All categories

3 years ago

Which is the best interpretation of the solution set for the compound inequality?

Mathematics

1 answer:

saw5 [17]3 years ago

8 0

For this case we must find the solution set of the given inequalities:

Inequality 1:

$3 (2x + 1)> 21$

Applying distributive property on the left side of inequality:

$6x + 3> 21$

Subtracting 3 from both sides of the inequality:

$6x> 21-3\\6x> 18$

Dividing by 6 on both sides of the inequality:

$x> \frac {18} {6}\\x> 3$

Thus, the solution is given by all the values of "x" greater than 3.

Inequality 2:

$4x + 3$

Subtracting 3x from both sides of the inequality:

$4x-3x + 3$

Subtracting 3 from both sides of the inequality:

$x$

Thus, the solution is given by all values of x less than 4.

The solution set is given by the union of the two solutions, that is, all real numbers.

Answer:

All real numbers

You might be interested in

Mariana [72]

Answer:

x = 6

Step-by-step explanation:

∠ DBC + ∠ ABC = ∠ ABD , substitute values

5x - 4 + 8x - 3 = 79

13x + 1 = 79 ( subtract 1 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

8 0

3 years ago

5 pounds of apples costs $7.45 . what is the dependent and the independent variables

Vlada [557]

$7.45

5pounds

13.74065 US$

5 0

3 years ago

You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

2 years ago

. Compute the required sample size given the required confidence in the sample results is 99.74% (Z score of 3). The level of al

Shtirlitz [24]

Answer:

900 sample size

Step-by-step explanation:

To determine the sample size for a proportion, the margin of error formula is used to determine this:

$E=Z_{\frac{\alpha}{2} }*\sqrt{\frac{\hat p \hat q}{{n} }$

$n=\hat p \hat q*(\frac{Z_{\frac{\alpha}{2} }}{E} )^2$

Where p is the proportion, E is the margin of error, n is the sample size, q = 1 - p, $Z_\frac{\alpha }{2}$ is the z score.

Since the proportion is not known, the sample size needed to guarantee the confidence interval and error is at p = 0.5 and q = 1 - p = 1 - 0.5 = 0.5

E = 5% = 0.05, $Z_\frac{\alpha }{2}$ = 3. Hence:

$n=0.5*0.5*(\frac{3}{0.05} )^2\\\\n = 900$

6 0

3 years ago

Number line question PLEASE HELP

AleksandrR [38]

The answer is
A) 3 1/4 feet

3 0

3 years ago