Can someone plss help me with this!!!!

Mathematics

1 answer:

vredina [299]2 years ago

8 0

Domain: x>-5 ; It goes on from -5.

Range: y>-1 ; It goes on from -1.

Function: Slope is 6/7 ;

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What is the answer to –(d+1)>3

aleksandrvk [35]

Answer:

−(d+1)>3

Step 1: Simplify both sides of the inequality.

−d−1>3

Step 2: Add 1 to both sides.

−d−1+1>3+1

−d>4

Step 3: Divide both sides by -1.

$\frac{-d}{-1}$ > $\frac{4}{-1}$

d < -4

5 0

3 years ago

How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the i

pishuonlain [190]

Answer:

In total, $120$ permutations of three items can be selected from a group of six distinct elements.

In particular, there are $6$ ways to order three distinct items.

$\begin{aligned}\rm B-D-F \\ \rm B-F-D \\ \rm D-B-F \\ \rm D-F-B \\ \rm F-B-D \\ \rm F-D-B\end{aligned}$ .

Step-by-step explanation:

The formula $\displaystyle P(n,\, r) = \frac{n!}{(n - r)!} = n \, (n - 1) \cdots (n - r + 1)$ gives the number of ways to select and order $r$ items from a group of $n$ distinct elements.

To select and order three items from a group six distinct elements, let $n = 6$ and $r = 3$ . Apply the formula:

$\begin{aligned} P(6,\, 3) &= \frac{6!}{(6 - 3)!} = \frac{6!}{3!} \\ &= \frac{6 \times 5 \times 4 \times 3\times 2 \times 1}{3 \times 2 \times 1} \\ &= 6 \times 5 \times 4 = 120 \end{aligned}$ .

In other words, there are $120$ unique ways to select and order three items (select a permutation of three items) from a group of six distinct elements.

Consider: what's the number of ways to order three distinct items? That's the same as asking: how many ways are there to select and order three items from a group of three distinct elements? Let $n =3$ and $r = 3$ . Apply the formula for permutation:

$\begin{aligned} P(3,\, 3) &= \frac{3!}{(3 - 3)!} = \frac{3!}{0!} && \left(\text{$0! = 1$ by convention.}\right) \\ &= 3! = 3 \times 2\times 1 \\ &= 6\end{aligned}$ .

To find the permutations, start by selecting one element as the first of the list. A tree diagram might be helpful. Refer to the attachment for an example.