All categories

3 years ago

Which graph shows the solution set for |x - 3| < 4?

Mathematics

2 answers:

ikadub [295]3 years ago

4 0

Answer:

see below

Step-by-step explanation:

|x - 3| < 4

To remove the absolute values, we need to make two inequalities, one positive and one negative

x-3 < 4 and x-3 > -4

Add 3 to each side

x-3+3<4+3 and x-3+3 > -4+3

x<7 and x >-1

-1 <x <7

lawyer [7]3 years ago

4 0

Answer:

Step-by-step explanation:

One way to do this is to interpret |x - 3| < 4 is to say: "the distance of variable x from the center 3 is less than 4."

On the left side: measuring 4 units to the left from 3, mark an open circle (since x does not actually touch -1).

On the right side: measuring 4 units to the right from 3, mark an open circle at 7.

So the correct graph consists of the line segment connecting x = -1 and x = 7 but not touching or including these two numerical values.

Next time, please share the four possible answers.

You might be interested in

Use the summation formulas to rewrite the expression without the summation notation. summation_k = 1^n 12k(k - 1) / n^3 Use the

kvasek [131]

Answer:

$Sum=4*[\frac{n^2-1}{n^2}]$

For n=10:

Sum=3.96

For n=100:

Sum=3.9996

For n=1000:

Sum=3.999996

For n= 10000:

Sum=3.99999996

Step-by-step explanation:

Formula:

$\sum_{k=1}^n \frac{12k(k-1)}{n^3}$

Rearranging the above formula:

$\sum_{k=1}^n \frac{12}{n^3}*k(k-1)\\\sum_{k=1}^n \frac{12}{n^3}*(k^2-k)$ Eq (1)

According to summation formula:

$\sum_{k=1}^n\ k= \frac{n(n+1)}{2}\\ \sum_{k=1}^n\ k^2= \frac{n(n+1)(2n+1)}{6}\\$

Putt these in Eq (1), and we will get:

$=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\$

Taking $2(n+1)$ as common:

$=2(n+1)*\frac{2n+1-3}{n^2} \\=(2n+2)*\frac{2n-2}{n^2}\\=\frac{4n^2-4}{n^2}$

After more simplifying,

$Sum=4*[\frac{n^2-1}{n^2}]$

Now ,for n=10:

$Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96$

For n=100:

$Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996$

For n=1000

$Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996$

For n=10000:

$Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996$

4 0

3 years ago

Find an exponential function that passes through each pair of points.<br><br>(2,1.75) & (-2,28)

dusya [7]

Answer:

$f(x) = 7\, ((1/2)^{x})$ .

Step-by-step explanation:

An exponential function is typically in the form $f(x) = a\, (b^{x})$ , where $a$ and $b$ ( $b > 0$ ) are constants to be found.

In this question:

$f(2) = 1.75$ means that $a\, (b^{2}) = 1.75$ .

$f(-2) = 28$ means that $a\, (b^{-2}) = 28$ .

Divide one of the two equations by the other to eliminate $a$ and solve for $b$ .

The number of the right-hand side of the second equation is larger than that of the first equation. Hence, divide the second equation with the first:

$\displaystyle \frac{a\, (b^{-2})}{a\, (b^{2})} = \frac{28}{1.75}$ .

$\displaystyle b^{-4} = 16$ .

$b^{-1} = 2$ .

$\displaystyle b = \frac{1}{2}$ .

Substitute $b = (1/2)$ back into either equation (for example, the first equation) and solve for $a$ :

$a\, ((1/2)^{2}) = 1.75$ .

$a = 7$ .

Substitute $a = 7$ and $b = (1/2)$ into the other equation. That equation should also be satisfied.

Therefore, this function would be:

$f = 7\, ((1 / 2)^{x})$ .

8 0

2 years ago

Y'all- this question make's 0 sense to my big brain help me out

gregori [183]

Answer:

D. for the first one, A. for the second (not certain)

Step-by-step explanation:

1. 36/2 (two books every visit) = 18, multiplied by 3 because that's how many often he does to the library (every 3 weeks)

2. 13/2 = w/5 because for every 13 cups of water, there is two cups of cleaner, so for w (unknown amount of water) there would be 5 cups of concontrated cleaner.

3 0

3 years ago

Evulate: m/5<br><br> When: m= 30

lianna [129]

Answer:

Step-by-step explanation:

30/5= 6

7 0

3 years ago

Factorise: x^2/y^2+1+y^2/X^2

rewona [7]

Answer: