George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.

Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.


A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.

How many feet of fencing will George need for the dog run?

Answer: 30

Step-by-step explanation:

     A LCD, or least common denominator, is the lowest common multiple of both denominators.

     Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...

     Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...

    We can see the LCD of 3/5 and 5/6 is:

           30

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The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal.  In this case, the problem is asking us to determine the LCD or least common denominator of two numbers.  We are provided with two fractions that we will use to help determine our solution.  However, before solving for the LCD let us first define what LCD means.

Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.

Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.

[tex]5x+2y = 4~~~~~~~~~~...(i)\\\\7x +3y = 5~~~~~~~~~~...(ii)\\\\\text{Write in AX = B form.}\\\\~~~~~~\begin{bmatrix}5&2\\7&3 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\begin{bmatrix}5&2\\7&3 \end{bmatrix}^{-1}\\\\\\[/tex]

[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-7\\-2&5\end{bmatrix}^{T}}{\begin{vmatrix}5&2\\ 7&3 \end{vmatrix}}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}}{5(3) -2(7)}\\\\\\[/tex]

[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}12-10\\-28+25 \end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}2\\-3\end{bmatrix}\\\\\\\text{Hence,}~ (x,y) = (2,-3)[/tex]

There are 6 terms in the sequence greater than 1.

A geometric series is  sum of infinite numbers which has a common ratio between its successive terms.

The missing common ratio value is -1/2

It is given in the question that

the number of terms in the sequence = 300

Sum = a₁ (1-rⁿ)/(1-r)

nth term is given by

aₙ = a₁r⁽ⁿ⁻ ¹⁾

1337(1/2)^(n - 1) = 1

(1/2)^(n - 1)  = 1/1337

Applying log on both sides

log (1/2)^(n - 1) = log (1/1337)

(n - 1) log(1/2)  = log(1/1337)

n  = log (1/1337)/ log (1/2) + 1 ≈ 11.384

the 11th term  is 1337(-1/2)^(10)  ≈ 1.305

and

And the 12th term is 1337(-1/2)^11  =  -.653

As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.

Therefore there are 6 terms in the sequence greater than 1.

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The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)

From the question, we are to determine the solutions to the given system of equations

The given system of equations are

x + y = 3 ----------- (1)

y = x² - 9 ----------- (2)

From equation (1)

x + y = 3

We can write that

y = 3 - x -------- (3)

Substitute this into equation (2)

y = x² - 9

3 - x = x² - 9

x² +x -3 - 9 = 0

x² +x -12 = 0

Solve quadratically

x² +x -12 = 0

x² +4x -3x -12 = 0

x(x +4) -3(x +4) = 0

(x -3)(x +4) = 0

∴ x -3 = 0 OR x +4 = 0

x = 3 OR x = -4

Now, using equation (3)

When x = 3

y = 3 - x

y = 3 - 3

y = 0

When x = -4

y = 3 - -4

y = 3+4

y = 7

∴ When x = 3, y = 0; and when x = -4, y = 7

Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)

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Answer: See the attached images below.

The steps and explanations are on those screenshots, so there's not much for me to mention right here on this main page. The decimal results are approximate to 6 decimal places. Make sure your calculator is in degree mode.

Answer:

1: sin B, cos B, and tan B = 36.87°

2: x = 11.7

Step-by-step explanation:

Question 1: As toy can see they all have the same angle answer just different methods of finding it

Question 2:

adjacent is the closest side to the angle

opposite is the side across from the angle

hypotenuse is always the longest side

x = 11.7025

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you’ll make it thru <3

DONT BE AFRAID TO ASK IF YOU CANT READ MY HANDWRITTING

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^k~~ = ~~\cfrac{1}{x^{-1}}\implies x^k~~ = ~~x^1\implies k=1[/tex]

the awnser is B x-2                    

The correct statement is AngleL = 25° AngleL' = 25°.

We have given that,

Triangle JKL is transformed to create triangle J'K'L'.

We have to choose the correct option.

The following information should be considered:

In a rigid transformation, the image & pre-image are congruent.

Reflection, translation, and rotation are rigid transformations.

In a non-rigid transformation, the image and pre-image are similar.

Dilation is a non rigid transformation.

In a rigid or nonrigid transformation, the corresponding angles are the same.

If the corresponding sides are the same, then it is a rigid transformation.

If the corresponding sides are proportional, then it is a nonrigid transformation.

It can be a rigid or a nonrigid transformation based on whether the corresponding side lengths have the same measures.

Therefore option 3 is correct.

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Answer:

Length C, B= 90 mi

Step-by-step explanation:

The small square in the corner in any shape always represent 90°

Hope it helps!!

The solution to the system of equation is x = -7+√17/2 and -7-√17/2

Equations are expressions separated by an equal sign

Given the equation

x^2 = –7x – 8

Equate to zero

x^2+7x+8 = 0

Factorize

x = -7±√49-4(8)/2

x =  -7±√17/2

x = -7+√17/2 and -7-√17/2

Hence the solution to the system of equation is x = -7+√17/2 and -7-√17/2

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Answer:

Option 4

Step-by-step explanation:

The answer above is correct.

to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]

The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that.  Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.

The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.

Distribute

After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.

Subtract 12 from both sides

The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h.  Then we will simplify the expression and that will give us our final answer.

Divide both sides by -2

Simplify the expression

We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.

The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos

A) The percentage of respondents who do not like both hamburgers and burritos is; 33/250 * 100% = 16.09%

B) Marginal relative frequency of all customers that like hamburgers will be the ratio of the sum of the customers that like hamburgers to the total number of respondents. Thus;

MRF = 134/205 = 0.65

C) Let us first find the ratio of all the four data with the total;

Ratio of those who like Hamburgers and burritos = 39/134 = 0.29

Ratio of those who like Hamburgers but not burritos = 95/134 = 0.71

Ratio of those who like burritos but not Hamburgers = 38/71 = 0.53

Ratio of those who do not like burritos or Hamburgers = 33/71 = 0.47

Thus, The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10[/tex]

Answer:

Add and Divide.

Mean = 84

Step-by-step explanation:

Mean ( math word) and average (common usage word) tell us to ADD up the numbers in the list of data and DIVIDE by the number of pieces of data.

Here we add:

(80 + 84 + 88)

then divide by 3, because there's 3 numbers in this list.

(80 + 84 + 88)/3

= 252/3

= 84

The mean, or average is 84.

Answer:

[tex]x = 2\\y = 2\sqrt{3}[/tex]

Step-by-step explanation:

**Look at the picture

[tex]a\cdot a^2+b\cdot a+c=a^3+ab+c[/tex]

Answer: 130 degrees

Step-by-step explanation:

If we are assuming this is an isosceles trapezoid, then this means angles B and C are congruent.

Answer:

Given:

Cylinder: height = 16 cm ; radius = 5 cm

cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³

Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³ 

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5s^2}{s}[/tex]

[tex]\\ \rm\Rrightarrow 5s[/tex]

After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent. [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We have:

A philanthropist pledges to donate 10% of a fund each year.

We can find the amount left after 7 years as follows:

A = 450000(1 - 0.1)⁷

10% of a fund each year.

Rate r = 10% = 0.1

A = 450000(0.9)⁷

A = $2152336.05

Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.

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Answer:  25

Reason:

The exponent 25 is not a multiple of 3. If it was something like 24, then we would have a perfect cube as shown below

[tex]w = 125x^{18}y^3z^{24}\\\\w = 5^{1*3}x^{6*3}y^{1*3}z^{8*3}\\\\w=(5^1x^6y^1z^8)^3\\\\w = (5x^{6}yz^{8})^3\\\\[/tex]

When going from step 2 to step 3, I used the rule that [tex](abcd)^e = a^eb^ec^ed^e[/tex]. Basically the exponent e gets applied to each factor inside.

Answer:

25

Step-by-step explanation:

The factors of the expression x^2 - 9x + 14 are (x - 7) and (x - 2)

The expression is given as:

x^2 - 9x + 14

Expand

x^2 - 2x - 7x + 14

Factorize the expression

x(x - 2) - 7(x - 2)

Factor out x - 2 from the expression

(x - 7)(x - 2)'

Hence, the factorized expression of x^2 - 9x + 14 is (x - 7)(x - 2)'

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Answer:

As a fraction:

x | y

________

|

7/3 | 2

3 | 4

11/3 | 6

13/3 | 8

As a mixed fraction:

x | y

________

|

2 ⅓ | 2

3 | 4

3 ⅔ | 6

4 ⅓ | 8

As a decimal:

x | y

___________

|

2.33.. | 2

3 | 4

3.66.. | 6

4.33.. | 8

You should start with x values since the y values will be easier to plot. x's will not be easy to represent.

For example:

x | y

________

|

0 | -5

1 | -2

2 | 1

3 | 4

4 | 7

5 | 10

Answer:

3 teaspoons

Step-by-step explanation:

Three teaspoons are equivalent to one tablespoon

The correct answer is option C which is  [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

The multiplication of the matrix will be calculated as:-

M = [tex]\dfrac{1}{2}\left[\begin{array}{cc}12&64&\\78&30&\\\end{array}\right][/tex]

M  =    [tex]\left[\begin{array}{cc}\dfrac{12}{2}&\dfrac{64}{2}&\\\dfrac{78}{2}&\dfrac{30}{2}&\\\end{array}\right][/tex]

M =     [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

Therefore the correct answer is option C which is  [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

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Supplementary Angles:

[tex]\boxed{100°} and \boxed{80°}[/tex]

Arithmetically speaking, the closest 2 supplementary angles can get (in 3 and 2 digits respectively) is the upwritten.

Complementary Angles:

[tex]\boxed{45°} and \boxed{45°}[/tex]

Simply, in this case, for angles to be numerically as close as possible - make both the angles 45°.

Answer:

9

Step-by-step explanation:

[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]