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2 years ago

11

Renee bought a magazine subscription for a year. She paid $27. Renee wanted to find the price, p, of the subscription each month

. She created the model shown to help find this price.

1 answer:

kirza4 [7]2 years ago

3 0

The price is 2.25, I found that answer by dividing 27 and 12 for that it would be 12p=27 divide 12 from both sides, p=2.25

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A piano teacher charges students $20.25 each month, plus $5.25 per hour for lessons.

Tomtit [17]

Answer:

99$

Step-by-step explanation:

you take the 5.25$ per hour and multiply it by the 15 hours, and then you add the 20.25$ per month

8 0

3 years ago

Read 2 more answers

If (62)x = 1 what is the value of x? Explain your answer.

Alex

Whenever you solve an equation with a single variable you need to isolate the variable by itself on one side of the equal sign. Just be sure that whatever operations you perform on one side you perform on the other sides as well.

62x=1 divide both sides by 62

x=1/62

3 0

3 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

In the past year Pablo watched 12 movies that he thought were very good. He watched 60 movies over the whole year. Of the movies

kumpel [21]

It would be 20 percent, I believe. First you would put it into a fraction of 12\60, then you would simplify that into 3\15 then divide as shown. You end up with .2 which would be 20 percent.

7 0

3 years ago

Which expression is the factorization of x2 + 10x + 212

Montano1993 [528]

Answer:

The answer is option 1.

Step-by-step explanation:

Firstly, you have to elaborate the expression :

${x}^{2} + 10x + 21$

$= {x}^{2} + 3x + 7x + 21$

Next you have to take out the common factors and factorize it :

${x}^{2} + 3x + 7x + 21$

$= x(x + 3) + 7(x + 3)$

$= (x + 7)(x + 3)$

8 0

3 years ago

Read 2 more answers