You are going to have a swimming pool put your back yard this summer. The dimensions of the pool are going to be 15 ft by 30 ft. There is going to be a concrete walkway around the outside of the pool, but they are not sure how wide it will be. The design of the pool, including the walkway, is shown below.

Answers

Answer 1

Answer:

The perimeter of a shape is the sum of the all visible side lengths of the shape. The perimeter of the pool including the walkway is 90 + 8x

Given that:

$Length = 15$

$Width = 30$

Let the width of the walkway be x.

The dimension of the pool including the walkway is calculated by adding the dimension of the pool to the width of the walkway (on both sides):

So, we have:

$Length = 15 + x + x$

$Length = 15 + 2x$

$Width = 30 + x + x$

$Width = 30 + 2x$

The perimeter (P) of the walkway is then calculated using:

$P = 2 * (Length + Width)$

This gives:

$P = 2 * (15 + 2x + 30 + 2x)$

Collect like terms

$P = 2 * (15 + 30+ 2x + 2x)$

$P = 2 * (45+ 4x)$

Open brackets

$P = 2 * 45+ 2 * 4x$

$P = 90+ 8x$

Hence, the perimeter of the pool including the walkway is 90 + 8x (see attachment)

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Answers

The character of the story "Rules of the Game" written by Amy Tan who is described to be invincible in chess is Waverly Place Jong also known as Meimei. Although she cannot find any opponent who can eventually beat hear in chess, she finds a bigger opponent at home- her mom.

Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture? StartFraction 1 Over 5 EndFraction cup. Cup StartFraction 1 Over 4 EndFraction cup. Cup StartFraction 3 Over 4 EndFraction cup. Cup StartFraction 4 Over 5 EndFraction cup. CupFifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors? 0.15(40) + 0.6x = 0.25(40 + x) 0.15(40) + 0.6(x – 40) = 0.25(x) 0.15(40) + 0.6x = 0.25(40 – x) 0.15(40) + 0.6(x + 40) = 0.25(x)

Answers

Correct question is;

1) Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?

2) Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?

A) 0.15(40) + 0.6x = 0.25(40 + x)

B) 0.15(40) + 0.6(x – 40) = 0.25(x)

C) 0.15(40) + 0.6x = 0.25(40 – x)

D) 0.15(40) + 0.6(x + 40) = 0.25(x)

Answer:

1) Amount of cream = ¼cup

2) Option D: 0.15(40) + 0.6(x - 40) = 0.25x

Step-by-step explanation:

1) First of all, let x represent the amount of cup of milk and let y represent the of cup of cream.

We are told that the volume of the mixture is 1 cup.

Thus;

x + y = 1 - - - (eq 1)

We are now told that the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat

Thus, x contains 0.02 fat, y contains 0.18 fat and the 1 cup of mixture contains 0.06 fat.

Thus, we will multiply the respective terms in eq 1 by these %fat content.

Thus;

0.02x + 0.18y = 0.06(1)

0.02x + 0.18y = 0.06 - - - (eq 2)

From eq 1, let's make y the subject which is the amount of cup of cream.

Thus,

y = 1 - x

Let's put 1 - x for y in eq 2 to get;

0.02x + 0.18(1 - x) = 0.06

0.02x + 0.18 - 0.18x = 0.06

0.18x - 0.02x = 0.18 - 0.06

0.16x = 0.12

x = 0.12/0.16

x = 3/4 cup

From,y = 1 - x;

y = 1 - (3/4)

y = ¼ cup

Amount of cream = ¼cup

2) We are given;

15% of the pigment in paint color A is black.

60% of the pigment in paint color B is black.

We are now told that Alan unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.

If we assume the total amount of paint in the mixture is x like we are told, it means that based on the given data, we have a sum of;

0.15(40) + 0.6(x - 40)

Thus is because we know the amount of paint A used as 40 but don't know the amount of paint B used.

Now we are told that this sum produces a mixture that contains 25% black pigment. Since the total amount in the mixture is x. Thus, this final product is 0.25x.

Therefore to derive an equation to find the total amount of paint in the mixture of the two colors, we will equate the sum of the 2 Mixtures to the final product.

This gives;

0.15(40) + 0.6(x - 40) = 0.25x

Solve 2cos^2x+5cosx+2=0

Answers

$2cos^2x+5cosx+2=0\n x\in<-1;1>\n \Delta=b^2-4ac\n \Delta=9\n √(\Delta)=3\n cosx=1\n or\n cosx=-6\n -6\notin<-1;1>\n$

Then using trygonometric table or a graph we read that:
$cosx=1\Leftrightarrow(x)=0$

Period of cosinus function = 2π
So the last answer is $x=0+2k\pi\n$

How do I solve 4cos^2 x -1=0

Answers

$(cosx)^(2) = 1/4$ <=> cosx = +1/2 or cosx = -1/2;
cosx = +1/2 => x = +π/3 + 2kπ, where k is an integer or x = -π/3 + 2kπ, where k is an integer;
cosx = -1/2 => x = +2π/3 + 2kπ, where k is an integer or x = -2π/3 + 2kπ, where k is an integer;

Answer:

pi/3? 2pi/3?

Step-by-step explanation:

Graph: y – 3=1/2(x+2)