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Trava [24]
2 years ago
5

Solve the inequality 5y+4 ≤ 22-y and graph the solution set on a number line. Please explain how to do it!

Mathematics
2 answers:
gtnhenbr [62]2 years ago
4 0

Answer:

y≤3

Step-by-step explanation:

5y+4≤22−y

<em>Step 1: Simplify both sides of the inequality.</em>

5y+4≤−y+22

<em>Step 2: Add y to both sides.</em>

5y+4+y≤−y+22+y

6y+4≤22

<em>Step 3: Subtract 4 from both sides.</em>

6y+4−4≤22−4

6y≤18

<em>Step 4: Divide both sides by 6.</em>

6y/6≤18/6

y≤3

Sati [7]2 years ago
3 0

Hey there!

Let's solve your inequality step-by-step.

\fbox{5y+4≤22−y}

Step 1: Simplify both sides of the inequality.

\fbox{5y+4≤−y+22}

Step 2: Add y to both sides.

\fbox{5y+4+y≤−y+22+y}

\fbox{6y+4≤22}

Step 3: Subtract 4 from both sides.

\fbox{6y+4−4≤22−4}

\fbox{6y≤18}

Step 4: Divide both sides by 6.

\fbox{6y/6 ≤ 18/6}

\fbox{y≤3}

Answer:

\fbox{y≤3}

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GaryK [48]
<h3>Answer:</h3>

f(x) = -(x -2)² +3

<h3>Step-by-step explanation:</h3>

We can fill in the vertex (h, k) values immediately in the vertex form ...

... f(x) = a(x -h)² +k

To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:

... -1 = a(0 -2)² +3

... -4 = 4a . . . . . . . . . subtract 3, simplify

... -1 = a . . . . . . . . . . . divide by 4

Now, we know the function is ...

... f(x) = -(x -2)² +3

5 0
3 years ago
What is the value of 4 x minus 7 when x = 4?191623
katen-ka-za [31]

Solution:

Given:

4x-7

when x = 4,

\begin{gathered} Substitute\text{ }x=4\text{ into }4x-7 \\ 4x-7=4(4)-7 \\ =16-7 \\ =9 \end{gathered}

The answer is 9.

7 0
1 year ago
A jewelry store purchases necklaces for n dollars each. The necklaces are then marked up by 20%, and costumers are charged 5% sa
Aleksandr [31]

Answer:

Step-by-step explanation:

Cost price = $n

Mark up price = selling price- cost price

= (20% × $n)

Selling price = $n + (20% × $n)

Sales tax = 5% × ($n + (20% × $n))

Total cost = selling price + sales tax

Total cost = $n + (20% × $n) + 5% × $n + (20% × $n)

= 1.2 × $n + 0.06 × $n

= 1.26 × $n.

8 0
3 years ago
A circle has an area of 3.14 cm^2 . What is its radius?
Anni [7]

Answer:

Cant be determined

Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
A. Describe the connection of the pattern of outcomes to Pascal’s triangle.
pychu [463]

Answer:

The answer to the question is;

A. The pattern of outcomes of 0 heads, 1 head, 2 heads ... n heads when arranged in the Pascal's triangle is given by the row of the triangles with the lowest at the edges and highest  outcome in the middle potion of the rows in the Pascal's triangle.

B. The number of total possible outcomes in a row n is 2ⁿ.

Step-by-step explanation:

To solve the question, we note that.

Pascal's triangle is an important sequence of numbers formed by starting with 1 at the top of the triangle followed by 1s on the outer edges of the triangle and the numbers directly below two adjacent numbers is the sum of the two adjacent numbers.

In probability theory, such as in throwing a coin,  Pascal's triangle indicates the number of possible heads obtained when n number of coins is thrown, that is, 0 heads, 1 head 2 heads etc. as follows

Number of coins                          Possible head outcome             Total outcome

0 coin                                                      1                                                 1

1 coin                                                      1  1                                               2

2 coins                                                  1  2 1                                             4

3 coins                                                 1  3  3 1                                          8

4 coins                                               1  4  6 4  1                                       16

The above triangle means that when

0 coin is flipped, the number of 0 heads is  1

1 coin  is flipped, the number of 0 heads is 1 (T) and 1 head is 1 (H)

2 coins are flipped, the number of 0 heads is 1, (TT), 1 head is 2 (TH), (HT) and 2 heads is 1 (HH)

3 coins are flipped 0 heads = 1 (TTT), 1 head = 3, (TTH), (THT), (HTT), the number of 2 heads = 3, (HHT), (HTH), (TTH) and the number of 3 heads = 1, (HHH).

B. The pattern in the number of total possible outcomes is

1, 2, 4, 8, 16 which is =2 raised to the power of the number of coin tossed for a particular row as follows

Number of coin tossed = 0  = 2⁰ = 1 = Total possible outcome

Number of coin tossed = 1  =  2¹ =  2 = Total possible outcomes

Number of coin tossed = 2  = 2² = 4 = Total possible outcomes

Number of coin tossed = 3  = 2³ = 8 = Total possible outcomes

Number of coin tossed = 4  = 2⁴ = 16 = Total possible outcomes

Therefore total number of possible outcome = 2ⁿ where n = number of coins tossed.

6 0
3 years ago
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