Find the area of a square with side length x when x is equal to the given value.
Are the area of a square and the length of its side directly proportional? Justify
your answer.
x = 10 in.

Answer:

The maximum area is therefore is 93750 ft²

Step-by-step explanation:

The given parameter are;

The a]length of fencing available = 1500 ft.

The perimeter of the figure = 9·x + 4·y

Therefore, 9·x + 4·y = 1500 ft.

The area of the figure = 6 × (x × y) = 3·x × 2·y

From the equation for the perimeter, we have;

9·x + 4·y = 1500

y = 1500/4 - 9/4·x = 375 - 9/4·x

y = 375 - 9/4·x

Substituting the value of y in the equation for the area gives;

Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²

Area = 2250·x - 27/2·x²

The maximum area is found by taking the derivative and equating to zero as follows;

d(2250·x - 27/2·x²)/dx = 0

2250 - 27·x = 0

x = 2250/27 = 250/3

x = 250/3

y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5

The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²

The maximum area is therefore = 93750 ft.²

Given :

Tickets cost $3 for students and $5 for adults.

A total of 125 people attended the concert for a total ticket sales of $475.

To Find :

The number of students and adults that attended the concert.

Solution :

Let, number of students and adults that attended the concert is x and y.

Mathematical equation of given conditions :

x + y = 125    ....1)

3x + 5y = 425   ....2)

Putting value of x from 1 to equation 2 is :

3( 125 - y ) + 5y = 425

375 - 3y + 5y = 425

2y = 50

y = 25

x = 125 - 25

x = 100

Therefore, number of students and adults that attended the concert is 100 ans 25 respectively.

Hence, this is the required solution.

Answer:

The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Example: Here, XYUV=123=4 . So, the scale factor is 4 .

Step-by-step explanation:

:D

Answer:

$6,524.96

Step-by-step explanation:

His quarter commission times four is the awnser

Answer:

Answer:

x ≤ 1000 W

Step-by-step explanation:

Since the circuit becomes overloaded when the load exceeds 1800W and the toaster uses 800 W.

Let the additional watts be x

Therefore;

800 + x ≤ 1800

x ≤ 1800 -800

x ≤ 1000 W

Answer:

thank you. someone had to say it

Step-by-step explanation:

Answer:

Omg ik what you mean i feel you

Step-by-step explanation:

Answer:

The equation is y = 3x + 15.

The second equation is y = 3 * 50 + 15

If you have a value of 50 berries picked, you would make 165 dollars.

Answer:

a.15.6

Step-by-step explanation:

simplify all the ratios to their simplest forms.

15/3:6/3

5:2

Answer:

Step-by-step explanation:

ind her earnings for the first two weeks of the month at the $5.50 an hour rate.

5.50 × (18 + 20.50) = 5.50 × 38.5  

= 211.75  

She earned $211.75 the first two weeks of the month.

Find her new hourly rate, if she raises her rate by $0.55.

5.50 + 0.55 = 6.05  

Her new hourly rate is $6.05.

Find how many hours she would need to work at $6.05 an hour in order to earn $211.75.

211.75 ÷ 6.05 = 35  

She would need to work 35 hours.

Answer:

A.) -8h

Step-by-step explanation:

a.) . (5 – 2h) (3 + h)  

a.) (5 – 2h) (3 + h)  

(5+3) (h-2h)

8(-h)

-8h

Answer:

[tex]39.29\ \text{km/h}[/tex]

Step-by-step explanation:

s = Speed of the train

m = Money spent on maintanence

[tex]s\propto m^{\dfrac{1}{3}}[/tex]

Let k be the constant of proportionality so

[tex]s=k (m)^{\dfrac{1}{3}}[/tex]

Now a case is given where 25 km/hr is possible on a stretch for which 450,000 is spent so

s = 25

m = 450000

[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow k=\dfrac{s}{m^{\dfrac{1}{3}}}\\\Rightarrow k=\dfrac{25}{450000^{\dfrac{1}{3}}}\\\Rightarrow k=0.326[/tex]

Now when m = 1750000

[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow s=0.326\times 1750000^{\dfrac{1}{3}}\\\Rightarrow s=39.29\ \text{km/h}[/tex]

The maximum speed of the train would be [tex]39.29\ \text{km/h}[/tex].

Answer:

-3 > x

Step-by-step explanation:

Answer:

50. ☺️☺️

Step-by-step explanation:

I'm going to assume you need this inequality solved.

First, write it as numbers, not words.

7/10n + 14 < 49

where "n" is the unknown number.

Second, if I were you, I'd change that fraction into a decimal, as it'll make life easier later on.

7/10 = 0.7

Now, solve it like you would any other equation.

0.7n + 14 < 49

0.7n +14 - 14 < 49 - 14

0.7n < 35

0.7n ÷ 0.7 < 35 ÷ 0.7

n < 50

The answer is n < 50

Answer: 50

Step-by-step explanation:

49 - 14 = 35

35/7 = 5

10 x 5 = 50

Since, 35 is Seven tenths of a number, One tenth is 5 and there are ten tenths, One tenth which is 5 times ten since there are ten tenths equals to 50 (5 x 10 = 50).

Answer:

stop cheating boi

Step-by-step explanation:

Answer:

where is the graph?

Step-by-step explanation:

Step-by-step explanation:

The formula for calculating the area of a square is expressed as;

A = x² where;

x is the length of one side of the square

Given

x = 10in

A = 10²

A = 10 * 10

A = 100in²

Area of the square with side length 10in is 100in²

From the equation A = x², we can see that as the value of x increases, the value of the area also increases and vice versa. This means that the area of the square is directky proportional to its length. Hence we can say YES, the area of a square and the length of its side directly proportional

Answer:

100 sq in

Step-by-step explanation:

No, not proportional

Answer: 432 ft^2

Step-by-step explanation:

If 1"=3', and the box is 8"x6", then we can simply multiply the 8 and 6 by three. You would get 24 by 18.

Follow this up by the equation a=w*l to get

a=24*18 = 432 ft^2.

Given :

Collection in third week, C = $25,992,412.50 .

Average ticket price, T = $8.35 .

To Find :

Number of people who saw movie in  week.

Solution :

Let, number of people are x.

[tex]\text{Number of people }=\dfrac{\text{Total amount }}{\text{Average price}}\\\\= \dfrac{25,992,412.50 }{8.35}\\\\[/tex]

≈ 3112864

Therefore, around 3112864 people saw the movie this week.

Hence, this is the required solution.

Answer:

Step-by-step explanation:

2x+1       - the first odd integer

2 x+1 + 2 = 2x+3   - the next odd integer consecutive to 2x+1

2x+3+2 = 2x+5 - the odd integer consecutive to 2x+3 (the third consecutive odd integer)

2x+1 + 2x+3 + 2x+5  - the sum of three consecutive odd integers

therefore the equation:

                                     2x+1 + 2x+3 + 2x+5 = -3

6x + 9 = -3

6x = -12

x = -2

2x+1=2(-2)+1=-3

2x+3=2(-2)+3=-1

2x+5=2(-2)+5=1

the three consecutive odd integers whose sum is -3 are: -3,-1,1

Answer:

x = 11

Step-by-step explanation:

this answer can be solved by simple operations

5x + 20 = 75

5x = 55 (subtracted the 20 from 75)

x = 11 (divided the 5 by 55)

hope this helps !!

- emily

Answer:

128

Step-by-step explanation:

Answer:

y=6x+18

Step-by-step explanation:

add the -6x to the other side to get y alone

Answer:

-6x + y = 18 reduced is -2x + y = 2

Step-by-step explanation:

it is called the Hamber Pickering Formula according to STUIPDPEDIA LOL!

Answer:

C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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

The three roots are going to give - 18 so only A and D can be correct. Why minus? because at some point 3 and 2 and - 3 will all be multiplied together. When they are, the result is - 18

So why did I write x + 2 rather than x - 2? Because the roots turn an equation into 0. You are looking for a way to make x + 2 = 0. It will do that when x = - 2

which is what you were given.

Now to get the answer

(x - 3)(x + 3) = x^2 - 9

(x^2 - 9)(x + 2) = x^3 + 2x^2 - 9x - 18 = f(x)

Answer:

non

Step-by-step explanation: