A bag holds 12 red marbles, 11 green marbles, 17 blue marbles, and 5 yellow marbles. What is the probability that you will not c

The options presented are:

(1) division property of equality

(2) factoring the binomial

(3) completing the square

(4) subtraction property of equality

Response: (2) factoring the binomial

Step 1:

Step 2:

In step 2, 'a' is extracted from . Upon factoring out 'a', we divide all terms by 'a', resulting in .

Step 2 involves the binomial factorization process.

, in which indicates the overall number of rooms. Step-by-step explanation: It is given that Martin has 4 rooms left to clean and takes 7 hours for the task. The equation in standard form for the number of rooms remaining after x hours, y, is set up as follows: The remaining rooms , indicates the quantity after hours. The cleaning rate is established as follows: Considering Martin cleans 4 rooms in 7 hours, the rate at which he cleans is given by: Hence, the equation can be expressed as

(Answer)

Response: 8n

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Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.

Answer:

The amount of wool required for a sweater was 400 grams.

A hat needed 80 grams of wool.

A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

(5y)+y+(y-5)=555

7y=560

y=80 grams

Now, find x

x=5(80)=400 grams

Next, determine z

z=80-5=75 grams

In conclusion,

400 grams of wool was required for the sweater,

the hat needed 80 grams of wool, and

the scarf required 75 grams of wool.