To describe a specific arith-
metic sequence, Elijah wrote
the recursive formula:
[ f(0) = 30
f(n+1)=f(n)+7
Write a linear equation that
models this sequence

Step-by-step explanation:

Hi there!

The best way to approach this problem is Soh Cah Toa.

In this case you can use sine. sine is opposite over hypotenuse.

so sin(17)= b/15

then to solve for b you multiply 15 on both sides to get 4.4

Answer:

Step-by-step explanation:

This question is an application of the sine law

Equation

b/sin(B) = c / Sin(C)

Givens

b = ????

B = 17

c = 15

C = 140

Solution

Keep in mind that this may not work.

b/sin(17) =   15 / sin(140)                          Multiply both sides by sin(17)

b = 15*sin(17)/sin(140)

b = 15*0.2924/0.6428

b = 6.8233

Answer:

B about $98,000

Step-by-step explanation:

The equation that models the sales of the product after an initial release is:

[tex]S = 16 \sqrt{3t} + 25[/tex]

where s represents the total sales (in thousands) and t represents

the time in weeks after release.

The table and graph is shown in the attachment.

From the graph we estimate the sales

7 weeks after release to be about 98 thousands dollars.

The correct choice is B.

Final answer:

The volume of the oblique rectangular prism is calculated using the length, width, and height. The formula V = l  times w  times h gives a volume of 504 cubic centimeters.

Explanation:

To find the volume of an oblique rectangular prism, we use the same formula as for a right rectangular prism because the volume is not affected by the obliquity of the sides. The formula for the volume (V) is the product of the length (l), width (w), and height (h). So, using the provided dimensions:

V =l  times w  times h = 8 cm  times 7 cm times 9 c

Now, let's calculate:

V = 8  times 7  times 9 = 504 cm

Therefore, the volume of the oblique rectangular prism is 504 cubic centimeters.

39

52 divided by 4 is 13. 52 pickles divided into 4 pickles for each meal is 13. 39 patties divided by 3 patties is 13 aswell so. the answer: 39

The number of meat patties that are needed if 52 pickles are used is:

                                     39 meat patties.

It is given that:

The Big Burger recipe calls for 3 meat patties, 2 slices of cheese, and four pickles.

This means that for every 4 pickles there are 3 meat patties.

This means that for every 1 pickles there are: 3/4 meat patties.

Hence, for every 52 pickles there are: 3/4×52 meat patties

                                                            = 39 meat patties.

Answer:

-7/5 if your function really is f(x)=-5x-7

Step-by-step explanation:

The zeros of an expression are the numbers you can plug into that expression that will make that expression 0.

So what value of x will make the expression

-5x-7=0.

You don't have to this by observation. We can just solve it and see.

-5x-7=0

Add 7 on both sides:

-5x. =7

Divide both sides by -5:

x. =7/-5

x. =-7/5

So -7/5 will make the expression equal to 0.

Let's test this:

-5x-7 when x=-7/5

-5(-7/5)-7

7-7

0

So it does indeed.

Answer:

remain the same, may change

Step-by-step explanation:

When a figure is rotated, its angle measured remains the same and its orientation remains the same.

The circular movement of an object around a rotation axis is known as rotation. An infinite number of rotation axes can exist in a three-dimensional object.

Therefore When a figure is rotated, its angle measured remains the same and its orientation remains the same.

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Answer:

The roots are rational

Step-by-step explanation:

Given

x² = 144 ( take the square root of both sides )

x = ± [tex]\sqrt{144}[/tex] = ± 12 ← both rational

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers.

12 = [tex]\frac{12}{1}[/tex] ← thus rational

- 12 = [tex]\frac{-12}{1}[/tex] ← thus rational

Answer:

The answer is that x^2=144 is rational

Answer:

Part 6) Option B $3.20

Part 7) Option C. 8,295 students

Step-by-step explanation:

Part 6)

Let

x -----> the cost of one hamburger

y ----> the cost of one soda

we know that

7x+3y=27.95 ------> equation A

5x+4y=23.40 ----> equation B

Solve the system by graphing

Remember that the solution by graphing is the intersection point both graphs

using a graphing tool

The solution is the point (3.2,1.85)

see the attached figure N 1

therefore

The cost of one hamburger is $3.20

Part 7)

Let

x -----> the number of students

y -----> the number of teachers

we know that

x=35y ------> equation A

x+y=8,544-12

x+y=8,532 -----> equation B

Solve the system by substitution

substitute equation A in equation B and solve for y

35y+y=8,532

36y=8,532

y=237 teachers

Find the value of x

x=35y ------> x=35(237)=8,295

therefore

The number of students is 8,295

Answer:

The correct answer is A. Aimee's graph is correct because the ratio [tex]\frac{2}{3} :1[/tex] is equal to 2:3, which her graph shows in each point.

Step-by-step explanation:

We are given that Aimee noticed her plant grew 2/3 of an inch every week since it sprouted and a graph is drawn to show the plant growth.

We are to determine whether which of the given statements is correct.

The ratio [tex]\frac{2}{3} :1[/tex] is basically equal to 2:3. Therefore, the graph is correct as it shows the same ratio at each point.

For the points (6, 4) and (3, 2) = [tex]\frac{4-2}{6-3} =\frac{2}{3}[/tex]

Answer:it’s A great got it right on edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) + n - shift a graph of f(x) n units up

f(x) - n - shift a graph of f(x) n units down

f(x + n) - shift a graph of f(x) n units to the left

f(x - n) - shift a graph of f(x) n units to the right

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

We have

[tex]f(x)=x^2,\ g(x)=x^2+(-8x)+7[/tex]

Convert the equation of g(x) to the vertex formula:

[tex]y=a(x-h)^2+k[/tex]

[tex]g(x)=x^2+(-8x)+7\\\\g(x0=x^2-2(x)(4)+7\\\\g(x)=\underbrace{x^2-2(x)(4)+4^2}-4^2+7\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\g(x)=(x-4)^2+7=f(x-4)+7\\\\\text{shift the graph of f(x) 4 units to the right and 7 units up}[/tex]

Answer:

Part 1) The library is located at point (3.25,-1.5)

Part 2) The library is 1.5 miles from Road X

Part 3) The library is 3.25 miles from Road Y

Step-by-step explanation:

step 1

Find the coordinates of the library

we know that

Observing the graph

The length of each square in the graph is 0.5 miles

so

The coordinates of point L are (3.25,-1.5)

therefore

The library is located at point (3.25,-1.5)

step 2

Find the distance of the library from road X

we know that

The distance of point L from road X is the perpendicular distance of point L to the Road X

The perpendicular distance is the absolute value of the y-coordinate of point L

therefore

The library is 1.5 miles from Road X

step 3

Find the distance of the library from road Y

we know that

The distance of point L from road Y is the perpendicular distance of point L to the Road Y

The perpendicular distance is the absolute value of the x-coordinate of point L

therefore

The library is 3.25 miles from Road Y

Answer:

445 dollars

Step-by-step explanation:

You are given he charges 47.5 per hour so 47.5x is how much you will pay for x hours and he charges a 65 dollar service fee.

So together he is charge you 47.5x+65 for x hours.

If it spends 8 hours, the cost will be 47.5(8)+65=445.

The total charges if it takes the plumber 8hours to complete the task is $445.00

According to the question,

For 1 hour the charge is $47.50

∴ For 8 hours, the charge is $(47.50 x 8) = $ 380

The service charge is to be added now.

∴ The final amount of money = $(380.00 + 65.00) = $445.00

The total charge is $ 445.00

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Answer:

center ( -5 , 7).

Step-by-step explanation:

Given  : If the equation of a circle is (x + 5)² + (y - 7)² = 36.

To find : Find its center .

Solution : We have given (x + 5)² + (y - 7)² = 36.

Standard equation of circle : (x – h)² + (y – k)² = r².

Where, (h ,k) = center , r =  radius .

On comparing (x + 5)² + (y - 7)² = 36.

h = -5 , k = 7

So, the center ( -5 , 7).

Therefore, center ( -5 , 7).

Answer:

Step-by-step explanation:

It's a right triangle.

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

a, b - legs

Find x-intercept and y-intercept of a line 4x + 5y = 20.

x-intercept (y = 0):

4x + 5(0) = 20

4x + 0 = 20

4x = 20     divide both sides by 4

x = 5

y-intercept (x = 0):

4(0) + 5y = 20

0 + 5y = 20

5y = 20      divide both sides by 5

y = 4

Therefore the legs are a = 5, b = 4.

Substitute:

[tex]A=\dfrac{(5)(4)}{2}=\dfrac{20}{2}=10[/tex]

Look at the picture.

recall your d = rt, distance = rate * time.

p = speed of the plane

w = speed of the wind

let's keep in mind that, when the plane is going with the wind, is not really going "p" fast is actually going "p + w" since the wind is adding speed to it, likewise, when the plane is going against the wind, the plane is going "p - w" fast, since the wind is subtracting speed from it.

[tex]\bf \begin{array}{lcccl} &\stackrel{km s}{distance}&\stackrel{kph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&3605&p-w&5\\ \textit{with the wind}&4605&p+w&5 \end{array}~\hfill \begin{cases} 3605=(p-w)5\\ \frac{3605}{5}=p-w\\ 721=p-w\\ 721+w=\boxed{p}\\ \cline{1-1} 4605=(p+w)5 \end{cases} \\\\\\ 4605=(p+w)5\implies \cfrac{4605}{5}=p+w\implies \stackrel{\textit{substituting in the 2nd equation}}{921=\left( \boxed{721+w} \right)+w}[/tex]

[tex]\bf 921=721+2w\implies 200=2w\implies \cfrac{200}{2}=w\implies \blacktriangleright 100=w \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{p=721+w\implies }p=721+100\implies \blacktriangleright p=821 \blacktriangleleft[/tex]

Final answer:

The value of the discriminant of the quadratic equation -2x² - 8x + 8 is 128. The positive discriminant suggests that the equation has two distinct real roots.

Explanation:

The discriminant of a quadratic equation can be calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.

In the given quadratic equation -2x² - 8x + 8, a = -2, b = -8, and c = 8. Substituting these values into the discriminant formula:

D = (-8)² - 4(-2)(8) = 64 - (-64) = 128.

The value of the discriminant is 128. The discriminant value can provide information about the nature of the roots of the quadratic equation. If the discriminant is positive (greater than 0), then the equation has two distinct real roots. If the discriminant is 0, then the equation has one real root (a repeated root). If the discriminant is negative, then the equation has no real roots.

Answer:

1/2 hr.

Step-by-step explanation:

Make a whole number of the wall. In this case, multiply by 2:

1/2 x 2 = 2

Because you multiplied 2 to the wall, you must also multiply 2 to the hours:

1/4 x 2 = 2/4

Remember to simplify:

(2/4)/(2/2) = 1/2

It will take you 1/2 hr to paint one wall.

~

30 minutes

A quarter of an hour is 15 minutes, because 60÷4=15.

So, this means that half of a wall equals to 15 minutes.

If you painted half of a wall, you have another half remaining.

Therefore, 2×15=30

30 minutes is the answere

Step-by-step explanation:

Average=total numbers of songs /registered users

Average= 4*10^9/5*10^7

Average=40*10^8/5*10^7

Average=8*10^(8-7)

Average=8*10^(1)

Average=80 songs downloaded per user

The Average number is 80 songs downloads per user.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers.

Given:

Total Registered user = 5 x [tex]10^7[/tex]

Downloaded songs = 4 x [tex]10^9[/tex]

So, Average=total numbers of songs /registered users

Average = 4 x [tex]10^9[/tex]/ 5 x [tex]10^7[/tex]

Average= 40 x [tex]10^8[/tex]/ 5 x [tex]10^7[/tex]

Average = 8 x [tex]10^{(8-7)[/tex]

Average= 8 x 10

Average= 80 songs.

Hence, 80 songs downloaded per user.

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To solve the system of equations, we can use the method of substitution. However, when we substitute the expression for x in the second equation, we get an equation that is not true, indicating that the system has no solution.

To solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6, we can use the method of substitution. First, we can solve one of the equations for either variable, then substitute that expression into the other equation to solve for the other variable. Let's solve the first equation for x:

5x - 2y = -6

5x = 2y - 6

x = (2y - 6)/5

Now, substitute this expression for x in the second equation:

15((2y - 6)/5) - 6y = 6

6y - 18 - 6y = 6

-18 = 6

This leads to the equation -18 = 6, which is not true. Therefore, the system of equations has no solution. So, the correct answer is C. No solution.

Answer:

the line of best feet passes through three poin

Step-by-step explanation:

1st three points are green, yellow and red

2nd three point are green yellow and upward green

Final answer:

The outlier with a large residual indicates it does not fit the line of best fit, and removing it can improve the model's accuracy. After recalculating without the outlier, a stronger correlation coefficient of 0.9121 suggests that the line of best fit models the data better.

Explanation:

Understanding Residuals and Outliers in Linear Regression

In the context of linear regression, a residual is the difference between the observed value of the dependent variable (y) and the predicted value (ý) provided by the regression model. We are testing the residuals to determine how closely the regression line models the actual data points. If a residual is larger than twice the standard deviation (in this case, greater than 32.8 or less than -32.8), the corresponding data point is considered an outlier. The single large outlier identified with a grade of 65 on the third exam and 175 on the final exam has a substantial residual of 35, indicating that this data point does not fit well with the line of best fit. This outlier can significantly affect the regression line's slope and y-intercept.

Outliers can have a significant impact on the best-fit line, potentially skewing the results and affecting predictions. To assess the outlier's influence, we can remove it and re-calculate the best-fit line and correlation coefficient. If the coefficient is closer to 1 or -1 and the sum of squared errors (SSE) is lower after re-calculating, this indicates a better fit. In this case, the line of best fit without the outlier provides a correlation coefficient of 0.9121, suggesting a stronger linear relationship between the third exam and final exam scores after removing the outlier.

Answer:

$390.

Step-by-step explanation:

first you need to find out hour much the secretary gets paid an hour.  So you will divide $262.50 by 35 hours

262.50 / 35 = 7.50

so we know that she worked over time of 6 hours and that will be time and half

to figure out how much for time and a half.  We are going to divide her hourly rate by 2.  

7.50 / 2 = 3.75

then to find out how much she made for that 6 hours we will add

7.50 + 3.75 = 11.25

to get the amount for over time on Saturday we will multiply

11.25 x 6 = 67.50

Now for the double time we will double her pay so will add

7.50 + 7.50 = 15

so then we are going to multiply to get your pay for the 4 hours overtime

15(4) = $60

Now to find the total amount we are going to add all of our totals together.  

262.50 + 67.50 + 60 = 390.

Her total gross wage for the week is $390.

Answer:

$390.

Step-by-step explanation:first you need to find out hour much the secretary gets paid an hour.  So you will divide $262.50 by 35 hours

262.50 / 35 = 7.50

so we know that she worked over time of 6 hours and that will be time and half

to figure out how much for time and a half.  We are going to divide her hourly rate by 2.  

7.50 / 2 = 3.75

then to find out how much she made for that 6 hours we will add

7.50 + 3.75 = 11.25

to get the amount for over time on Saturday we will multiply

11.25 x 6 = 67.50

Now for the double time we will double her pay so will add

7.50 + 7.50 = 15

so then we are going to multiply to get your pay for the 4 hours overtime

15(4) = $60

Now to find the total amount we are going to add all of our totals together.  

262.50 + 67.50 + 60 = 390.

Her total gross wage for the week is $390

Answer:

-4x^2-6x+6

(third choice)

Step-by-step explanation:

To do f(x)-g(x) we must insert the expression for f(x) and g(x) into this:

This will give us:

(8x^2-2x+3)

-(12x^2+4x-3)

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

-4x^2-6x+6

Horizontally if you prefer:

(8x^2-2x+3)-(12x^2+4x-3)

Distribute and get rid of paranthesis:

8x^2-2x+3-12x^2-4x+3

Pair up like terms:

8x^2-12x^2-2x-4x+3+3

Combine the like terms:

-4x^2-6x+6

Answer:

h(x) =  -4x^2 - 6x + 6

Step-by-step explanation:

f(x) - g(x)

=  8x^2 - 2x + 3 - (12x^2 + 4x - 3)    (Note the parentheses around g(x))

Distributing the negative over the parentheses:

= 8x^2 - 2x + 3 - 12x^2 - 4x + 3

= -4x^2 - 6x + 6 = h(x).

Answer:

A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)

Step-by-step explanation:

* Lets revise the rotation and translation

- If point (x , y) rotated about the origin by angle 90° counterclockwise

 ∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° counterclockwise

 ∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° counterclockwise

 ∴ Its image is (y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Now lets solve the problem

- The vertices of the polygon are:

  A = (-7 , 8) , (B = (-4 , 6) , C = (-4 , 3) , D = (-8 , 3) , E = (-9 , 6)

- The polygon rotates 270° counterclockwise about the origin

∵ Point (x , y) rotated about the origin by angle 270° counterclockwise

∴ Its image is (y , -x)

∵ A = (-7 , 8)

∴ Its image = (8 , 7)

∵ B = (-4 , 6)

∴ Its image = (6 , 4)

∵ C = (-4 , 3)

∴ Its image = (3 , 4)

∵ D = (-8 , 3)

∴ Its image = (3 , 8)

∵ E = (-9 , 6)

∴ Its image = (6 , 9)

- After the rotation the image will translate 2 units to the left and

 3 units up

∴ We will subtract 2 units from each x-coordinates of the vertices and

  add 3 units to each y-coordinates of the vertices

∵ Point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

∵ Point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

∴ A' = (8 - 2 , 7 + 3)

∴ A' = (6 , 10)

∴ B' = (6 - 2 , 4 + 3)

∴ B' = (4 , 7)

∴ C' = (3 - 2 , 4 + 3)

∴ C' = (1 , 7)

∴ D' = (3 - 2 , 8 + 3)

∴ D' = (1 , 11)

∴ E' = (6 - 2 , 9 + 3)

∴ E' = (4 , 12)

* The coordinates of its image are:

  A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)

After a 270° counterclockwise rotation and 2 units left and 3 units up translations, the polygon's image has the new coordinates A''(-10,-4), B''(-8,-1), C''(-5,-1), D''(-5,-5), and E''(-8, -6).

In trigonometry and geometry, a 270° counterclockwise rotation of a point (x, y) about the origin gives a new point (-y, x). Now, let us consider the transformation of point A(-7, 8). After a 270° rotation, the new point is A'(-8, -7) and after translating 2 units left and 3 units up, the final transformed point A'' is (-8-2, -7+3) = (-10, -4).

Following the same process, B'(-6, -4), C'(-3, -4), D'(-3, -8), E'(-6, -9) and, after translation, B''(-8, -1), C''(-5, -1), D''(-5, -5), E''(-8, -6). Thus, the coordinates of the polygon A'B'C'D'E' after a 270° counterclockwise rotation and a 2 unit left and 3 units up translations are A''(-10,-4), B''(-8,-1), C''(-5,-1), D''(-5,-5), and E''(-8, -6).

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Answer:

C'D'=3 units

Step-by-step explanation:

we know that

The translation of a segment does not modify its length

so

The length of the segment CD and the length of the segment C'D' are equal

therefore

C'D'=3 units

Verify

Let

The coordinate of point C equal to x1 and the coordinate of point D equal to x2

so

The length of segment CD is equal to

CD=x2-x1=3

The rule of the translation is

x ------> x+2

The new coordinates will be

C'=x1+2

D'=x2+2

The length of segment C'D' is equal to

(x2+2)-(x1+2)=(x2-x1)=3 units

Answer:

D 3

Step-by-step explanation:

Answer:

2)A plane has length and width.

3)A plane extends infinitely in all directions

5)A plane is a flat surface.

Step-by-step explanation:

We can think of a plane as a line in space with no height, only length and width.

Yes, a plane is a two-dimensional surface, hence it has length and width.

2)A plane has length and width (TRUE)

The plane surface extends infinitely far, therefore it extends infinitely in all direction.

3)A plane extends infinitely in all directions (TRUE)

5)A plane is a flat surface(TRUE)

The correct options are 2,3 and 5.

See attachment

Answer:

B,C,E

Step-by-step explanation:

Step-by-step explanation:

Let's say the two digit number is 10x + y, where x is the first digit and y is the second digit.

The sum of the digits is 8:

x + y = 8

If 8 is subtracted from the number, the digits switch place.

10x + y − 8 = 10y + x

Simplify the second equation:

9x − 8 = 9y

Substitute from the first equation.

y = 8 − x

9x − 8 = 9 (8 − x)

9x − 8 = 72 − 9x

18x = 80

x = 4.444

There's a problem.  x isn't an integer.  Are you sure you copied the problem correctly?  Perhaps you meant if 18 is subtracted from the number, the digits switch place.

9x − 18 = 9 (8 − x)

9x − 18 = 72 − 9x

18x = 90

x = 5

y = 8 − x

y = 3

So the number is 53.

[tex]x+y=8\\10x+y-8=10y+x\\\\x+y=8|\cdot9\\9x-9y=8\\\\9x+9y=72\\\underline{9x-9y=8}\\18x=80\\x=\dfrac{80}{18}=\dfrac{40}{9}[/tex]

x is not integer, so there must be a mistake in the problem.

To find the value of x, we set the expressions for the sides of the rectangle equal to each other (4x - 16 = x + 5) and solve for x to get x = 7.

The student has asked to find the value of x given that QRST is a rectangle with sides RT and SQ. Since in a rectangle opposite sides are equal, we can set the expressions for RT and SQ equal to each other:

RT = SQ

4x – 16 = x + 5

To solve for x, we must do some algebra. Subtract x from both sides of the equation:

4x – x – 16 = 5

Combine like terms:

3x – 16 = 5

Add 16 to both sides:

3x = 21

Divide by 3:

x = 7

Therefore, the value of x is 7.

Answer:

m∠B = 90°

Step-by-step explanation:

Note that the figure given to you is a triangle, which has 3 angles, and the total measurement of 3 angles is = 180°.

Let m∠B = x

     m∠A = 60°

     m∠C = 30°

Set the equation:

m∠A + m∠B + m∠C = 180°

Plug in the corresponding numbers to the corresponding variables:

60 + x + 30 = 180

Isolate the variable, x. Combine like terms:

x + (60 + 30) = 180

x + (90) = 180

Isolate the variable, x. Subtract 90 from both sides:

x + 90 (-90) = 180 (-90)

x = 180 - 90

x = 90

m∠B = 90°

Answer: [tex]80\ ft^2[/tex]

Step-by-step explanation:

You know that the model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 and the new area will be 160 square feet.

Since you know that the area of the new enlarged patio will be 160 square feet, you need to divide the area  of the new enlarged patio  in order to find the area of the landscaper’s model.

This is:

[tex]Area_(model)=\frac{160\ ft^2}{2}\\\\Area_(model)=80\ ft^2[/tex]

Answer:

I think its 40

Step-by-step explanation:

i come back and see:)

I got it right. good luck

Answer:

Option 1: {x | x > 12 or x < 6}

Step-by-step explanation:

Given inequalities will be solved one by one:

[tex]\frac{2}{3}x >8\\2x > 8*3\\2x>24\\x > \frac{24}{12} \\x>12[/tex]

Or

[tex]\frac{2}{3}x<4\\2x<4*3\\2x<12\\x < \frac{12}{2}\\ x<6[/tex]

Hence we can see that the solution of both inequalities combined is:

x>12 or x<6

Hence, option 1 is correct ..