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2 years ago

Solve x - 3 < -1. Graph the solution.

Mathematics

1 answer:

LuckyWell [14K]2 years ago

3 0

Answer: x < 2

Explanation: To solve for x in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.

Since 3 is being subtracted from x, we add 3

to both sides of the inequality to get x < 2.

Before we graph, write your answer in set notation.

We can write this as {x: x < 2}.

It's important to understand what this means.

This means that any number less than 2 is a solution to this inequality.

I have graphed the inequality for you below.

Start with an open dot on +2.

We use an open dot because +2 is not included as a solution.

Then draw an arrow going to the left.

You might be interested in

What is f(2)>0 telling me about a graph?

Firdavs [7]

"f(2)>0" tells you that if you evaluate the function f(x) at 2, the result is: 1) positive, or 2) greater than zero.

4 0

2 years ago

Find all solutions by transforming the system to reduced echelon form and back substituting. (If there are an infinite number of

Zolol [24]

Answer:

The system has infinite solutions described in the set $\{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}$

Step-by-step explanation:

The augmented matrix of the system is $\left[\begin{array}{cccc}-1&-1&-1&4\\2&1&0&2\end{array}\right]$ .

We apply row operations:

1. We add the first row to the second row twice and obtain the matrix $\left[\begin{array}{cccc}-1&-1&-1&4\\0&-1&-2&10\end{array}\right]$

2. multiply by -1 the rows of the previous matrix and obtain the matrix $\left[\begin{array}{cccc}1&1&1&-4\\0&1&2&-10\end{array}\right]$ that is the reduced echelon form of the matrix associated to the system.

Now we aply backward substitution:

1. Observe that the reduced echelon form has a free variable, then the system has infinite solutions.

$x_2+2x_3=-10\\x_2=-10-2x_3$

$x_1+x_2+x_3=-4\\x_1-10-2x_3+x_3=-4\\x_1-x_3=-4+10\\x_1=6+x_3$ .

Then the set of solutions is $\{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}$

3 0

3 years ago

What is the correct answer to this multiple choice question? Please help!

exis [7]

Answer:

p = 26.3

Step-by-step explanation:

Using the law of sines

sin 101 sin 38

--------- = ------------

42 p

Using cross products

p sin 101 = 42 sin 38

p = 42 sin 38 / sin 101

p=26.34175

To the nearest tenth

p = 26.3

8 0

2 years ago

Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was

abruzzese [7]

Answer:

There is no convincing evidence at α = 0.10 level that the average vertical jump of students at this school differs from 15 inches.

Step-by-step explanation:

We have to make a hypothesis test to prove the claim that the average vertical jump of students differs from 15 inches.

The null and alternative hypothesis are:

$H_0: \mu=15\\\\H_a: \mu\neq15$

The significance level is 0.10.

The sample mean is 17 and the sample standard deviation is 5.37.

The degrees of freedom are df=(20-1)=19.

The t-statistic is:

$t_{19}=\frac{M-\mu}{s_M/\sqrt{n}} =\frac{17-15}{5.37/\sqrt{20}}=\frac{2}{5.37/4.47} =2/1.20=1.67$

The two-sided P-value for t=1.67 is P=0.11132.

This P-value is bigger than the significance level, so the effect is not significant. The null hypothesis can not be rejected.

There is no convincing evidence at α = 0.10 level that the average vertical jump of students at this school differs from 15 inches.

7 0

2 years ago

Use dimensional analysis to make each conversion.

algol13

You subtract them (X,Y)

3 0

2 years ago