What's the system of linear equations by the solution graphed below

Mathematics

2 answers:

AfilCa [17]3 years ago

8 0

D should be the correct answer. <span>Hope this helps! Brainliest would be appreciated!</span>

bija089 [108]3 years ago

7 0

<h2>Answer:</h2>

The system of linear equation that is graphed is:

Option: A

A. y > -1 and y ≤ -x

<h2>Step-by-step explanation:</h2>

By looking at the graph we observe that the first inequality:

Is a strict inequality (since the graph is a dotted line which passes through (0,-1) and is a horizontal line parallel to the x-axis )

Also, the shaded region is above the line i.e. towards the origin.

This means that the line passes the zero point test.

Hence, the inequality which satisfies this condition is:

y > -1

Also, the graph of the second inequality:

Is a solid line (i.e. the inequality is not strict) and the line satisfies the relation y= -x and the shaded region lie below the line i.e. the inequality is given by:

y ≤ -x

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Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.

Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ , we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

$= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}$

$= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} } \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du } \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}] \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\$