A country has 50 million people, 30 million of whom are adults. Of the adults, 5 million are not interested in working, another 5 million are interested in working but have given up looking for work, and 5 million are still looking for work. Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time. What is this country's labor force participation rate?

Answer:

65.8 in²

Step-by-step explanation:

Given a triangle with 2 sides and the included angle then the area (A) is

A = 0.5 × a × b × sinΘ

where a, b are the 2 sides and Θ the included angle

here a = 18, b = 12 and Θ = 147°, hence

A = 0. 5 × 18 × 12 × sin147°

   = 108 × sin147° ≈ 65.8 ( to the nearest tenth )

Answer:

The area of triangle is 59.2 in².

Step-by-step explanation:

If a, b and c are three sides of a triangle then the area of triangle by heron's formula is

[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex]          .... (1)

where,

[tex]s=\frac{a+b+c}{2}[/tex]

From the given figure it is clear that the length of sides are 12 in, 18 in and 28.8 in. The value of s is

[tex]s=\frac{12+18+28.8}{2}=29.4[/tex]

Substitute s=29.4, a=12, b=18 and c=28.8 in equation (1).

[tex]A=\sqrt{29.4(29.4-12)(29.4-18)(29.4-28.8)}[/tex]

[tex]A=\sqrt{3499.0704}[/tex]

[tex]A=59.15294[/tex]

[tex]A\approx 59.2[/tex]

Therefore the area of triangle is 59.2 in².

Answer:

Step-by-step explanation:

x is a "corresponding" angle for the one marked 63°. Here, corresponding angles are congruent, so x = 63°.

__

x and z are "same-side interior angles," so are supplementary. Their sum is 180°. x + z = 180°.

__

Because x and z are supplementary and z and 63° are supplementary, you know that ...

  z = 180° -63°

  z = 117°

_____

Comments on the other answer choices

The value of y can be computed using the fact that the sum of angles interior to the triangle is 180°. The unmarked triangle interior angle is a vertical angle to the one labeled 63°, so it is 63°. Then the value of y is ...

  y° = 180° -47° -63° = 70° . . . . . . . not 47°

__

We already know that 63° + y + 47° = 180° and x = 63°. That means ...

  x + y + 47° = 180°

so it cannot be true that x+y = 180.

Answers are 1,3, and 5

Answer:

Step-by-step explanation:

The number of packets is the greatest common divisor of the given numbers of pencils, erasers, and sharpeners.

It can be helpful to look at the differences between these numbers:

  748 -646 = 102

  646 -527 = 119

The difference of these differences is 17, suggesting that will be the number of packets possible.

  527 = 17 × 31

  646 = 17 × 38

  748 = 17 × 44

The numbers 31, 38, and 44 are relatively prime (31 is actually prime), so there can be no greater number of packets than 17.

There will be 31 pencils, 38 erasers, and 44 sharpeners in each of the 17 packets.

_____

We may have worked the wrong problem. The way it is worded, the maximum number of items in each packet will be 527 pencils, 646 erasers, and 748 sharpeners in one (1) packet. The minimum number of items in each packet will be the number that corresponds to the maximum number of packets. Since 17 is the maximum number of packets, each packet's contents are as described above.

17 is the only common factor of the given numbers, so will be the number of groups (plural) into which the items can be arranged.

Answer:

(A)

Step-by-step explanation:

Answer:

Option A is correct.

Step-by-step explanation:

Given  : [tex]f(x) =2^{x}[/tex] and [tex]g(x) =2^{x+4}[/tex].

To find : How will the graph of g(x) differ from the graph of f(x).

Solution : We have given that  

[tex]f(x) =2^{x}[/tex] and g(x)   [tex]g(x) =2^{x+4}[/tex]

By the transformation Rule : If f(x) →→ f(x +h) if mean graph of function shifted to left by h units .

Then  graph of [tex]g(x) =2^{x+4}[/tex] is the graph of [tex]f(x) =2^{x}[/tex] is shifted by 4 unt left.

Therefore, Option A is correct.

Answer:

  see the attachment

Step-by-step explanation:

The graph attached shows the secant function in red. The restriction to the interval [0, π/2] is highlighted by green dots, and the corresponding inverse function is shown by a green curve.

The restriction to the interval [π/2, π] is highlighted by purple dots, and the corresponding inverse function is shown in purple.

The dashed orange line at y=x is the line over which a function and its inverse are mirror images of each other.

Answer:

Step-by-step explanation:

As the value of a increases, the radical function sweeps out higher, increasing the range of the function.  The k value moves it up or down.  A "+k" moves up (for example, +3 moves the function up 3 from the origin).  The h value moves it side to side.  A positive h value moves to the right and a negative h value moves to the left.  For example, √x-3 moves 3 to the right and √x+3 moves 3 to the left.

In summary, a and k affect the range of the function, k being the "starting point" and a being the "ending point"; h affects the domain of the function.

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

The volume of a sphere is [tex]\frac{4}{3} \pi r^{3}[/tex]

Just plug in 1/2 for r

[tex]\frac{4}{3} \pi (\frac{1}{2}) ^{3}[/tex]

The answer is [tex]\frac{\pi }{6}[/tex]

Answer:

1 hour and 40 minutes

Step-by-step explanation:

Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour.

Levi's dad take time to wash the car by himself will be

We know that the time is inversely proportional to the work.

Let t₁ is the time taken by Levi and t₂ is the time taken by Levi's dad.

We know that the formula

[tex]\begin{aligned} \dfrac{1}{t_1} + \dfrac{1}{t_2} &= 1\\\\\dfrac{1}{2.5} +\dfrac{1}{t_2} &= 1\\\\\dfrac{1}{t_2} &= 1 - \dfrac{1}{2.5}\\\\\dfrac{1}{t_2} &= \dfrac{3}{5}\\\\t_2 &= \dfrac{5}{3}\\\\t_2 &= 1.667 \end{aligned}[/tex]

Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

Check the picture below.

Answer:

x = 60°

Step-by-step explanation:

From ΔOPQ,

∠OPQ = 120°   [ angle at the center inscribed by arc PQ ]

PQ ≅ OQ

so opposite angles to PQ and OQ will be equal

∠OPQ  ≅ ∠OQP

∠OPQ + ∠OQP + ∠POQ = 180°

∠OPQ + ∠OPQ + 120 = 180°

2∠OPQ = 180 - 120 = 60°

∠OPQ = 30°

Since radius OP is perpendicular to tangent.

so ∠OPQ + Y = 90°

y + 30° = 90°

y = 90 - 30 = 60°

Answer x = 60°

Answer:

Step-by-step explanation:

(1) +(2) ⇒ (x -y -2z) +(-x +3y -z) = (4) +(8)

  2y -3z = 12

__

2(1) +(3) ⇒ 2(x -y -2z) +(-2x -y -4z) = 2(4) +(-1)

  -3y -8z = 7

___

The reduced system of equations is ...

Answer:

2y - 3z = 12.

-3y - 8z = 7.

Step-by-step explanation:

x - y - 2z = 4     (1)

-x + 3y - z = 8    (2)

-2x - y - 4z = -1   (3)

Adding (1) + (2):

2y - 3z = 12.

2 * (1) + (3) gives:

-3y - 8z = 7.

Answer:

The dimensions of the brand name television are [tex]26\frac{2}{3}\ in[/tex] by  [tex]66\frac{2}{3}\ in[/tex]

Step-by-step explanation:

we know that

The generic version was based on the brand name and was 3/5 the size of the brand name

Let

x----> the length of the size of the brand name

y----> the width of the size of the brand name

Find the length of the size of the brand name

we know that

[tex]40=\frac{3}{5}x[/tex] -----> equation A

Solve for x

Multiply by 5 both sides

[tex]5*40=3x[/tex]

Rewrite and divide by 3 both sides

[tex]x=200/3\ in[/tex]

Convert to mixed number

[tex]200/3=(198/3)+(2/3)=66\frac{2}{3}\ in[/tex]

Find the width of the size of the brand name

we know that

[tex]16=\frac{3}{5}y[/tex] -----> equation B

Solve for y

Multiply by 5 both sides

[tex]5*16=3y[/tex]

Rewrite and divide by 3 both sides

[tex]x=80/3\ in[/tex]

Convert to mixed number

[tex]80/3=(78/3)+(2/3)=26\frac{2}{3}\ in[/tex]

Answer:89

Step-by-step explanation:

Given scott had an average of 83 on his first three exams

i.e. the sum of first three exams [tex]\sum S_1=83\times 3[/tex]

later he scored an average on the next six exams

i.e. the sum of later 6 exams is [tex]\sum S_2=92\times 6[/tex]

[tex]\sum S_1+\sum S_2=83\times 3+92\times 6=801[/tex]

therefore his average score is =[tex]\frac{801}{9}=89[/tex]

Thus his average score is 89

To find Scott's average for all nine exams, add up the scores from the first three and next six exams, then divide by the total number of exams.

To find Scott's average for all nine exams, we need to calculate the overall average using the given averages for the first three and next six exams.

The average of the first three exams is 83, and the average of the next six exams is 92. To find the average for all nine exams, we can use the formula:Total sum of scores / Number of exams

So, Scott's average for all nine exams is:(83*3 + 92*6) / 9 = 89.1111...

Rounding to the nearest tenth, Scott's average for all nine exams is 89.1.

Learn more about Calculating averages here:

https://brainly.com/question/18554478

#SPJ3

Answer:

Component form of u is (-18,13)

The magnitude of u is 22.2

Step-by-step explanation:

The component form of a vector is an ordered pair that describe the change is x and y values

This is mathematically expressed as (Δx,Δy) where Δx=x₂-x₁ and Δy=y₂-y₁

Given ;

Initial points of the vector as (14,-6)

Terminal point of the vector as (-4,7)

Here x₁=14,x₂=-4, y₁=-6 ,y₂=7

The component form of the vector u is (-4-14,7--6) =(-18,13)

Finding Magnitude of the vector

║u=√(x₂-x₁)²+(y₂-y₁)²

║u=√-18²+13²

║u=√324+169

║u=√493

║u=22.2

Answer:

  see below

Step-by-step explanation:

To find miles per hour, divide miles by hours:

  (5 2/3 mi)/(2 2/3 h) = (17/3 mi)/(8/3 h) = (17/8) mi/h = 2 1/8 mi/h

Hours per mile is the reciprocal of that:

  1/(17/8 mi/h) = 8/17 h/mi

Answer:

b. y+7=5x

Step-by-step explanation:

a. 1-3x^2     is a quadratic

b. y+7=5x    is a linear function:  y = 5x - 7

c. x^3 + 4 = y   is a cubic function

d. 9(x^2-y) = 3    is a quadratic function

e.y-x^3=8   is a cubic function

[tex]

\Sigma_{n=1}^{4}-2\cdot(-3)^{n-1} \\

(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1} \\

-2+6-18+54 \\

\boxed{40}

[/tex]

So the answer is C,

[tex]\Sigma_{n=1}^{4}-2\cdot(-3)^{n-1}=40[/tex]

Hope this helps.

r3t40

The sum of the finite geometric series (-2)(-3)ⁿ⁻¹ for n=1 to n=4 is 40, calculated using the geometric series sum formula.So,option C is correct.

The sum of a finite geometric series with a general term given as (-2)(-3)ⁿ⁻¹ where 'n' ranges from 1 to 4. To find the sum of a geometric series, we need to identify the first term (a) and the common ratio (r), and then use the formula Sₙ = a(1 - rⁿ) / (1 - r), where n is the number of terms.

The first term of the series can be found by substituting n = 1 into the general expression, yielding a = (-2)(-3)¹⁻¹ = -2. The second term, with n = 2, is (-2)(-3)²⁻¹ = -6(-3) = 18, indicating a common ratio of -3.

Thus, the sum of the series for the first four terms can be calculated as:

S₄ = (-2)(1 - (-3)⁴) / (1 - (-3))

S₄= (-2)(1 - 81) / (1 + 3)

S₄= (-2)(-80) / 4

S₄ = 160 / 4

S₄ = 40

Therefore, the sum of the given geometric series is 40.

Answer:

=20s³+50s²+32s+6

Step-by-step explanation:

We multiply each of the term in the initial expression by the the second expression as follows:

4s(5s²+10s+3)+2(5s²+10s+3)

=20s³+40s²+12s+10s²+20s+6

Collect like terms together.

=20s³+50s²+32s+6

Answer:

  x = 117°, 297°

Step-by-step explanation:

Subtract 1 from both sides of the equation and you have ...

  tan(x) = -2

Then the arctangent function tells you ...

  x = arctan(-2) ≈ 116.5651°, 296.5651°

  x ≈ 117° or 297°

Answer:

Point-slope form:

[tex]y-0=\frac{1}{3} (x-1)\\f(x)-0=\frac{1}{3}(x-1)[/tex]

Slope-intercept form:

[tex]y=\frac{1}{3}x-\frac{1}{3} \\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]

Step-by-step explanation:

You have points on that line at (-2, -1) and (1, 0). To find your slope using those points, use the slope formula.

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{0-(-1)}{1-(-2)} \\\\\frac{0+1}{1+2} \\\\\frac{1}{3}[/tex]

Now that we have your slope, you can use your slope and one of your points to write an equation in point-slope form.

[tex]y-y1=m(x-x1)\\y-0=\frac{1}{3} (x-1)\\y=\frac{1}{3} x-\frac{1}{3}[/tex]

To put it in function notation, substitute y for f(x).

[tex]f(x)-0=\frac{1}{3} (x-1)\\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]

First answer is y+1=(1/3) (x+2)

Second answer is f(x) =(1/3) x-(1/3)

Answer:

  (y² +1)/y

Step-by-step explanation:

Invert the denominator fraction and multiply. Factor the difference of squares.

[tex]\displaystyle\frac{\left(\frac{6y^2-6}{8y^2+8y}\right)}{\left(\frac{3y-3}{4y^2+4}\right)}=\frac{6(y^2-1)}{8y(y+1)}\cdot\frac{4(y^2+1)}{3(y-1)}\\\\=\frac{24(y+1)(y-1)(y^2+1)}{24y(y+1)(y-1)}=\frac{y^2+1}{y}[/tex]

Circle theorem:

The angle at the centre (T) is double the angle at the circumference (Q)

---> That also means that:

The angle at the circumference (Q) is half the angle at the centre (T)

Since T = 130 degrees;

Q = 130 divided by 2

   = 65°

___________________________________

Answer:

∠Q = 65°

Answer:

m<Q = 65°

Step-by-step explanation:

It is given that <T = 130°

To find the <Q

From the figure we can see that <T is the central angle made by the arc RS

And <Q is the angle made by the arc RS on minor arc.

We know that m<Q = (1/2)m<T

We have m<T = 130°

Therefore m<Q = 130/2 = 65°

Answer:

E) -3, 5

Step-by-step explanation:

x – 15 / x = 2

x^2 - 15 = 2x

x^2 - 2x - 15 = 0

(x - 5)(x + 3) = 0

x - 5 = 0; x = 5

x + 3 = 0; x = -3

Solutions: -3, 5

For this case we must solve the following equation:

[tex]x- \frac {15} {x} = 2[/tex]

We manipulate the equation algebraically:

[tex]\frac {x ^ 2-15} {x} = 2\\x ^ 2-15 = 2x\\x ^ 2-2x-15 = 0[/tex]

To solve, we factor the equation. We must find two numbers that when multiplied by -15 and when summed by -2. These numbers are:

+3 and -5.

[tex](x + 3) (x-5) = 0[/tex]

So, the roots are:

[tex]x_ {1} = - 3\\x_ {2} = 5[/tex]

Answer:

Option E

Answer:

Answer C

Step-by-step explanation:

Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.

f and h, because the log of a quotient is the difference of the log.

The answer is option C.

Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.

A logarithm is a power to which a range of should be raised for you to get a few different wide varieties (see segment 3 of this Math evaluate for extra approximately exponents). As an example, the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.

Learn more about logarithm here: https://brainly.com/question/25710806

#SP2

Answer:

So we have the two real points (3/2 , 9/2)  and (-1,2).

(Question: are you wanting to use the possible rational zero theorem? Please let me know if I didn't answer your question.)

Step-by-step explanation:

y=2x^2

y^2=x^2+6x+9

is the given system.

So my plain here is to look at y=2x^2 and just plug it into the other equation where y is.

(2x^2)^2=x^2+6x+9

(2x^2)(2x^2)=x^2+6x+9

4x^4=x^2+6x+9

I'm going to put everything on one side.

Subtract (x^2+6x+9) on both sides.

4x^4-x^2-6x-9=0

Let's see if some possible rational zeros will work.

Let' try x=-1.

4-1+6-9=3+(-3)=0.

x=-1 works.

To find the other factor of 4x^4-x^2-6x-9 given x+1 is a factor, I'm going to use synthetic division.

-1   |  4     0     -1     -6    -9

    |         -4     4     -3      9

    |________________ I put that 0 in there because we are missing x^3

        4    -4     3     -9      0

The the other factor is 4x^3-4x^2+3x-9.

1 is obviously not going to make that 0.

Plug in -3 it gives you 4(-3)^3-4(-3)^2+3(-3)-9=-162 (not 0)

Plug in 3 gives you 4(-3)^3-4(-3)^2+3(-3)-9=72 (not 0)

Plug in 3/2 gives you 4(3/2)^2-4(3/2)^2+3(3/2)-9=0 so x=3/2 works as a solution.

Now let's find another factor

3/2  |     4       -4           3        -9

      |                6           3          9

      |________________________

            4          2           6        0

So we have 4x^2+2x+6=0.

The discriminant is b^2-4ac which in this case is (2)^2-4(4)(6). Simplifying this gives us (2)^2-4(4)(6)=4-16(6)=4-96=-92.  This is negative number which means the other 2 solutions are complex (not real).

So the other real solutions that satisfy the system is for x=3/2 or x=-1.

Since y=2x^2 then for x=3/2 we have y=2(3/2)^2=2(9/4)=9/2 and for x=-1 we have y=2(1)^2=2.

So we have the two real points (3/2 , 9/2)  and (-1,2)

Answer:

  15/17

Step-by-step explanation:

You can use what is called the Pythagorean identity:

  sin(θ)² + cos(θ)² = 1

  (-8/17)² + cos(θ)² = 1

  cos(θ)² = 1 - 64/289 = 225/289

  cos(θ) = √(225/289)

  cos(θ) = 15/17 . . . . . . . cosine is positive in the 4th quadrant

Answer:

  $495

Step-by-step explanation:

After the 5% raise, her weekly pay was ...

  $550 × 1.05 = $577.50

If she works 35 hours for that pay, her hourly rate is

  $577.50/35 = $16.50

Then, working 30 hours, her weekly pay will be ...

  30 × $16.50 = $495.00

To find the new amount of weekly pay, multiply the increase in pay by the new number of hours. The new amount is $577.50.

To find the new amount of weekly pay, we need to calculate the increase in pay and then multiply it by the new number of hours.

The employee's pay increased by 5 percent. This means the pay increased by 5% of $550, which is equal to 0.05  imes 550 = $27.50.

Her new hourly rate of pay is the same, so it remains at $550 + $27.50 = $577.50.

Finally, we need to calculate the new amount of weekly pay, taking into account the reduced number of hours. The new pay per hour is $577.50 / 30 = $19.25. Multiply this by the new number of hours to get the new amount of weekly pay: $19.25  imes 30 = $577.50.

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-5)}{4-2}\implies \cfrac{1+5}{2}\implies \cfrac{6}{2}\implies 3[/tex]

Answer:

3lbs of Cashews

Step-by-step explanation:

lbs of Cashews, and 7 lbs of Peanuts

$4.00P + 6.50C = ($4.75/lbs)(10lbs)

$4.00(7) + $6.50(3) = $47.50

$28.00 + $19.50 = $47.50

$47.50 = $47.50

Therefore it's 3lbs of Cashews

Answer:

3lbs of Cashews

hope it helps! x

Answer:

  C'(4, 4)

Step-by-step explanation:

We assume dilation is about the origin, so all coordinates are multiplied by the scale factor:

  C' = 2C = 2(2, 2) = (4, 4)

Answer:

The area of rectangle EFGH is [tex]242\ in^{2}[/tex]

Step-by-step explanation:

For this problem I assume that rectangle ABCD and rectangle EFGH are similar

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Let

z ------> the scale factor

The scale factor is the ratio between the diagonals of rectangles

so

[tex]z=\frac{22}{12}=\frac{11}{6}[/tex]

step 2

Find the area of rectangle EFGH

we know that

If two figures are similar, then the ratio of its areas is the scale factor squared

Let

z------> the scale factor

x -----> area of rectangle EFGH

y ----> area of rectangle ABCD

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{11}{6}[/tex]

[tex]y=72\ in^{2}[/tex]

substitute and solve for x

[tex](\frac{11}{6})^{2}=\frac{x}{72}[/tex]

[tex]\frac{121}{36}=\frac{x}{72}[/tex]

[tex]x=\frac{121}{36}(72)[/tex]

[tex]x=242\ in^{2}[/tex]

The area of rectangle EFGH is approximately 242 square inches.

To find the area of rectangle EFGH given the diagonal lengths of both rectangles and the area of rectangle ABCD, we need to use the properties of rectangles and their diagonals.

Step 1: Analyze Rectangle ABCD

For rectangle ABCD:

- Area [tex]\(A_{ABCD} = 72\)[/tex] square inches

- Diagonal [tex]\(d_{ABCD} = 12\)[/tex] inches

We know the area of a rectangle is given by:

[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]

Let the length be l and the width be w. So,

[tex]\[ l \times w = 72 \][/tex]

Also, for the diagonal of a rectangle, we use the Pythagorean theorem:

[tex]\[ d = \sqrt{l^2 + w^2} \]\\Given \(d_{ABCD} = 12\),\[ 12 = \sqrt{l^2 + w^2} \]\[ 144 = l^2 + w^2 \][/tex]

Step 2: Solve for l and w

We have two equations:

[tex]1. \( l \times w = 72 \)\\2. \( l^2 + w^2 = 144 \)[/tex]

We can solve these equations simultaneously. First, express \(w\) in terms of \(l\):

[tex]\[ w = \frac{72}{l} \]\\Substitute this into the second equation:\[ l^2 + \left(\frac{72}{l}\right)^2 = 144 \]\[ l^2 + \frac{5184}{l^2} = 144 \][/tex]

Multiply every term by [tex]\(l^2\)[/tex] to clear the fraction:

[tex]\[ l^4 + 5184 = 144l^2 \]\[ l^4 - 144l^2 + 5184 = 0 \]Let \(x = l^2\). Then the equation becomes:\[ x^2 - 144x + 5184 = 0 \][/tex]

Solve this quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\[ x = \frac{144 \pm \sqrt{144^2 - 4 \cdot 1 \cdot 5184}}{2 \cdot 1} \]\[ x = \frac{144 \pm \sqrt{20736 - 20736}}{2} \]\[ x = \frac{144 \pm 0}{2} \]\[ x = 72 \][/tex]

So, [tex]\( l^2 = 72 \) and \( w^2 = 72 \)[/tex]. Therefore:

[tex]\[ l = \sqrt{72} = 6\sqrt{2} \]\[ w = \sqrt{72} = 6\sqrt{2} \][/tex]

Step 3: Analyze Rectangle EFGH

For rectangle EFGH:

- Diagonal [tex]\(d_{EFGH} = 22\)[/tex] inches

Let the length be L and the width be W. The relationship for the diagonal is:

[tex]\[ d_{EFGH} = \sqrt{L^2 + W^2} \]Given \(d_{EFGH} = 22\),\[ 22 = \sqrt{L^2 + W^2} \]\[ 484 = L^2 + W^2 \][/tex]

Step 4: Determine Area of Rectangle EFGH

Since the diagonals scale, we assume the rectangles are similar. Thus, the ratios of the corresponding sides (lengths and widths) are the same, and their areas scale with the square of the ratio of the diagonals:

[tex]\[ \text{Area ratio} = \left(\frac{d_{EFGH}}{d_{ABCD}}\right)^2 = \left(\frac{22}{12}\right)^2 = \left(\frac{11}{6}\right)^2 = \frac{121}{36} \][/tex]

So, the area of EFGH is:

[tex]\[ A_{EFGH} = A_{ABCD} \times \frac{121}{36} = 72 \times \frac{121}{36} = 72 \times 3.3611 \approx 242 \text{ square inches} \][/tex]

Thus, the area of rectangle EFGH is approximately 242 square inches.