Carmen plans to buy a $60.00 video game from the Game Shop. There is a 5% sales tax on every game purchase. What is the amount of the sales tax?

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

[tex]Area = 128[/tex]

Let the dimension of the paper be x and y;

Such that:

[tex]Length = x[/tex]

[tex]Width = y[/tex]

So:

[tex]Area = x * y[/tex]

Substitute 128 for Area

[tex]128 = x * y[/tex]

Make x the subject

[tex]x = \frac{128}{y}[/tex]

When 1 inch margin is at top and bottom

The length becomes:

[tex]Length = x + 1 + 1[/tex]

[tex]Length = x + 2[/tex]

When 2 inch margin is at both sides

The width becomes:

[tex]Width = y + 2 + 2[/tex]

[tex]Width = y + 4[/tex]

The New Area (A) is then calculated as:

[tex]A = (x + 2) * (y + 4)[/tex]

Substitute [tex]\frac{128}{y}[/tex] for x

[tex]A = (\frac{128}{y} + 2) * (y + 4)[/tex]

Open Brackets

[tex]A = 128 + \frac{512}{y} + 2y + 8[/tex]

Collect Like Terms

[tex]A = \frac{512}{y} + 2y + 8+128[/tex]

[tex]A = \frac{512}{y} + 2y + 136[/tex]

[tex]A= 512y^{-1} + 2y + 136[/tex]

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

[tex]A' = -512y^{-2} + 2[/tex]

Set

[tex]A' = 0[/tex]

This gives:

[tex]0 = -512y^{-2} + 2[/tex]

Collect Like Terms

[tex]512y^{-2} = 2[/tex]

Multiply through by [tex]y^2[/tex]

[tex]y^2 * 512y^{-2} = 2 * y^2[/tex]

[tex]512 = 2y^2[/tex]

Divide through by 2

[tex]256=y^2[/tex]

Take square roots of both sides

[tex]\sqrt{256=y^2[/tex]

[tex]16=y[/tex]

[tex]y = 16[/tex]

Recall that:

[tex]x = \frac{128}{y}[/tex]

[tex]x = \frac{128}{16}[/tex]

[tex]x = 8[/tex]

Recall that the new dimensions are:

[tex]Length = x + 2[/tex]

[tex]Width = y + 4[/tex]

So:

[tex]Length = 8 + 2[/tex]

[tex]Length = 10[/tex]

[tex]Width = 16 + 4[/tex]

[tex]Width = 20[/tex]

To double-check;

Differentiate A'

[tex]A' = -512y^{-2} + 2[/tex]

[tex]A" = -2 * -512y^{-3}[/tex]

[tex]A" = 1024y^{-3}[/tex]

[tex]A" = \frac{1024}{y^3}[/tex]

The above value is:

[tex]A" = \frac{1024}{y^3} > 0[/tex]

This means that the calculated values are at minimum.

Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Answer:

The ratio of green apples to red apples is .

Step-by-step explanation:

Given,

Number of red apples = 21

Number of green apples = 18

We have to find out the ratio of green apples to red apples.

Solution,

For finding the ratio we have to divide the number of green apples to the number of red apples.

So, we can frame the above sentence as;

Ratio = number of green apples/number of red apples

Now substituting the values, we get;

Ratio= 18/21 = 6/7

Hence The ratio of green apples to red apples is . 6/7

Answer:

(x - 12)(x + 4)

Step-by-step explanation:

The two numbers have equal the b term which is -8

You know you have to subtract to get your answer because there is a minus sign in front of the c term

Find what factors of 48 subtract to = -8

-12 + 4 = -8

Answer:

50

Step-by-step explanation:

good luck!!

Answer:

50

Step-by-step explanation:

hope its correct..............

have absolutley no idea.. i might want to learn this to lol

Given :

A sixth-grade student bought three cans of tennis balls for $4 each.

The sales tax for each can was $0.95.

To Find :

The total amount the student spent.

Solution :

Price of each can including taxes :

p = $( 4 + 0.95 )

p = $4.95

So, price of 3 such cans including tax is :

P = p×3

P = $( 4.95×3 )

P = $14.85

Therefore, total amount spend by the student is $14.85 .

Answer:if the answer you are looking for has to do with the diagram its the one with the arrow pointing to the left

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

(4*100)/6

=400/6

=66.67

Round to get 67

Answer:

139°

Step-by-step explanation:

According to the question

The equation is

4r+17+4r+115=180

8r+132=180

8r=48

r=6

So BYF =

4.6+115

24+115

139°

Answer:

139

Step-by-step explanation:

Answer:

B) 120

Step-by-step explanation:

hope this helpssssss

Answer:

x = 84°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

129° is an exterior angle of the triangle, thus

x + 45° = 129° ( subtract 45° from both sides )

x = 84°

The 2 triangles formed by the tree/ shadow and Jordan/ shadow are similar and ratio of corresponding sides are equal, that is

let h be the height of the tree, then

[tex]\frac{h}{7}[/tex] = [tex]\frac{50}{10}[/tex] = 5 ( multiply both sides by 7 )

h = 35

The height of the tree is 35 ft

Answer:

black

Step-by-step explanation:

Answer:

2x and 8y

Step-by-step explanation:

Distribute:

5*x=5x

5*y=5y

-3*x=-3x

-3*-y=3y

Combine:

5x+-3x= 2x

5y+3y= 8y

Hope this helps!!!

Answer:

32 Students

Step-by-step explanation:

3/5 = 12/20

This means you add the boys and girls to get 32.

Answer:

The answer is "5.7"

Step-by-step explanation:

Using the cosine rule.

[tex]\cos T = \frac{r^2+s^2-t^2}{2rs} \\\\t^2= r^2+s^2-2rs \cos T ........(i)\\\\r=1.7\\s=7.3\\T=15\\\\t^2= (1.7)^2+(7.3)^2-2(1.7)(7.3) \cos 15^{\circ} \\\\[/tex]

   [tex]=2.89+53.29-24.82(0.9659)\\\\=32.2064[/tex]

[tex]t= 5.6751 =5.7[/tex]

Answer:

Honestly dude try your hardest u got this i belive in u ask your mom or dad or big brother or big sister if your seeing this right now im trying to help if if u love your mom u would do the same.

Step-by-step explanation:

Answer:

the product of the given radical is [tex]\sqrt[5]{12}[/tex]

Step-by-step explanation:

The computation of the product of the given radicals is as follows

According to the question, the following radical is

[tex]\sqrt{50} \ and \sqrt[5]{6}[/tex]

Now simplify it

[tex]\sqrt{25 \times 2} and \sqrt[5]{6}\\\\\sqrt{25} \sqrt{2} and \sqrt[5]{6}\\\\\sqrt[5]{2} and \sqrt[5]{6}\\\\\sqrt[5]{12}[/tex]

Hence, the product of the given radical is [tex]\sqrt[5]{12}[/tex]

This is the answer but the same is not given in the options

y=-5x

Step-by-step explanation:

Answer:

no what you mean by 218√

Step-by-step explanation:

there has to be a 90 degree angle for it to be a right triangle

Answer:

-12/5 or -2.4

Step-by-step explanation:

(-4/5) / (1/3) =

(-4/5) x (3/1) =

-12/5

-12/5 = -2.4

Answer:

[tex]\frac{-(\frac{4}{5})}{\frac{1}{3}} = -(\frac{4}{5}) * (\frac{3}{1} )= -\frac{12}{5}[/tex]

Step-by-step explanation:

1. Dividing fractions means multiplying the reciprocal-- so turn the fraction upside down and multiply by the first.

hsjsudiejejfjnfkekek

Answer:

24

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

n-14=2

add 14 on both sides to get 16

In the statement, A number subtracted from 14 is 2 the unknown number

is 12.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A number subtracted from 14 is 2.

Let the unknown number be 'n'.

∴ 14 - n = 2.

- n = 2 - 14.

- n = - 12.

n = 12.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ2

Answer:

-90

Step-by-step explanation:

Step-by-step explanation:

1. Given

2. Definition of midpoint

3. Theorem: Congruence of segments is reflexive.

4. SSS

Tye answer to this problem is 9 hours

Answer:

Step-by-step explanation:

It’s 9

Answer:

612

Step-by-step explanation:

Answer:

Option a

Step-by-step explanation:

It is made up of only rational numbers

Answer:

vvvgghhi

hi

Step-by-step explanation:

ggguuuuuuuuhh