All categories

3 years ago

What is a solution to 4x+6<(with a line under it ) 18

Mathematics

1 answer:

JulsSmile [24]3 years ago

7 0

Answer:

$\textbf{$x \in (-\infty, 3] $}\\$

Step-by-step explanation:

$\textup{Given:}\\$ 4x + 6 $\textup{Subtracting $6$ from both the sides }\\$ 4x \leq 18 - 6 \hspace{5mm} (=12) $\\\textup{Dividing by $4$ on both the sides: \hspace{15mm} [Note that the sign of the inequality changes only when we divide it by a negative number]}\\$$ x \leq 3 $$\\\textup{$x$ can be any real number less than or equal to 3.}\\$ \iff x \in R^- \cup \{a : 0 \leq a \leq 3\} $$

You might be interested in

A tractor, starting from a stationary position, drives down the road. It accelerates at 4 m/s2 for 10 seconds, then travels at a

chubhunter [2.5K]

Answer:

B. 1400 meters.

Step-by-step explanation:

According to the statement, there are two stages for the motion of the tractor, in which we need to find the travelled distance:

(i) Uniform accelerated motion.

$s_{i} = s_{o,i} +v_{o,i}\cdot t_{i} + \frac{1}{2}\cdot a\cdot t_{i}^{2}$ (1)

$v_{i} = v_{o,i}+a\cdot t_{i}$ (2)

Where:

$s_{o,i}$ - Initial position of the tractor, measured in meters.

$s_{i}$ - Final position of the tractor, measured in meters.

$v_{o,i}$ - Initial velocity of the tractor, measured in meters per second.

$t_{i}$ - Time, measured in seconds.

$a$ - Acceleration, measured in meters per square second.

$v_{i}$ - Final velocity of the tractor, measured in meters per second.

(ii) Uniform motion.

$s_{ii} = s_{i} + v_{i}\cdot t_{ii}$ (3)

Where:

$s_{ii}$ - Final position of the tractor, measured in meters.

$t_{ii}$ - Time, measured in seconds.

The distance covered by the tractor ( $\Delta s$ ), measured in meters, is:

$\Delta s = s_{ii}$ (4)

If we know that $a = 4\,\frac{m}{s^{2}}$ , $t_{i} = 10\,s$ , $v_{o,i} = 0\,\frac{m}{s}$ , $s_{o,i} = 0\,m$ and $t_{ii} = 30\,s$ , then distance covered by the tractor is:

By (1) and (2):

$s_{i} = 0\,m + \left(0\,\frac{m}{s} \right)\cdot (10\,s)+ \frac{1}{2}\cdot \left(4\,\frac{m}{s^{2}} \right) \cdot (10\,s)^{2}$

$s_{i} = 200\,m$

$v_{i} = \left(0\,\frac{m}{s} \right)+\left(4\,\frac{m}{s^{2}} \right)\cdot (10\,s)$

$v_{i} = 40\,\frac{m}{s}$

By (3):

$s_{ii} = 200\,m + \left(40\,\frac{m}{s} \right)\cdot (30\,s)$

$s_{ii} = 1400\,m$

By (4):

$\Delta s = 1400\,m$

The correct answer is B.

4 0

3 years ago

Which ones are a parallelogram and which are not?

vladimir2022 [97]

1,4,3 are parallelogram and the the second one is not necessarily a parallelogram

4 0

4 years ago

(07.04)

dolphi86 [110]

Answer:

1. 6

2. $1.63

3. 4.6

4. 32

5. 34n = 306

6. 3/8

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

ABCD is a rhombus and DB=10 Find the length of DC

erik [133]

Step-by-step explanation:

DC = 12

................

4 0

3 years ago

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are

USPshnik [31]

The appropriate hypothesis which is used to test the dropout rate are $H_{0}:p > =0.081\\$ and $H_{1}: p < 0.081$ .

Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.

The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.

The parameter of interest is the proportion to high school drop outs is p.

Sample proportion= $p^{1}$ =0.065

The hypothesis can be formed as under:

$H_{0}:p > =0.081$ (null hypothesis)

$H_{1}:p < 0.081$ ( alternate hypothesis)

Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.

$Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}$

= $0.065-0.081/\sqrt{(0.081*0.0919)/1000}$

=-1.85

Hence the appropriate hypothesis are $H_{0}:p > =0.081$ and $H_{1}:p < 0.081$ .

Learn more about hypothesis at brainly.com/question/11555274

#SPJ4

4 0

2 years ago