10 points need help finding area

The dimensions of the garden with the largest area she can enclose are given by 24*14 square yards.

The area (A) of the rectangle with length L and Width W is given by,

A=L*W

The maximum of [tex]y=ax^2+bx[/tex] occurs at x = -b/2a

Let the length and width of the garden be L and W respectively.

Now let my friend use cedar fencing for one width and cheaper metal fencing for rest sides.

Rate of cedar fencing is $17/yard

Then she has to pay for cedar fencing = 17W

rate of cheaper metal fencing is $7/yard

Then she has to pay for metal fencing = 7W+7*2L = 7W+14L

Then according to condition,

17W+7W+14L = 672

24W+14L = 672

12W+7L = 336

7L = 336-12W

L = (336-12W)/7

Then the area of the rectangular garden is given by,

A = L*W

[tex]A=\frac{336-12W}{7}\times W\\A=-\frac{12}{7}W^2+48W[/tex]

So here a = -12/7 and b = 48

Then maximum of W occurs at,

W = -48/(2*(-12/7)) = (48*7)/(2*12) = 336/24 = 14

Then maximum width = 14 yards

then length (L) = (336-12*14)/7 = 168/7 = 24 yards

Hence the dimensions with the leargest area she can enclose is given by = 24 * 14 square yards.

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We have to use the formula  [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex]  to find the number of terms of a finite geometric sequence.

If a be the first term of a finite sequence, r be the common ratio between consecutive terms and n be the number of terms.

So, we have to use the formula of sum of sequence and then calculate it to reduce the equation to find the value of number of terms, that is n.

Then, Sum of the sequence (Sn) = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]

Here, in the given problem,

Sum(Sn) = 280, First term of the sequence(a) = 40, Common ratio(r) = 0.75

So, Sn = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]

   ⇒ [tex]1-r^{n} =\frac{S_{n}(1-r) }{a}[/tex]

   ⇒ [tex]r^{n} =1+\frac{S_{n}(1-r) }{a}[/tex]

   ⇒ [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex]          

Now you have to put the values and get the number of terms.

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Answer:

15

Step-by-step explanation:

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

Answer:

[tex]y=-4; y=28[/tex]

Step-by-step explanation:

The way I like to think about it, with absolute value meaning the distance is

"find which number are 16 apart from 12". Which means 28 (to the right) or -4 (to the left).

More formally, applying the definition of absolute value,

[tex]|y-12|=16 \leftrightarrow y-12=\pm16\\y-12=-16 \rightarrow y=-4\\y-12=+16 \rightarrow y=28[/tex]

Answer: Choice B) One-sixth

In other words, the fraction 1/6

===========================================================

Explanation:

The base, aka horizontal component, is 6 units long. Count out the spaces from -5 to 1 to get a result of 6.

Or you could subtract and use absolute value in either of these two ways

Where A = -5 and B = 1 are the endpoints mentioned. Absolute value is used to ensure the result of the subtraction isn't negative. Negative distance on a number line doesn't make sense.

----------

However you determine the base, we'll multiply it by the unknown height which we'll call h. This leads to the area of the rectangle. The area is 6h.

Rule: The area under a probability density curve must always be 1.

So the area 6h must be 1 which helps us see that...

6h = 1

h = 1/6

Divide both sides by 6 to isolate h fully.

Answer:

B

Step-by-step explanation:

The equation to model the above scenario is [tex]x^{2}[/tex] +22x - 23 = 0

The perimeter of the expanded rectangle is 48 units

A rectangle is a quadrilateral with its 4 angles 90°

Analysis:

First rectangle:

length = 10 + x

width = x

Second rectangle:

length = x + 14

width = x + 8

Area of expanded rectangle = 135 square unit

(x+8)(x+14) = 135

[tex]x^{2}[/tex] + 8x + 14x + 112 = 135

[tex]x^{2}[/tex] + 8x + 14x -23 = 0

[tex]x^{2}[/tex] + 22x -23 = 0

[tex]x^{2}[/tex] + 23x - x - 23 = 0

(x-1)(x+23) = 0

Therefore x = 1

Expanded length = 1+14 = 15

Expanded width = 1+8 = 9

Perimeter = 2(9+15) = 48 units

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Answer:

12

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{ASSUMING}[/tex]

[tex]\mathsf{x^{2y}}[/tex]

[tex]\huge\textbf{IF SO, FOLLOW THESE STEPS TO}\\\huge\textbf{SOLVE FOR YOUR RESULT}[/tex]

[tex]\mathsf{x^{2y}}\\\mathsf{= 3^{2(6)}}\\\mathsf{= 3^{2\times6}}\\\mathsf{= 3^{12}}\\\mathsf{= 3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3}\\\mathsf{= 9\times9\times9\times9\times9\times9}\\\mathsf{= 81\times81\times81}\\\mathsf{= 6,561\times81}\\\mathsf{= 531,441}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{531,441}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

25:16

50:32

100:64

Step-by-step explanation:

The inverse of g(5) and the inverse of h(x) are 2 and [tex]h^{-1}=\frac{-x-13}{4}[/tex] respectively

Inverse of a function

Given the following coordinates and function

g = {(-6, -5), (2, 5), (5,6), (6,9)}

The inverse of "g" is determined by switching the coordinates to have:

g^-1(x) =  {(-5, -6), (5, 2), (6, 5), (9,6)}

Since the value of the y-coordinate when x = 5 is 2, hence g^-1(5) = 2

Given the function expressed as:

h(x) = -4x - 13

y = -4x - 13

Replace y with x

x = -4y - 13

4y = -x - 13

y = (-x-13)/4

[tex]h^{-1}=\frac{-x-13}{4}[/tex]

Determine the composite function [tex](hoh^{-1})(-1)[/tex]

h(h(x)) = h(-4x-13)
h(h(x)) =[tex]\frac{-(-4x-13)-13}{4} \\[/tex]

[tex]h(h(x))=\frac{4x}{4} \\h(h(x)) = x\\h(h(-1)) = -1[/tex]

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Answer:

340 i am pretty sure

Step-by-step explanation:

Answer:

option 4 and option 3 are the answers respectively

Answer:

[tex] \sqrt{ {2}^{3} } \\ \sqrt{3} \\ .............[/tex]

Answer:

=  -10

Step-by-step explanation:

p + (-q) - 2 = x

if:

p = -3

q = 5

then:

-3 + (-5) - 2 = x

we know that:

+(-) = -

then:

-3 +(-5) - 2 = -3 - 5 - 2 = x

x = -10

The value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.

It is defined as the combination of constants and variables with mathematical operators.

We have given an expression:

= P + (-q) - 2

Plug p = -3

q = 5

= -3 + (-5) - 2

= -3 - 5 - 2

= -10

Thus, the value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.

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Answer: (1, -10)

Step-by-step explanation:

Since both of the equations are set equal to y, we can conclude that:

[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]

If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]

Thus, the solution is (1, -10)

Answer:

314 in²  (nearest whole number)

Step-by-step explanation:

Radius of a regular polygon: The distance from the center of the polygon to any vertex.  The radius of a hexagon is equal to the length of one side.

Therefore, from inspection of the given diagram:

To find the area of a regular polygon, we first need to calculate the apothem.   The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.

[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]

Area of a Regular Polygon

[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]

[tex]\implies \sf A=314.3672216...[/tex]

[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]

Answer:

See below

Step-by-step explanation:

Slope = rise / run

           from 0,-1   to  1.5 , 0

               this is    1 / 1.5    =   2/3

y xis intercept = -1

y = 2/3 x   -1            Slope intercept form

2/3 x - y   = 1             another form

2x - 3y = 3                Standard form (I think this is 'standard form' ....yah?)

Answer:

72 Degrees

Step-by-step explanation:

We know that its 72 because of VAT, the vertical angle theorem.

Two (2) lines are considered to be parallel if their slopes are the same (equal) and they do not intersect.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

In conclusion, two (2) parallel lines are shown in the image attached below for more understanding,

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In logarithmic form, we get In(2e^9)= ln(2)+9.

We are given,

 ln(2[tex]e^{9}[/tex])

We know that, ln(ab) = ln(a) + ln(b)

So we get,

 ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])

Since ln(m^n)=n ln(m)  

And ln(e)= 1, we will get,

ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)

          = ln(2) +9

Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.

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Answer:

operant conditioning and schedules of reinforcement

Parallel lines have equivalent slopes, so as the slope of the given line is 1, the slope of the line we want to find is also 1.

Substituting into point-slope form and rearranging into slope-intercept form,

[tex]y-2=1(x+6)\\\\y-2=x+6\\\\\boxed{y=x+8}[/tex]

Step-by-step explanation:

2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)

2x+4+5x+25=4x-32+2x-4

7x+29=6x-36

7x-6X=-36-29

X=-65

Answer:

x = -65

Step-by-step explanation:

2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2) ​

Distribute:

2(x + 2): 2x + 4

5(x + 5): 5x + 25

=

4(x - 8): 4x - 32

2(x - 2): 2x - 4

Combine like terms:

(2x + 4) + (5x + 25) = (4x - 32) + (2x - 4)

5x + 2x: 7x              =  4x + 2x: 6x

4 + 25 = 29             =  -32 - 4: -36

7x + 29 = 6x - 36

Now we want to separate like terms,

subtract 29 from both sides

subtract 6x from both sides

7x + 29 - 29 - 6x = 6x - 29 - 6x- 36

7x - 6x = - 29 - 36

x = -65

Answer:

the answer is -7+-25=-32

Answer:

370 + 80x ≤ 1090

Step-by-step explanation:

By using letter variables for the unknown numbers, we can break down the question into mathematical terms:

If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.

If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.

The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:

$370 (1 day) + $80 (x hours) ≤ $1090 per day

The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.

To simplify this, we can rewrite it as:

370 + 80x ≤ 1090

The probability will be equal to 60%.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The best thing to do here is to put it into a fraction. as 30 landed heads up, 20 (50-30) must be tails.

You can then put this into a fraction, which becomes 20/50.

To turn this into a decimal, you can then divide 1 by 50

1/50= 0.02

As you've got 22 lots of this, you then need to multiply 0.02 by 20.

0.2x20= 0.40

To find the percentage, you've then got to multiply the decimal by 100.

100x0.40= 40.

Therefore, 40% of the tosses would be tails

As you've found what one percentage is, you simply need to take this number away from 100 to find the other, rather than having to go through the process again.

100-40= 60

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The correct answer is  CI = (71.415%, 78.915%)

The correct option is (A)

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Given:

x = 376

Sample = 500 students

CI= [(376/500-1.96 √((376/500)*(124/500)/500) , (376/500-1.96                

                                                                         √((376/500)*(124/500)/500)]

CI = (71.415%, 78.915%)

Hence, CI = (71.415%, 78.915%)

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The statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = |2x - 1|   and

g(x) = |2x - 5|

After plotting on a coordinate plane.

The y-intercept of f(x) is 1

The y-intercept of g(X) is 5

Or plug x = 0 to find the y-intercept.

The y-intercept of g is 4 units above the y-intercept of f

Thus, the statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

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