Solve the inequality. - 6 < 2x - 4 <4

Mathematics

1 answer:

ale4655 [162]3 years ago

5 0

Answer:

-1 < x < 4.

Step-by-step explanation:

- 6 < 2x - 4 <4

2x - 4 < 4

2x < 8

x < 4. Also we have:

2x - 4 > -6

2x > -2

x > -1.

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A hydro company is laying down power lines in the ground. They have two sections of cable so far that are 325.0 m and 430.0 m lo

Hoochie [10]

The length of extra cable that is required to connect the two pieces of existing cable is equal to 182 meters.

<h3>How to determine the length of extra cable?</h3>

In order to determine the length of extra cable that is required to connect the two pieces of existing cable, we would apply the law of cosine as follows:

B² = A² + C² - 2(A)(C)cosB

Substituting the given parameters into the formula, we have;

B² = 325.0² + 430.0² - 2(325.0)(430.0)cos23

B² = 105,625 + 184,900 - 279,500(0.9205)

B² = 290,525 - 257,279.75

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B = √33,245.25

B = 182.33 ≈ 182 meters.

Read more on cosine law here: brainly.com/question/11000638

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2 years ago

F(x) = x^2-3<br> What is the average rate of change on the interval [-5, 2] ?

Mumz [18]

Answer:

$(-3)$ .

Step-by-step explanation:

Over this interval, the change in the value of this function is:

$f(-5) - f(2) = 22 - 1 = 21$ .

The corresponding change in the value of $x$ :

$(-5) - 2 = -7$ .

The average rate of change of function $f$ over this interval is equal to the change in the function value divided by the corresponding change in $x$ :

$\begin{aligned}& (\text{average rate of change}) \\ =\; & \frac{(\text{change in function value})}{(\text{change in $x$})} \\ =\; & \frac{f(-5) - f(2)}{(-5) - 2} \\ =\; & \frac{22 - 1}{-7} \\ =\; & \frac{21}{-7} \\ =\; & -3\end{aligned}$ .