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Vaselesa [24]
3 years ago
8

Suppose we want to choose a value of x within 3 units of 11. [This means a value of x that is less than 3 units away from 11.] T

hink about some values of x that meet this constraint. Write an inequality that represents all values of x that meet this constraint. On the number line below, represent all values of x that meet this constraint.

Mathematics
2 answers:
Dahasolnce [82]3 years ago
5 0

Answer:

(a) [8, 14]

(b)  8 \leq x \leq 14

(c)See attachment

Step-by-step explanation:

We want to choose a value of x within 3 units of 11.

(a)Now, 11-3=8 and 11+3=14

The possible values of x ranges is in the closed interval [8,14]

(b) Since x is within 3 units of 11., we have:

|11-x|\leq3

Solving the absolute inequality

-3 \leq 11-x \leq 3\\$In $ -3 \leq 11-x\\ x \leq 11+3\\x \leq 14\\\\$In $ 11-x \leq 3\\ 11-3 \leq x\\8 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\8 \leq x \leq 14

(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.

Crank3 years ago
4 0

Answer:

A. x ± 3 < 11

B.  x < 14

C. See the attachment

Step-by-step explanation:

A. Since the value of x is less than 3 units away from 11, we represent it in inequality form as x ± 3 < 11.

B. We now solve this inequality to obtain the values of x which satisfy the constraint.

So, x ± 3 < 11.

x + 3 < 11   and x - 3 < 11

x < 11 - 3  and x < 11 + 3

x < 8  and x < 14

Combining both inequalities,

x < 14

So for x to be less than 3 units away, x must be less than 14.

C. Find the representation on the number line in the attachment.

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Answer:

x=-4

Step-by-step explanation:

Dividing both sides by -3, you get x+2=-2. So x=-4.

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3 years ago
Read 2 more answers
Expres each of the folowing as a single matrix.
Elden [556K]

Answer:

\left[\begin{array}{cc}6&-3\\10&-1\end{array}\right]+\left[\begin{array}{cc}-2&8\\3&-12\end{array}\right]=\left[\begin{array}{cc}4&5\\13&-13\end{array}\right]

Step-by-step explanation:

If you have two matrices:

A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]\\\\\\A+B=\left[\begin{array}{cc}a+e&b+f\\c+g&d+h\end{array}\right]

We have:

A=\left[\begin{array}{cc}6&-3\\10&-1\end{array}\right]\\and\\B=\left[\begin{array}{cc}-2&8\\3&-12\end{array}\right]

And we need to express as a single matrix:

A+B=\left[\begin{array}{cc}6&-3\\10&-1\end{array}\right]+\left[\begin{array}{cc}-2&8\\3&-12\end{array}\right]\\\\\\A+B=\left[\begin{array}{cc}6+(-2)&-3+8\\10+3&-1+(-12)\end{array}\right]\\\\\\A+B=\left[\begin{array}{cc}6-2&5\\13&-1-12\end{array}\right]\\\\\\A+B=\left[\begin{array}{cc}4&5\\13&-13\end{array}\right]

The answer is:

\left[\begin{array}{cc}6&-3\\10&-1\end{array}\right]+\left[\begin{array}{cc}-2&8\\3&-12\end{array}\right]=\left[\begin{array}{cc}4&5\\13&-13\end{array}\right]

It is expressed as a single matrix.

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Step-by-step explanation:

The quickest way to find this is to count the whole numbers between each point given in the answers and look for the answer that falls between 2 and 3 units.

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