What is the time elaplsed between 1:20 and 2:00

Answer:

5.) Proportionality is 3/1 or 3 simplified

• b x 3 = p
• b= boxes
• p= pens in box

6.) Proportionality is 1/6

• m ÷ 6 = p
• m = muffins
• p= pack(s) of muffins

Step-by-step explanation:

You would take the first column (or in this case row (pens and packs) and place the 2nd row under it in fraction form.

• 5.) 3/1 = 3
• 6.) 1/6 = 1/6

That would be your proportion

Then you would (in place of numbers) use letters to symbolize in the equation

• 5.) p = pens: b= boxes
• 6.) m= muffins; p= pack

Then create an equation to figure out how to get the correct numbers.

• 1 box holds 3 pens so:
• 5.) b x 3 = p
• Check: 2 boxes x 3 pens per box = 6 pens (check table) Correct!
• 6 muffins in 1 pack so:
• 6.) m ÷ 6 = p
• 12 muffins ÷  6 muffins in per box = 2 packs (check table) Correct!

Answer:

The vertex is at ( 3.5, -0.25)

and the axis of symmetry is x = 3.5.

Step-by-step explanation:

Convert to vertex form:

y = x^2 - 7x + 12

y = (x - 3.5)^2 - 3.5^2 + 12

y = (x - 3.5)^2 - 0.25

y = (x - 3.5)^2 - 0.25.

So the vertex is at ( 3.5, -0.25)

and

the axis of symmetry is x = 3.5.

Final answer:

The vertex of the parabola y = x² - 7x + 12 is at (3.5,-0.25) and the equation of the axis of symmetry is x = 3.5.

Explanation:

The given quadratic equation is y = x² - 7x + 12. To determine the vertex and the equation of the axis of symmetry, we need to first find the x-coordinate of the vertex, which is determined by the formula -b/2a. Here in our equation, a = 1 (coefficient of x²) and b = -7 (coefficient of x), so x = -(-7)/(2*1) = 3.5.

The x-coordinate of the vertex is thus 3.5. Now, to get the y-coordinate of the vertex, we substitute x = 3.5 into our equation, so y = (3.5)² - 7*(3.5) + 12 = -0.25. Therefore, the vertex of the parabola is at (3.5,-0.25). The line of symmetry of a parabola always passes through the vertex, so the equation of the axis of symmetry is x = 3.5.

Learn more about Vertex and Axis of Symmetry here:

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By using division, it is obtained that

Helen will do 9 problems on Friday

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

Here,

Total number of problems given on Monday = 45

Number of days from Monday to Friday = 5

Number of problems Helen solve on Friday = = 9

Helen will solve 9 problems on Friday

To learn more about division, refer to the link:

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Helen would have to do 9 problems each day. 45/5=9