The McDonald's Play Place is going to increase its ball pit size to allow for more fun! The ball pit was originally 10 feet by 12 feet. They have decided to increase each side by the same amount. Express the area of the new pit as a polynomial in simplest form.

Answer:

[tex]6x-6y-16=0[/tex]

Step-by-step explanation:

Consider the following system of equations:

[tex]a_1x+b_1y+c_1=0\\\\a_2x+b_2y+c_2=0[/tex]

The system of equations has infinite solutions if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

One equation is [tex]3x-3y=8[/tex]

[tex]3x-3y-8=0[/tex]

Take another equation as [tex]6x-6y-16=0[/tex]

So, the two equations are [tex]3x-3y-8=0[/tex] and [tex]6x-6y-16=0[/tex]

[tex]a_1=3,b_1=-3,c_1=-8,a_2=6,b_2=-6,c_2=-16[/tex]

[tex]\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\\ \frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\\ \frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}[/tex]

So,

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

Therefore, another equation can be [tex]6x-6y-16=0[/tex]

Answer:

300 ≥ 40 + 80 + 120 + x

x ≥ 60

Step-by-step explanation:

Monday = 40 toys

Tuesday = 2(40) = 80 toys

Wednesday = 3(40) = 120 toys

Thursday = x toys

At least means ≥

300 ≥ 40 + 80 + 120 + x

300 ≥ 240 + x

300 - 240 ≥ x

60 ≥ x

x ≥ 60

Answer:

22 hens and 78 sheep

Step-by-step explanation:

Let the number of hens = x

Number of sheep = y

Total heads = 100

x +  y = 100      --------------------(I)

 x = 100 - y

Number of legs of 'x' hen = 2*x = 2x

Number of legs of 'y' sheep = 4*y = 4y

total legs = 356

2x + 4y =  356 -----------------------(II)

Substitute x = 100 -y in equation (II)

2(100 - y) + 4y = 356

2*100 - 2*y + 4y = 356

200 - 2y + 4y    = 356 {Combine like terms}

        200  + 2y = 356          {Subtract 200 from both sides}

                   2y = 356 - 200

                  2y = 156       {Divide both sides by 2}

                    y = 156/2

                  y = 78

Plugin  y = 78 in equation (I)

x + 78 = 100

       x = 100 - 78

       x = 22

22 hens and 78 sheep

Answer:

E

Step-by-step explanation:

Answer: 42 degrees

Step-by-step explanation: sum of angles in triangle is 180 degrees.

So third angle is 180-44-94= 42

Answer: 42°

Steps:

44° + 94° + x = 180°

138° + x = 180°

x = 180° - 138°

x = 42°

Check:

44° + 94° + 42° = 180°

180° = 180° ✅

Would appreciate brainliest if the answer was helpful, correct and had clear steps! :)

Answer:

theres no numbers?

Step-by-step explanation:

Answer:

ok, so, since the angles in a traingle all sum up to 180°, that would make:

36°+61°+(4x-17)°=180°

We simplify it:

95°+(4x-17)°=180°

Then, we subtract 95° on both sides:

95°+(4x-17)°=180°

-95°               -95°

Then we get:

4x-17°=85

We add 17° on both sides

4x-17°=85

   +17°  +17°

And we get:

4x=102°

Divide 4 on both sides...

4x=102°

➗4 ➗4

Therefor:

X=25.5

Hope this helps, but tell me if i'm wrong, and have a good day!

Answer:

A/C ≅ 2

Step-by-step explanation:

diameter of circle d = 8 in

Circumference of the circle C= 25 in

Let us assume we have to find the area of the circular lid  A = [tex]\frac{\pi}{4}d^2[/tex]

⇒ A= [tex]\frac{\pi}{4}\times8^2= 50.24 in^2[/tex]

Therefore ratio of area to circumference A/C = 50.24/25 = 2.0096≅2

Step-by-step explanation:

I think it is a good day and the answer is 3

Answer:

Step-by-step explanation:

you do 10/2 for the radius, so that will be 5. then you do 3.14*5*5= 78.5

Answer:

76+76=152

Step-by-step explanation:

Answer: i believe it’s 12ft

Step-by-step explanation:

Answer:

I think it would be a 20 percent

Step-by-step explanation:

because the 4 red is 40% the blue is another 40% then the green is only 20 I could be wrong though hope this helped

Answer:

40°

Step-by-step explanation:

If your are reffering to a triangle the answer would be 40 since the three angles of a triangle must always add up to 180° so you would add b+d (110+30) resulting in 140 which you would then subtract from 180 getting you 40°

Answer:

They are both 47 degrees

Answer:

15%

Step-by-step explanation:

Since 23 is 115% of 20, we can therefore know that it's 15% increase from 20.

Answer:

El reloj de Nuestra Basílica de Chiquinquirá empleará 20 segundos para indicar las 8 a.m.

Step-by-step explanation:

De acuerdo a la información proporcionada, sabes que el reloj de Nuestra Basílica de Chiquinquirá señala cada hora con igual número de campanadas, por lo que a las 8 a.m. tocará 8 campanadas y puedes usar una regla de tres para encontrar cuantos segundos empleará en hacerlo dado que conoces que las 6 campanadas se demoran 15 segundos:

6 campanadas → 15 segundos

8 campanadas →         x

x=(8*15)/6

x= 20

De acuerdo a esto, la respuesta es que el reloj de Nuestra Basílica de Chiquinquirá empleará 20 segundos para indicar las 8 a.m.

Answer:

Step-by-step explanation:

here is what I got but I hope it helps :)

Answer:

Step-by-step explanation:

Answer:

Center (6, -3)

Radius 5

Answer:

becuz their colour is black and white. b and w is so cute

Answer:

5

Step-by-step explanation:

as the 2nd term is b, and the coeffiecnt is the number next to the term

Answer:

I think the calculation answer will be 9,999,811,112

Answer:

x-8

......................

Step-by-step explanation:

-8x-12+9x+4

-8x+9x-12+4

x-8

x-8=0

x=8

9514 1404 393

Explanation:

For proofs of this nature, it often works well to replace everything possible with appropriate equivalents. Here, we'll use sin² to represent sin²(A), and equivalent notation for other trig functions.

We will change the left side to the form of the right side.

  [tex]\displaystyle \frac{\tan^2-\cot^2}{1+\cot^2}=\frac{\sin^2-\cos^2}{\cos^2}\\\\=\frac{(\sec^2-1)-(\csc^2-1)}{\csc^2}\\\\=(\sin^2)(\sec^2-\csc^2)\\\\=\frac{\sin^2}{\cos^2}-1=\frac{\sin^2-\cos^2}{\cos^2}\qquad\text{Q.E.D.}[/tex]

__

The equivalents (identities) used are ...

  1+tan² = sec²

  1+cot² = csc²

  1/csc = sin

  sec = 1/cos

Answer:

f^−1(x)=2^x/4

Step-by-step explanation:

The inverse of the function will be;

⇒ [tex]f ^{-1} (x) = \frac{2^{x}}{4}[/tex]

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ y = log₂ (4x)

Now,

Since, The function is,

⇒ y = log₂ (4x)

Find the inverse of the function as;

⇒ y = log₂ (4x)

⇒ [tex]2^{y} = 4x[/tex]

⇒ [tex]\frac{2^{y}}{4} = x[/tex]

⇒ [tex]f ^{-1} (x) = \frac{2^{x}}{4}[/tex]

Thus, The inverse of the function y = log₂ (4x) is,

⇒ [tex]f ^{-1} (x) = \frac{2^{x}}{4}[/tex]

Learn more about the function visit:

https://brainly.com/question/28361556

#SPJ2

The correct question is:

[tex]\angle QPS=88[/tex]  

[tex]\angle RPS=5x+34[/tex]

[tex]\angle QPR=8x+15[/tex].

Find ∠QPR.

Answer:

[tex]\angle QPR = 39[/tex]

Step-by-step explanation:

From the attached figure:

[tex]QPS = QPR + RPS[/tex]

This gives:

[tex]88 = 8x + 15 + 5x + 34[/tex]

Collect like terms

[tex]88 - 15 - 34 = 8x + 5x[/tex]

[tex]39 = 13x[/tex]

Divide both sides by 13

[tex]3 = x[/tex]

[tex]x =3[/tex]

Substitute [tex]x =3[/tex] in [tex]\angle QPR=8x+15[/tex]  

[tex]\angle QPR = 8 * 3 + 15[/tex]

[tex]\angle QPR = 24 + 15[/tex]

[tex]\angle QPR = 39[/tex]

Answer:

The right answer is 49, I did it on khan academy

Step-by-step explanation:

Answer:

[tex]\sqrt{655*655} =655[/tex]

Step-by-step explanation:

655*655 is pretty much equal to 655²

the square root of a number to the power of 2 is equal to the number without the power

so √655² would be equal to 655

Answer:

[tex]655[/tex]

Step-by-step explanation:

[tex] \sqrt{655 \times 655} \\ = 655[/tex]