A factory is to be built on a lot measuring 150 ft by 200 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be, and what are the dimensions of the factory?
width of lawn ft
factory dimensions ft (smaller length) by ft (larger length)

Answer:

ñ

Step-by-step explanation:

ñ

Answer:

Option D

Step-by-step explanation:

Given the inequality statement: 5 + 8x < 3(2x + 4):

We must solve for the solution of the given inequality statement.

First, distribute 3 into the parenthesis:

5 + 8x < 3(2x + 4)

5 + 8x < 6x + 12

Next, subtract 6x from both sides:

5 + 8x - 6x < 6x - 6x + 12

5 + 2x < 12

Then, subtract 5 from both sides:

5 - 5 + 2x < 12 - 5

2x < 7

Divide both sides by 2 to solve for x:

[tex]\displaystyle\mathsf{\frac{2x}{2}<\:\frac{7}{2}}[/tex]

[tex]\displaystyle\mathsf{x<\:\frac{7}{2}}[/tex]  

Since  [tex]\displaystyle\mathsf{\frac{7}{2}}[/tex] = 3.5, and that the inequality symbol is "<," then it means that   [tex]\displaystyle\mathsf{\frac{7}{2}}[/tex] or 3.5 is not included as an endpoint.  This corresponds to an empty circle on the 3.5 mark on the number line, pointing towards the left (indicating that the values must be less than 3.5).

Therefore, the correct answer is Option D.

Answer:

15%

Step-by-step explanation:

A proportional relationship has a constant rate of change.

The given statement is true.

Step-by-step explanation:

A proportional relationship has a constant rate of change. We need to tell if this statement is true or false

A proportional relationship is given by equation:

where y is dependent variable while x is independent variable and k is constant of proportionality

The constant of proportionality is constant for all the values of y and x.

So, A proportional relationship has a constant rate of change.

The given statement is true.

The constant of proportionality (k) tells you how steep the graph of a proportional relationship is TRUE.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Let's consider a proportional relationship

y∝ x

y = kx

k = y/x

Now the value of y directly depends on upone k.

So, changing k will change the steepness of the line.

Hence "The constant of proportionality (k) tells you how steep the graph of a proportional relationship is TRUE".

For more information about ratios and proportions,

brainly.com/question/26974513

#SPJ2

Answer:

Noah

Step-by-step explanation:

Potential energy is the amount of energy that can be transfered to kinetic. This means that the higher person will have more potential energy.

Step-by-step explanation:

I solved the first four in the left side. You could solve the other ones by looking at the setup. if any doubt comment.

#5 ABD should be 32

Answer:

Step-by-step explanation:

Answer and Step-by-step explanation:

This equation is linear because the slope is changing at a constant rate.

Write in standard form:

Standard form on an equation is written like so: Ax + By = C

First combine the y-values.

12x = -3y

Now add 3y to both sides of the equation.

12x + 3y = 0   <-- This is the answer (equation) in standard form.

#teamseas #PAW (Plant And Water)

I hope this helps!

_________

[tex] \: [/tex]

2½m = 2.5 × 100 = 250cm

Soo :

[tex] \longmapsto\frac{3}{1 \cancel0} \times 25 \cancel0[/tex]

[tex] \longmapsto3 \times 25[/tex]

[tex] \longmapsto \bold{75cm}[/tex]

Answer:

tax is 10%

Step-by-step explanation:

because if you multiply 120 by 10% you get 12 so that means that the tax is 10%

Answer:

Step-by-step explanation:

For the first throw the probability that it does not land on four should be .35 not .25

On the top for the second throw the probabilities should be swapped (so land on 4= .65 and not land on four =.35)

Answer:

22 boxes

5 cookies left

Step-by-step explanation:

135 / 6 = 22.5

Lucy will have 3 cookies left over that won't fit into any full boxes. To find how many full boxes Lucy will have, we can divide the total number of cookies (135) by the number of cookies in each box (6).

Number of full boxes = Total number of cookies / Number of cookies in each box

Number of full boxes = 135 cookies / 6 cookies per box

Number of full boxes = 22.5

Since Lucy cannot have a fraction of a box, she will have 22 full boxes of gingerbread cookies.

To find how many cookies she will have left over, we can find the remainder after dividing the total number of cookies by the number of cookies in each box.

Number of cookies left over = Total number of cookies % Number of cookies in each box

Number of cookies left over = 135 cookies % 6 cookies per box

Number of cookies left over = 3

To know more about cookies:

https://brainly.com/question/34872820

#SPJ2

Answer:

Investors generally use ratios to evaluate companies and make comparisons between companies within an industry. Ratio analysis simplifies the process of comparing the financial statements of multiple companies.

Answer:

m∆T=44°

Step-by-step explanation:

> 180-108+28

> 180-136

> 44

Answer:

96-26=70 books she bought at the yard sale

Answer:

y= (2/3)-(1/2)

= (4-3)/6

= 1/6

=> A

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

I do mental math. I think this is right if not then I am sorry

Answer:

The speed of a boat in still water is 6 miles per hour.

Step-by-step explanation:

t = [tex]\frac{20}{s-2}[/tex]  (upstream)

t = [tex]\frac{40}{s+2}[/tex]  (downstream)

[tex]\frac{20}{s-2}[/tex] = [tex]\frac{40}{s+2}[/tex]

40 ( s - 2 ) = 20 ( s + 2 )

40s - 80 = 20s + 40

20s = 120

s = 6 mi / h

The speed of a boat in still water is 6 miles per hour.

Answer:

12%

Step-by-step explanation:

You subtract 336 from 300 which will give you 36, then you divide 36 by 300 and you will get .12 which is 12%

Answer: false

Step-by-step explanation:

Answer:

1/345 or 0.00289855 (for 1/5 / 69)

I feel like you're most likely talking about 69 / 1/5 which is 345

Try looking at the problem you are doing again :)

Answer:

0.00289855072

Step-by-step explanation:

1÷5 = 0.2

0.2 ÷ 69 = 0.00289855072

Answer:

9.51

Step-by-step explanation:

9 x 1 is equal to 9

5 x 1/10 is equal to 5/10 which is also 0.5

1 x 1/100 is equal to 1/100 which is also 0.01

Answer:

a = -3/2 = -1.5

Step-by-step explanation:

(1+ax) (2+3x)³

Formula

(a+b)^3=a^3+3a^2b+3ab^2+b^3

(1 + ax) [ 2^3 + 3*2^2*3x + 3*2*(3x)^2 + (3x)^3]

(1 + ax) [ 8 + 12*3x + 6*9x^2 + 27x^3]

8 + 12*3x + 6*9x^2 + 27x^3 + 8ax + 36ax^2 + 54ax^3 + 27ax^4

coefficient of x^2 is zero

54x^2 + 36ax^2

54 + 36a = 0

36a = -54

a = -3/2

a) The linear system as a matrix equation in the form AX= B as

[tex]\left[\begin{array}{ccc}-1&1&1\\0&-2&-1\\2&1&0\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{c}0\\-2\\4\end{array}\right][/tex]

b) The solution set is {x = 2, y = -4, z = -2}.

Given that A⁻¹ = [tex]\left[\begin{array}{ccc}-1&1&1\\2&-2&-1\\-4&3&2\end{array}\right][/tex],

To find the matrix equation in the form AX = B, multiply both sides of the equation by A⁻¹:

A⁻¹(A⁻¹X) = A⁻¹B

X = A⁻¹B

Therefore, the linear system as a matrix equation in the form AX = B is:

[tex]\left[\begin{array}{ccc}-1&1&1\\0&-2&-1\\2&1&0\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{c}0\\-2\\4\end{array}\right][/tex]

2. The given system of equations can be represented as:

                                    A = [tex]\left[\begin{array}{ccc}-1&1&1\\0&-2&-1\\2&1&0\end{array}\right][/tex]

                                    X  = [tex]\left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]

                                    B = [tex]\left[\begin{array}{c}0\\-2\\4\end{array}\right][/tex]

Using the given inverse of A:

A⁻¹ = [tex]\left[\begin{array}{ccc}-1&1&1\\2&-2&-1\\-4&3&2\end{array}\right][/tex]

Multiply A⁻¹ by B to solve for X:

[tex]X = A^{(-1)} B[/tex]

[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]   = [tex]\left[\begin{array}{ccc}-1&1&1\\2&-2&-1\\-4&3&2\end{array}\right][/tex]  [tex]\left[\begin{array}{c}0\\-2\\4\end{array}\right][/tex]

Performing the matrix multiplication:

|  x  | =  | (-1)(0) + (1)(-2) + (1)(4)|   |  2  |

|  y  | = | (-2)(0) + (3)(-2) + (2)(4)|  | -4  |

|  z  |   | (2)(0) + (-2)(-2) + (-1)(4)|   | -2  |

Therefore, the solution set is {x = 2, y = -4, z = -2}.

Learn more about Matrix here:

https://brainly.com/question/29132693

#SPJ4

Answer:

Step-by-step explanation:

Old weight = 60 pound

New weight = 80 pound

Finding:

Percent of increase in weight

Therefore:

Percent of expansion in weight = [(New weight - old weight)/Old weight]100

Percent of expansion in weight = [(80 - 60)/60]100

Percent of expansion in weight = [(20)/60]100

Percent of expansion in weight = 33.33% Approx.

The slope of a line is given by the ratio of the rise to the run of the line.

The value of, y is 4

Reasons:

The given points on the line are; (-4, y), and (5, 7)

The slope of the line, = [tex]\dfrac{1}{3}[/tex]

Required:

To find the value of y

Solution:

The formula for the slope is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where;

(x₁, y₁) = (-4, y)

(x₂, y₂) = (5, 7)

Which gives;

[tex]Slope, \, m =\dfrac{7-y}{5-(-4)} = \dfrac{7-y}{5+4} =\dfrac{1}{3}[/tex]

3·(7 - y) = 1·(5 + 4) = 9

21 - 3·y = 9

3·y = 21 - 9 = 12

[tex]y = \dfrac{12}{3} = 4[/tex]

The value of, y = 4

Learn more here:

https://brainly.com/question/1617757

Answer:

$0.95

Step-by-step explanation:

Since it cost $2.85 for 3 pounds of apples, dividing 2.85 by 3 will give us one pound of apples.

2.85/3 = $0.95

Hope this helps! Please comment if it does or not. :)

Answer:

For every 3 dollars donated, one puppy is adopted

Step-by-step explanation:

so rise would be money, run would be number of puppies adopted

Answer: 4 packages

Step-by-step explanation: the greatest common factor of 20 and 16 is 4.