MATHEMATICS MIDDLE SCHOOL

The circumference of the bas of the cylinder is 18π units. The cylinder is 30 units tall.Which of the following is the closest to the volume of the cylinder?
A 706 cubic units
B 1,414 cubic units
C 7,630 cubic units
D 21,195 cubic units

Answers

Answer 1
Answer:
The volume of a cylinder is    (pi) (radius)² (height).

We know the height, but we don't know the radius.
Is there a way we can find it ?
We know the circumference of the base.  Maybe that's a clue.
Can you find the radius of a circle when you know the circumference ?

             Circumference of a circle =  (pi) x (diameter)
 
                                    18 pi units = (pi) x (diameter)

Divide both sides by pi :  18 units = diameter

Divide both sides by 2 :    9 units = radius       yay !

Now we know the radius and the height of the cylinder,
so we can calculate the volume.

radius = 9
height = 30
we'll use  3.14  for pi .

Volume = (pi) (radius)² (height) =

             (3.14)    (9)²      (30) =

             (3.14)   (81)      (30) =   7,630.2 cubic units

Is there a choice close to that ?  I'll go up and look.   

Yes !  Choice 'C' is  7,630 cubic units.      yay !

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A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours?128
256
1,024
8,192

Answers

4 Bacteria double per hour to give 8 bacteria then in 8 hours it will become 64 then this 64 doubles to give us 128

Let me make it clear,


The bacteria culture begins with 4 bacteria and double up every hour. And the hours given is 8 hours.

Therefore, we can first list the equation: 4 x 2^8

And we can get the solution 1024 <- Answer


Hope it helps

A truck can travel 14 miles for each gallon of gasoline. The function d(x)=20x represents the distance d(x), in miles, that the truck can travel with x gallons of gasoline. How many miles can the truck travel with 15 gallons of gasoline?

Answers

The truck will travel 210 miles On 15 gallons of gasoline runing 14 miles per gallon of gas

If the quadratic equation x^2 + 18x +74=0 is rewritten in the form (x-p)^2 = Q what is the value of Q?A) -155

B) -74

C) 7

D) 9

Answers

If the quadratic equation x^2 + 18x +74=0 is rewritten in the form (x-p)²= Q. Then the value of Q is 7.

What is a quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Given

The quadratic equation \rm x^(2) + 18 x + 74 = 0.

How to find the value of Q?

If the quadratic equation \rm x^(2) +18x +74=0 is rewritten in the form

\rm (x - p)^2 = Q

Add and subtract 9² in the equation.

\rm x^2 + 18x + 9^2 - 9^2 + 74 =0

We know the formula

\rm (a + b)^2 = a^2 + 2ab + b^2

Then equation will be

\begin{aligned} \rm (x + 9)^2 - 81 + 74 &= 0\n\ \ \ \rm (x + 9)^2 - 7 &= 0\end{aligned}

Add 7 both the sides, then

\rm (x + 9 )^2 = 7

Thus the value of Q is 7.

More about the quadraticequation link is given below.

brainly.com/question/2263981

The value of Q "option C) 7" is correct option.

Step-by-step explanation:

The given quadratic equation:

x^2 - 18x +74=0

To find, the value of Q = ?

x^2 - 18x +74=0

Adding both sides 81, we get

x^2 - 18x +81+74=81

⇒ x^2 - 2(x)8 + 9^2 = 81 - 74

Using the algebraic identity,

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

⇒ (x-9)^(2) =7 is the form of  (x-p)^2 = Q

Here, P = 9 and Q = 7

Thus, the value of Q "option C) 7" is correct option.

Which is bigger 96 oz or 8 pts

Answers

8 pts is bigger then 96 oz.
8pts is bigger then 96 oz

Need help plz due on Monday I believe

Answers

Answer:

1(a) = 10

1(b) = 9

1(c) = 12

2(a) = 8

2(b) = 10

2(c) = 1

Step-by-step explanation:

1(a) = 22 - 2.6

     = 22 - 12 = 10

1(b) = 6 - 1/4 . 16 + 21 / 3

     = 6 - 16/4 + 7

     = 6 - 4 + 7

     = 9

1(c) = (8-5). (5-3)^2

     = 3*2^2

     = 3*4

     = 12

2(a) = 4(x-2)/(x-1) when x = 0

       = 4(0-2)/ (0-1)

       = 4*-2/-1

       = -8 / -1

       = 8

2(b) = (-3x^2 + 4) / 4 when x = -2

       = (6^2 + 4) / 4

        = (36 + 4) / 4

       = 40 / 4 = 10

2(c) = [-2x/4 + 4*(x-1)] / x^2 - 1 when x = 2

      = (-1 + 4 * 1) / 4 - 1

      = 3 / 3

      = 1

         
1) a. 10
b. 9
c. 12

2) a. 4(x-2) / (x-1)
= 4(0-2) / (0-1)
= 4(-2) / (-1)
= -8/-1
= 8
b. -3x^2 + 4 / 4
= -3(-2)^2 + 4 / 4
= -3(4) + 4 / 4
= -12 + 4 / 4
= -8 / 4
= -2
c. [-2x/4 + 4 (x-1)] / x^2 - 1
= [-2(2)/4 + 4 (2-1)] / 2^2 - 1
= [-2(2)/4 + 4(1)] / 2^2 - 1
= [-2(2)/4 + 4(1)] / 4 - 1
= (-4/4 + 4)/ 4 - 1
= (-1 + 4) / 4 - 1
= 3 / 3
= 1

Jim's cat, c, weighs 7 pounds. His dog weighs six times plus 3 pounds. more than his cat. Which equation represent the dogs weight, d?

Answers

c =7
d is 6 times c+3
d=6c+3

d=6d+3 is equation
(if you sub, you would get 45 is weight)
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