You want new sneakers that cost $540. You earn $45 per week. If you use all of your income to save for the sneakers, how long until you can buy them?

Answer: £3.38

Step-by-step explanation:

In the first year, the pocket money goes up by:

= 1 + (1 * 50%)

= £1.50

In the second year:

= 1.50 + (1.50 * 50%)

= £2.25

In the third year:

= 2.25 * ( 2.25 * 50%)

= £3.38

Answer:

The least amount of fencing needed for the rectangular pen is 72.19 feet.

Step-by-step explanation:

The area and perimeter equations of the pen are, respectively:

[tex]p = 2\cdot (x + y)[/tex] (1)

[tex]A = x\cdot y[/tex] (2)

Where:

[tex]p[/tex] - Perimeter, in feet.

[tex]A[/tex] - Area, in square feet.

[tex]x[/tex] - Width, in feet.

[tex]y[/tex] - Length, in feet.

Let suppose that total area is known and perimeter must be minimum, then we have a system of two equations with two variables, which is solvable:

From (2):

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

(2) in (1):

[tex]p = 2\cdot \left(x + \frac{A}{x}\right)[/tex]

And the first and second derivatives of the expression are, respectively:

[tex]p' = 2\cdot \left(1 -\frac{A}{x^{2}} \right)[/tex] (3)

[tex]p'' = \frac{4\cdot A}{x^{3}}[/tex] (4)

Then, we perform the First and Second Derivative Test to the function:

First Derivative Test

[tex]2\cdot \left(x - \frac{A}{x^{2}} \right) = 0[/tex]

[tex]2\cdot \left(\frac{x^{3}-A}{x^{2}} \right) = 0[/tex]

[tex]x^{3} - A = 0[/tex]

Given that dimensions of the rectangular pen must positive nonzero variables:

[tex]x^{3} = A[/tex]

[tex]x = \sqrt[3]{A}[/tex]

Second Derivative Test

[tex]p'' = 4[/tex]

In a nutshell, the critical value for the width of the pen leads to a minimum perimeter.

If we know that [tex]A = 169\,ft^{2}[/tex], then the value of the perimeter of the rectangular pen is:

[tex]x = \sqrt[3]{169\,ft^{2}}[/tex]

[tex]x \approx 5.529\,ft[/tex]

By (2):

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

[tex]y = \frac{169\,ft^{2}}{5.529\,ft}[/tex]

[tex]y = 30.566\,ft[/tex]

Lastly, by (1):

[tex]p = 2\cdot (5.529\,ft + 30.566\,ft)[/tex]

[tex]p = 72.19\,ft[/tex]

The least amount of fencing needed for the rectangular pen is 72.19 feet.

Answer: $ 91.50.

Step-by-step explanation:

Let x be the original price.

Since discount is applied before tax.

New price = (Original price - Discount)-Tax rate (Original price - Discount)

, where Discount = Discount rate x Original price.

Substituting values, we get

[tex]62.28=(x-0.25x)-0.0925(x-0.25x)[/tex]

[tex]62.28=(0.75x)-0.0925(0.75x)[/tex]

[tex]62.28=0.75x-0.069375x[/tex]

[tex]62.28=0.680625x[/tex]

[tex]x=\frac{62.28}{0.680625}[/tex]

[tex]x=91.50[/tex]

Hence, the original price was  $ 91.50.

Answer:

5%

Step-by-step explanation:

Given that:

Theoretical probability = 50%

The experimental probability = number of desired outcome / number of trials

Hence, experimental probability = 45 / 100 = 0.45

0.45 = 0.45 * 100% = 45%

Percentage difference in theoretical and experimental probability :

Theoretical - experimental

50% - 45% = 5%

Answer:

[tex]\displaystyle A_\text{shaded}=18-\frac{9}{2}\pi \text{ units}^2[/tex]

Step-by-step explanation:

First, find the area of the rectangle:

[tex]A_\text{rect}=9(3)=18\text{ units}^2[/tex]

In order to find the area of the shaded region, we can subtract the areas of the two sectors from the total area of the rectangle.

Find the area of the sectors. We can use the sector formula:

[tex]\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}[/tex]

The left sector has a radius of three units and an angle of 90°. Hence, its area is:

[tex]\displaystyle A_\text{L}=\pi (3)^2\cdot \frac{90}{360}=9\pi\cdot \frac{1}{4}=\frac{9}{4}\pi[/tex]

The right sector is identical to the left sector. So, the total area of the two sectors is:

[tex]\displaystyle A_{\text{T}}=\frac{9}{4}\pi +\frac{9}{4}\pi =\frac{9}{2}\pi[/tex]

Hence, the area of the shaded region is:

[tex]\displaystyle A_\text{shaded}=18-\frac{9}{2}\pi \text{ units}^2[/tex]

Answer:A

Step-by-step explanation:

m=(14-11)/(8-2)

m=3/6

m=1/2

y = 1/2x+b substitute one of the points

11=1/2(2)+b

11=1 + b

b=10

y = 1/2x+10

Answer:

Step-by-step explanation:

Note : In multiplication if the bases are same u can add their exponent while in division if the bases are same u can subtract their exponent.

Hope this helps u !!

Answer: B

Step-by-step explanation:

Answer:

We have to:

"All of the plots are the same length, x"

L = x

"and the width of each plot is 5 yards less than the length"

W = x-5

"The total number of plots Liam owns is 20 more than the length of a plot"

20 + x

"the total area of all the plots Liam owns is 2,688 square yards"

A = (20 + x) * (x) * (x-5)

A = (20x - 100 + x ^ 2 -5x) * (x)

A = (x ^ 2 + 15x - 100) * (x)

2688 = (x ^ 3 + 15x ^ 2 - 100x)

x ^ 3 + 15x ^ 2 - 100x = 2688

x ^ 3 + 15x ^ 2 - 100x - 2688 = 0

Answer:

*** The equation x3 + 15x2 - 100x - 2.688 = 0 can be used to find the length of each plot.

Answer:x^3+15x^2-100x-2,688=0

Step-by-step explanation:

Answer:x>=-2

Step-by-step explanation:x is also equal to -2 as the dot is closed.

Answer:

x=2

Step-by-step explanation:

Since the base angles are the same, the side lengths are the same, making this an isosceles triangle

7(x+2) = 4(9-x)

Distribute

7x+14 = 36 -4x

Add 4x to each side

7x+4x +14 = 36 -4x+4x

11x +14 = 36

Subtract 14 to each side

11x+14-14 = 36-14

11x = 22

Divide by 11

11x/11 =22/11

x=2

Answer: x=2

Step-by-step explanation:

This is an isosceles triangle. That means both of the sides marked are congruent.

That means we can set up this equation and solve it:

[tex]7(x+2)=4(9-x)[/tex]

First let's use the distributive property

[tex](7)(x)+(7)(2)=(4)(9)-(4)(x)\\7x+14=36-4x[/tex]

Now we can add 4x on both sides

[tex]7x+14+4x=36-4x+4x\\11x+14=36[/tex]

Next we subtract 14 from both sides

[tex]11x+14-14=36-14\\11x=22[/tex]

Finally we divide both sides by 11

[tex]\frac{11x}{11} =\frac{2}{11} \\x=2[/tex]

Answer:

The answer you're looking for is 8,200cm

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Divide by 4 on each side.

4x/4 and 8/4

Now we have just x on one side and 2 on the other.

So, x = 2.

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Unit place of 226 is 6 and so it is divisible by 2

226 = 2 * 113

Here ,  2 and 113 are prime numbers

Answer:

120 different ways

Step-by-step explanation:

The first person can be 5 different ways

Now there are 4 people left

The second person can be 4 different ways

And so on

5*4*3*2*1

120 different ways

Answer:

a) The ratio of used books to new books is of [tex]\frac{9}{4}[/tex].

b) The ratio of all books on the shelf to used books is of [tex]\frac{13}{9}[/tex]

Step-by-step explanation:

Ratio of a to b:

The ratio of a to b is given by:

[tex]\frac{a}{b}[/tex]

Ratio of b to a:

The ratio of b to a is given by:

[tex]\frac{b}{a}[/tex]

In this question:

13 books, 9 used, 4 new.

(a) What is the ratio of used books to new books?

9 used, 4 new. So

The ratio of used books to new books is of [tex]\frac{9}{4}[/tex].

(b) What is the ratio of all books on the shelf to used books?

13 books on the shelf, 9 used. So

The ratio of all books on the shelf to used books is of [tex]\frac{13}{9}[/tex]

Answer:

65 degree angle but when straight 180 degree angle

Step-by-step explanation:

sry if wrong :)

Answer:

x-intercept (2, 0)

Step-by-step explanation:

y = 2x² - 6x + 4

Factor

(2x - 2)(x - 2) = 0

2x - 2 = 0

2x = 2

x = 1

x-intercept (1, 0)

x - 2 = 0

x = 2

x-intercept (2, 0)

By using the factor method,

the other x-intercept of the parabola is (2, 0).

A parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the Directrix ).

Given:

One x-intercept for a parabola is at the point (1,0).

In factor form : (x - 1)

And the quadratic function,

y = 2x² - 6x + 4.

To find the factor of the equation:

2x² - 6x + 4 ÷ (x - 1)

We get,

(2x - 4) = 0

x = 4/2

x = 2

The other intercept of the parabola is (2, 0).

Therefore, the other x-intercept of the parabola is (2, 0).

To learn more about parabola;

https://brainly.com/question/21685473

#SPJ2

Answer:

Step-by-step explanation:

Step 1: Add -4y to both sides.

2x+4y+−4y=1+−4y

2x=−4y+1

Step 2: Divide both sides by 2.

2x

2

=

−4y+1

2

x=−2y+

1

2

Step 1: Add 5y to both sides.

3x−5y+5y=7+5y

3x=5y+7

Step 2: Divide both sides by 3.

3x

3

=

5y+7

3

x=

5

3

y+

7

3

The answer is 19 they worked it out right above the question.

Answer:

19

Step-by-step explanation:

3(x+6) = 5(x-4)

Distribute

3x+18 = 5x-20

Subtract 3x from each side

18 = 2x-20

Add 20 to each side

38 = 2x

Divide by 2

19 = x

The solution is 19

Answer:

v . u = < v1 , v2 > . <u1 , u2> = v1 u1 + v2 u2

Step-by-step explanation:

Answer:

2x-3

Step-by-step explanation:

f (x) = 3x - 1

g(x) = x + 2

(f - g)(x) = 3x-1 - ( x+2)

Distribute the minus sign

       = 3x-1 -x-2

Combine like terms

       = 3x-x-1-2

       = 2x-3

(f - g )( x ) = 2 x - 3

f ( x ) = 3x - 1

g ( x ) = x + 2

remove unnecessary parantheses

collect like terms

Answer:

e and f

Step-by-step explanation:

there is a great app to use called algebrator it helps me everyday for things like this <3

Answer:

its A. 48.125

Step-by-step explanation:

it just is

Answer:

a

Step-by-step explanation:

Answer:

65 + 30x.

Step-by-step explanation:

The $65 is a one-time fee for when you first purchase the instrument. The $30 is every month you rent it, and x = the months you rent it.

Therefore, to find the whole cost over time, you would do

65 (first month) + 30x (how much you'll spend over the time you rent the instrument).

Answer: 320 cents

Step-by-step explanation:

80/5 = 16

16*20= 320

Answer:

Cost 20 apples = 320

Step-by-step explanation:

5 apples cost = 80

cost of 20 apples = ?

First we should cost of 1 apple

1 apple cost = 80 ÷ 5

= 16

∴ Cost of 20 apples = 16 × 20

= 320