Nidhi is creating a rectangular garden in her back yard. The length of the garden is 10 feet. The perimeter of the garden must be at least 40 feet and no more than 76 feet. Write and solve a compound inequality to find the range of values for the width, w, of the garden.

Answer:

Step-by-step explanation:

1.

[tex]S = 2\pi rh\\Divide\:both\sides\:of\:the\:equation\:by\:2rh\\\\\frac{S}{2rh} = \frac{2 \pi rh}{2 rh} \\\\\pi = \frac{S}{2rh}[/tex]

2.

[tex]E = \frac{1}{2} mv^2\\\\E = \frac{mv^2}{2} \\\\Cross\:multiply\\\\2E =mv^2\\Divide\:both\:sides\:of\:the\:equation\:by\:m\\\frac{2E}{m} = \frac{mv^2}{m} \\\\\frac{2E}{m} =v^2\\Square\:root\:both\:sides\:of\:the\:equation\\\sqrt{\frac{2E}{m} } = \sqrt{v^2} \\\\\sqrt{\frac{2E}{m} } =v\\\\v =\sqrt{\frac{2E}{m} }[/tex]

3.

[tex]7a+2b =c\\Isolate\:b\\\\2b =c-7a\\2b= -7a+c\\Divide\:both\:sides\:of\:the\:equation\:by \:2\\\frac{2b}{2} =\frac{-7a+c}{2} \\\\b = \frac{-7a+c}{2}[/tex]

4.

[tex]y = \frac{1}{3} (x+1)\\\\y = \frac{x+1}{3}\\\\Cross\:multiply \\3y =x+1\\Isolate \:x\\3y -1=x\\\\x =3y-1[/tex]

Answer:

18

Step-by-step explanation:

g(3)+f(4)

=3²+1+2×4

=9+1+8

=18

Answer:

Explained below

Step-by-step explanation:

Sol: 1. Multiplication

Multiply the set S; the answer should also belong to the set S. For example, -1 x 0 = 0 Є S and -1 x 1 = -1 Є S, Hence the set S is closed under multiplication.

2. Addition

When we add two sets S elements, the answer should also belong to the set S, for example, 1 + 0 = 1 Є S but 1 + 1 = 2, which does not belong to set S; hence S is not closed under addition.

3. Subtraction

The set S is not closed under subtraction because  -1 – 1  = -2, -2 is not the set S.

4. Division

The set S is not a closed division because when we divide one S element to another element, the answer does not belong to the set S, for example -1/0 = undefined.

5. Squaring

The set is closed under squaring if we square an element of the set S, and the result also belongs to the set S, for example, (0)2 = 0 and (-1)2 = 1, which belongs to the set S. Hence set S is closed under squaring.

6. Square rooting

The set S is not closed under square rooting because when we take the square root of an element of set S, the answer does not belong to the set S. √-1 = undefined.

7. Averaging two numbers

Averaging two numbers mean the sum of two numbers of set S is divided by two. For example, 1 + 0/2 = 1/2, which is not belongs to set S. hence set is not closed under averaging two numbers.

8. Averaging three numbers

The sum of three numbers of set S is divided by 3; the answer should belong to the set S.

-1 + 0 + 1 / 3= 0, 0 belongs to set. Hence the set S is closed under averaging three numbers.

Answer is explained below. We can say that Subtraction is not closed under the set.

Given set S = {−1, 0 ,1}  we have to check the given set is closed or not.

1. Multiplication

Multiply the set S; the answer should also belong to the set S. For example, [tex]-1\times 0=0[/tex], 0 Є S and [tex]-1\times 1 = -1[/tex] , -1 Є S, so the set S is closed under multiplication.

2. Addition

On adding the any two values of the set, the result belong to the set itself, for ex if we add [tex]-1+0=-1\\[/tex] Є S  but 1. so we can say that the given set is closed under addition.

3. Subtraction

The set S is not closed under subtraction because  -1 – 1  = -2, -2 is not the set element S.

4. Division

The set S is not belongs to closed division because when we divide one S element to another element, the answer does not belong to the set S, for example -1/0 = undefined.

5. Squaring

The set is closed under squaring,since we square an element of the set S, and the result also belongs to the set S. for example, [tex]0^{2} =0[/tex] and[tex]-1^{2} =1[/tex] which belongs to the set S. Hence set S is closed.

Hence We can say that Subtraction is not closed under the set.

For more details on Set follow the link below:

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Answer:

50/b in

Step-by-step explanation:

Use the area formula A = (1/2)(base)(height).

Here the area A is given and is 25 in^2; the base is not given, so use 'b.'

Then, since A = (1/2)(base)(height),

(height) = 2A/(base) = 2(25 in^2)/b = 50/b in

Answer:

V  = 36Π cubic Centimetres

Step-by-step explanation:

Step(i):-

Volume of the solid

The Volume of the solid formed by revolving the region bounded by the curve y = f(x) and rotated around  the x-axis defined by

                [tex]V = \pi \int\limits^a_b {[f(x)]^{2} } \, d x[/tex]

Step(ii):-

Given two curves are y = x²  and y = 9

The point of intersection of two curves

                                y = x²...(i)

                        and y = 9 ...(ii)

Equating both equations , we get

                       x² - 9 =0

                 ⇒  x² - 3² =0

                 ⇒ (x+3)(x-3) =0

                 ⇒ x+3=0  and x-3=0

                 x = 3 ⇒ y = 9

                x = -3 ⇒y = 9

The point of intersection ( -3,9) and (3,9)

Step(iii):-

                 [tex]V = \pi \int\limits^a_b {[(f(x)]^{2} } \, -[g(x)]^{2})d x[/tex]

The limits x- varies from -3 to 3

                   [tex]V =\pi (\int\limits^3_3 {x^{2} } \, dx +\int\limits^3_3{9} \, dx[/tex]

                   [tex]V =\pi (\frac{x^{3} }{3} -9 x)^{3} _{-3}[/tex]

                 [tex]V= \pi ( \frac{27}{3} - 9(3) - (\frac{-27}{3} -9(-3))[/tex]

                V = π ( |-36| = 36Π cubic Centimetres

Final answer:-

The volume of the solid

  V = π ( |-36| = 36Π cubic Centimetres

Answer:

7020 codes

Step-by-step explanation:

For one upper case letter:

There are 26 letters in this scenario

For two upper case letters:

There are 26 * 26 letters in this scenario. Essentially, there are 676 letters in this scenario.

For one upper case letter:

There are 10 digits that can be applied to it. So therefore, there are 26 * 10 codes in this case.

That means, there are 260 codes for one upper case letter.

For two upper case letters:

There are 10 digits that can be applied to it. That is to day, there are 676 * 10 codes in this case.

This means, for two upper case letters, there are 6760 codes.

Finally, we add up the number of codes for one upper case letter, and that of two upper case letters together. As such, we have

6760 + 260 = 7020.

The company has 7020 codes available.

Please vote for brainliest.

Answer:

[tex]-6x^2 + 73x - 46[/tex]

Step-by-step explanation:

(3x-2)(22-2x+1)

simplify (22-2x+1)

(3x-2)(23-2x)

distribute

69x - 6x^2 - 46 + 4x

simplify

[tex]-6x^2 + 73x - 46[/tex]

Make a system of equations.

[tex]x-y=3[/tex]

[tex]x^2-y^2=69[/tex]

[tex]x=y+3[/tex]

[tex](y^2+6y+9)-y^2=69[/tex]

[tex]6y+9=69[/tex]

[tex]6y=60[/tex]

[tex]y=10[/tex]

[tex]x=10+3[/tex]

[tex]x=13[/tex]

[tex]x=13,y=10[/tex]

Hope this helps.

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Answer:

Step-by-step explanation:

2nd train DATA:

time = 2 hrs ; rate = x + 120 mph ; distance = 2(x+120) = 2x+240 miles

------

1st train DATA:

time = 8 hrs ; rate ; x mph ; distance = 8x miles

------------------

Equation:

distance = distance

8x = 2x+240

6x = 240

x = 40 mph (speed of the 1st train)

x+120 = 160 mph (speed of the 2nd train)

my regards #3Ss

Answer:

The second highest winning amount was of $213,876

Step-by-step explanation:

Given that the main prize of "The price is right" won is $ 262,743, and that the second highest prize in the history of said program is 81.4012% of said value, to obtain said number the following calculation must be performed:

(262,743 / 100) x 81.4012 = X

2,627.43 x 81.4012 = X

213,875.95 = X

Therefore, rounded to the nearest dollar, the second highest prize in the program was $213,876.

Answer:

the coordinate of the focus is: (0, 1/2)

the equation of the directrix is: y=-1/2

Step-by-step explanation: The standard equation for a parabola that opens upward- parallel to the y-axis, is: x2=4ay. Meaning, a = distance from the vertex to focus and the vertex is at origin: (0,0).

4a is equal to 2

a is equal to 2/4

a is equal to 1/2 or 0.5

The parabola has

focus: (0,1/2)

directix: y=-1/2

If the parabola is given by

y=a(x-h)²+k

then the focus of the parabola is given by

(h,k+1/4a)

and the directrix of the parabola is given by

y=k-a

Given parabola is x²=2y

So, the parabola is y=(1/2)x², when compared with y=a(x-h)²+k  we have

a=1/2, h=0 and k=0

So, the focus of the parabola is

[tex](0,\frac{1}{4\frac{1}{2}})= (0,\frac{1}{2})[/tex]

and, the directrix of the parabola is

y= -1/2.

Hence, the parabola has

focus: (0,1/2)

directix: y=-1/2

To learn more about parabola visit- https://brainly.com/question/4074088?referrer=searchResults

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Answer:

i'm not sure if it is right

Step-by-step explanation:

1, B

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

              g(-2x+2)=3.(-2x+2)+2=-6x+6+2=-6x+8

2,

#1: Write as a linear equation

     y=4x+8

#2: Swap x and y variables

     x=4y+8

#3: Solve for y

     4y+8=x

     4y=x-8

       y=[tex]\frac{x-8}{4}[/tex]

#4: Write in inverse notation:

[tex]f^{-1}[/tex](x)=[tex]\frac{x-8}{4}[/tex]= (x/4) - 2

Steps to solve:

2(x - 6) = 3(x + 9)

~Distribute both sides

2x - 12 = 3x + 27

~Add 12 to both sides

2x = 3x + 39

~Subtract 3x to both sides

-x = 39

~Divide both sides by -1

x = -39

Best of Luck!

Answer:

2×-12=3×+27

2×-3×=27+12

-×=39

Step-by-step explanation:

Grouping like terms

then simplify to get x

Answer:

well the length on both increases by x3 and the height increases by 2

Step-by-step explanation:

Answer:

3.5 units

Step-by-step explanation:

I'm big brain

The subsets of real numbers are known as:

Best of Luck!

Answer:

52

Step-by-step explanation:

everytime it adds by 9:

7+9=16

16+9=25

25+9=34

34+9=43

43+9=52

Answer:

52,500 sq feet

Step-by-step explanation:

150 x 350 = 52,500 sq feet

To find the area, you do width x length.

Hope this helps!!

Answer:

Step-by-step explanation:

The needed concentration is exactly halfway between the available concentrations, hence they must be mixed equally.

He should mix 30 mL each of the 10% and 40% solutions.

_____

The first step in solving any problem is to look at the given information, and at what is being asked for. Here, the mix that is being asked for is exactly halfway between the given concentrations, so you know without any further contemplation that the mix will be 50%/50% of each.

__

If the mix were something else, there are several ways the problem can be solved. I like to use a diagram that puts the available concentrations on the left in a column with the highest on top, the needed concentration in the next column in the middle, and the differences of these numbers on the diagonals in the right column.

Example: if the needed mix is 15%, the diagram would look like ...

   40            5

          15

   10           25

The numbers on the right tell you the proportions required (5:25 = 1:5). For this example, you need 1 part 40% solution and 5 parts 10% solution to make a mix that is 15%. That's a total of 6 parts, so each "part" is 10 mL for 60 mL of solution.

We chose this example so every number in the diagram is different, so you could see how the instructions for use apply.

__

Another way to solve this is to let a variable represent the amount needed of the highest concentration. If we let that variable be x, for the given problem, we can write the equation for the amount of acid in the mix as ...

  40%(x) + 10%(60 -x) = 25%(60)

  0.30x = 9 . . . . . . . . subtract 6, simplify

  x = 9/0.30 = 30 . . . . . mL of 40% solution

Given:

The expression is

[tex]-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)[/tex]

To find:

The value of the expression.

Solution:

We have,

[tex]-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)=-2\dfrac{1}{3}+10\dfrac{1}{6}[/tex]

Convert the mixed fraction in improper fraction.

[tex]=-\dfrac{2\times 3+1}{3}+\dfrac{10\times 6+1}{6}[/tex]

[tex]=-\dfrac{6+1}{3}+\dfrac{60+1}{6}[/tex]

[tex]=-\dfrac{7}{3}+\dfrac{61}{6}[/tex]

Taking LCM, we get

[tex]=\dfrac{-2(7)+61}{6}[/tex]

[tex]=\dfrac{-14+61}{6}[/tex]

[tex]=\dfrac{42}{6}[/tex]

Convert it into mixed fraction.

[tex]=\dfrac{6(7)+5}{6}[/tex]

[tex]=7\dfrac{5}{6}[/tex]

Therefore, the correct option is C.

Answer:

A.) asequence with six terms that starts with 1 and has a common ratio of 2

Answer:

[tex]a=-\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{5}{8}=\frac{1}{2}\left(a+2\right)\\\\Switch\: sides\\\frac{1}{2}\left(a+2\right)=\frac{5}{8}\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\2\times\frac{1}{2}\left(a+2\right)=\frac{5\times\:2}{8}\\\\Simplify\\a+2=\frac{5}{4}\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\a+2-2=\frac{5}{4}-2\\\\Simplify\\a=-\frac{3}{4}[/tex]

Answer: 198 total people

Step-by-step explanation:

so there are 11 floors and each obtain 9 rooms so if there are two people in each of the 9 rooms there will 18 total people in one floor and since there are 11 floors multiply it by 18 to find out how many people live in the apartment.

11 * 18 = 198

Answer:

answer is 6x+4

mark it as branliest.

Answer:

GK = 6x + 4

Step-by-step explanation:

3x + 5 - x + 4x - 1 - x + x

3x -x + 4x - x + x + 5 -1

6x + 4

≈ 0,5 m

≈ 50 cm

d = 2r => r = d/2 = 1,4m/2 = 0,7 m

V = πr²·h => h = V/πr²

770 l = 0,77 m³

h = 0,77m³/3.14×0,49m²

= 0,77m³/1,5386m²

= 0,5004 m

≈ 0,5 m

≈ 50 cm

Answer:

The  decision is to fail to reject the null hypothesis

This  means that  the population mean apartment rental rate now does not exceeds the level reported in 2002

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = \$895[/tex]

   The  population standard deviation is  [tex]\sigma = \$225[/tex]

   The sample  size is  [tex]n = 180[/tex]

   The sample mean is  [tex]\= x = \$ 915[/tex]

    The sample standard deviation is [tex]s = \$ 227.50[/tex]

   The  level of significance is [tex]\alpha = 0.01[/tex]

The null hypothesis is  [tex]H_o : \mu \le \$ 895[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > \$895[/tex]

   The test statistics is evaluated as

           [tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]

=>       [tex]t = \frac{ 915 - 895}{ \frac{225}{ \sqrt{180} } }[/tex]

=>       [tex]t =1.193[/tex]

So from  z-table  the p-value is obtained, the value is  

      [tex]p-value = P(Z > t) = P(Z > 1.193 ) = 0.11643[/tex]

So From the value obtained we see that

       [tex]p-value > \alpha[/tex] so  we  fail to reject the null hypothesis

Answer:

The answer is

Step-by-step explanation:

Since the triangle is a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we use tan

[tex] \tan(\theta) = \frac{opposite}{adjacent} [/tex]

From the question

the opposite is 12

the adjacent is 15

We have

[tex] \tan(x) = \frac{12}{15} \\ x = \tan^{ - 1} ( \frac{12}{15} ) \\ x = 38.659808[/tex]

We have the final answer as

Hope this helps you

If a factory made 7,737 toy cars each day for 6 days, to find the total number of cars, we can add 7,737 to itself 6 times or just multiply by 6.

[tex]7737*6=46422[/tex]

The factory made 46422 toys in the last 6 days.

Hope this helps.

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Answer:

3x

Step-by-step explanation:

Answer:

4;3 might be the answer