years ago
5 0

Answer: A

(–∞, 2)

Step-by-step explanation:

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<h2>Part 1)</h2>

Let's analyze each part of the function:

FROM x = 0 TO x = 5:

We can find the equation of this line by using The Slope-Intercept Form of the Equation of a Line, that states:

The \ graph \ of \ the \ equation: \\ \\ y=mx+b \\ \\ is \ a \ line \ whose \ slope \ is \ m \ and \ whose \ y-intercept \ is \ (0, b)

So the y-intercept here is (0,4) and m=\frac{4}{5}, therefore:

\boxed{y=\frac{4}{5}x+4}

FROM x = 0 TO x = 5:

From the previous line, we know that at x=5 the output is:

y=\frac{4}{5}x+4 \\ \\ y=\frac{4}{5}(5)+4 \\ \\ y=4+4=8

So the point P_{1}(5,8) lies on both lines.

For this new line, the slope is m=-\frac{3}{5}

So, with the Point-Slope Form of the Equation of a Line we can find the equation of this other line:

The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1})

So:

y-8=-\frac{3}{5}(x-5) \\ \\ y=8-\frac{3}{5}x+3 \\ \\ \boxed{y=-\frac{3}{5}x+11}

The graph is shown below.

<h2>Part 2)</h2>

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\bullet \ y=x^2+3 \\ \\ \bullet \ y=x^3 \\ \\ \bullet \ y=12-x^2

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1.
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