Write the ratio in simplest form for area of pool/ area of yard

Answer: x = 1 + 0.5c

Step-by-step explanation:

Looks like the integral should be

[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]

Expand the denominator:

[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]

Notice that

[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]

In order to use this substitution, expand the integral as

[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]

In the first integral, use the previously mentioned substitution:

[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]

[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]

In the second integral, complete the square in the denominator:

[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]

Now substitute

[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]

so that

[tex]\sec t=\dfrac{8x+13}5[/tex]

Then

[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]

and the integral becomes

[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]

[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]

[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]

So, the integral is

[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]

Answer:

36 x 2 + 21 x + 3

Step-by-step explanation:

Simplify the expression.

Add and subtract the second term to the expression and factor by grouping. You get 3 ( 4 x + 1 ) ( 3 x + 1 )

Answer:

37.77

Step-by-step explanation:

P= PV x i / 1- (1+i)^-n

PV = 745

I = .1684 / 12 = .01403

N = 4 x 12 = 48

.19 x (365 x 9) = 624.53

21.4338469 x 48= 1028.12

624.53 / (624.53+1028.12) = 37.77

The  percentage of the lifetime cost of the refrigerator did the electricity make up is : d. 37.77%.

Using this formula

P= Pv x i / 1- (1+i)^-n

Where:

Present value = 745

Interest= .1684 / 12 = .01403

Number of months = 4 x 12 = 48

Hence:

Percentage=.19 x (365 x 9)/(.19 x (365 x 9)+(21.4338469 x 48)

Percentage=624.53 / (624.53+1028.12)

Percentage= 37.77%

Inconclusion the  percentage of the lifetime cost of the refrigerator did the electricity make up is : d. 37.77%.

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Answer: The answer is 25%

Step-by-step explanation:

Answer:

L = 260 cm^2

Step-by-step explanation:

height h = 12 cm

slant height s = 13 cm

side length a = 10 cm

lateral edge length e = 13.928388277184 cm

1/2 side length r = 5 cm

volume V = 400 cm^3

lateral surface area L = 260 cm^2

base surface area B = 100 cm^2

total surface area A = 360 cm^2

Genda: h = height

s = slant height

a = side length

e = lateral edge length

r = a/2

V = volume

L = lateral surface area

B = base surface area

A = total surface area

Answer:  $415

Step-by-step explanation:  75 x $6 = 450.  450 - 35 = 415

Answer:

Step-by-step explanation:

Okay so solving an inequality is essentially the same as solving an expression, just with a different symbol.

We can first separate the x to the left and whole numbers to the right side.

TIP INPORTANT: Put your variable numbers on the left side and your whole numbers which are the numbers without variables on the right side

so,

4x ≤  10 + 2

which is,

4x ≤  12, therefore,

x ≤  3.

Hope this helps!

The solution is x ≤ 3

What is an Inequality Equation?

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

4 x - 2 ≤ 10

Adding 2 on both sides , we get

4 x ≤ 12

Divide by 4 on both sides , we get

x ≤ 3

Hence , the solution is x ≤ 3

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Answer:(-infinity,-29/6)

Step-by-step explanation:

Interval notation of this problem.

Step-by-step explanation:

Hey there!

The coordinates of a triangle are;

Now, We have;

P(x,y)----------- P'(kx, ky)

Keep formula;

A(1,2)---------- A'(-4×1 ,-4×2)

= A'(-4, -8)

B(1,-2)------------- B'(-4,8)

C(-2,-2)-------------C'(8,8)

[ The A' should be kept in (-4,-8). There was no place in this graph so, i kept it just below -7. Please while plotting remember to keep it on "-8".]

Hope it helps..

Answer: 85 units

Step-by-step explanation:

x^2 +35x + 35 = 10235

-10235 on both sides

x^2 + 35x -10200

Now Factor

( x - 85 ) ( x + 120 )

Now plug in for x using 85 or -120

(85)^2 + 35(85) + 35

7225 + 2975 + 35 = 10235

So 85 is the right answer

Answer:

Step-by-step explanation:

You observe that each term is 30 less than the previous one. This is the recursive rule. It also means the sequence is arithmetic with a common difference of -30.

Recursive equation

  f[1] = 60; f[n+1] = f[n] -30

__

Explicit equation

The general form of the explicit equation is ...

  f(n) = f(1) +d(n -1)

Here, we have f(1) = 60 and d = -30, so your equation is ...

  f(n) = 60 -30(n -1)

Answer:

5/11

explanation

Probability here is the chance of selection out of a total. So, we need to first find the total number of marbles.

total

=

5

+

3

+

2

+

1

=

11

So there are  

11

marbles total. The probability that we pick one of the  

3

green marbles out of the  

11

is simply that ratio:

P

green

=

3

11

Same idea for yellow:

P

yellow

=

2

11

The probability of picking either of these colors is simply the sum of their probabilities.

P

green or yellow

=

P

green

+

P

yellow

=

3

11

+

2

11

=

5

11

Answer:

The answer is "Nominal"

Step-by-step explanation:

Some of the data is missing which is defined in the attached file. please find it.

The standard measuring degree is nominal for the favorite type of music because the type of music it can be listening for depends on a variety of factors, like age, social or local environment, etc, and the wrong choice can be defined as follows:

Step-by-step explanation:

3. 7 = -2y + 4

2y = 4 - 7

2y = -3

y = -1.5

5. -3x - 2 = -17

17 - 2 = 3x

15 = 3x

3x = 15

x = 15/3

x = 5

Answer:

as reference angle is a

h=5

b=3

p=4

sinA= p/h= 4/5

cosA= b/h= 3/5

tanA= p/b=4/5

Step-by-step explanation:

Step-by-step explanation:

[tex]sine \: A = \frac{4}{5}\\\\

cosine \: A = \frac{3}{5}\\\\

tangent \: A = \frac{4}{3}\\\\[/tex]

Answer:

The middle two terms cancel out each time, and the final product is x2 plus the product of the positive coefficients of i in the original expression. All imaginary parts either cancel out or get replaced with -1, leaving an expression that doesn’t include imaginary numbers.

Step-by-step explanation:

Answer:

2.999 millions hours ago

Step-by-step explanation: :)

Answer:

38,500 pounds

Step-by-step explanation:

1 ton = 2000 pounds

Answer:

Step-by-step explanation:

A/b = c for b

A/b = c

A = bc

bc = A

b = A/c

Answer:

See below

Step-by-step explanation:

[tex]\frac{A}{b}=c\\\frac{A}{b} * b = c * b\\ A = c * b\\\frac{A}{c} = \frac{c*b}{c}\\\frac{A}{c} = b\\ b =\frac{A}{c}[/tex]

Answer:

KM= KL+LM

5x+10=3x+4x

5x+10=7x

2x=10

x=5

now

kl=3x=3*5=15

Answer:

7.28

Step-by-step explanation:

Answer: 7.28

Step-by-step explanation:

Answer:

c.  3 to 9

Step-by-step explanation:

It was right on edg 2020

Answer: c

Step-by-step explanation:

The question is incomplete. Here is the complete question

The ratio of the width to the length of a rectangle is 1:3. Which of the following ratios represents a rectangle with this same ratio?

Answer:

21:63

Step-by-step explanation:

The ratio of the width to the rectangle is 1:3

= 1/3

= 0.333333

From the options given we have the following ratios

=5:7

= 5/7

= 0.71428

= 6:9

= 6/9

= 0.666666

= 33:100

= 33/100

= 0.33

= 21:63

= 21/63

= 0.3333333

Hence the ratio which represents the rectangle given above is 21:63