MATHEMATICS HIGH SCHOOL

PLZZZ!!!!!! HELPA pillar candle is shaped like a cylinder with a radius of 1.5 inches. The candle holds 123 cubic inches of wax. How tall is the candle? Use 3.14 for pi. Round your answer to the nearest hundredth.
12.50 in
15.76 in
17.41 in
18.76 in

Answers

Answer 1
Answer:

Answer:  The correct option is (C) 17.41 in.

Step-by-step explanation:  Given that a pillar candle is shaped like a cylinder with a radius of 1.5 inches and the candle holds 123 cubic inches of wax.

We are to find the height of the candle.

We know that the VOLUME of a cylinder with radius r units and height h units is given by

V=\pi r^2h.

For the given cylindrical candle, we have

radius, r = 1.5 inches

and

VOLUME, V = 123 cubic inches.

height, h = ?

We have

V=\pi r^2h\n\n\Rightarrow 123=3.14* (1.5)^2* h\n\n\Rightarrow h=(123)/(3.14*2.25)\n\n\n\Rightarrow h=(123)/(7.065)\n\n\Rightarrow h=17.4097.

Rounding to nearest hundredth, h = 17.41 in.

Thus, the Candle is 17.41 inches tall.

Option (C) is CORRECT.
Answer 2
Answer: 17.41- The formula for the volume of a cylinder is pi radius squared times height. (i.e. the area of the base times the height).  You have pi 1.5 squared times height =123.  Then you square it so you have 2.25 pi h= 123. then you have 7.065h=123. The you do algebra and you get 17.409, and round it to 17.41.

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Correct or incorrect? the difference of two numbers is always less than at least one of the numbers

Answers

the answer is "correct"

Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4? Select the appropriate response:
Yes
or
No

Answers

Answer:

Yes

Step-by-step explanation:

f(x) = x^3 + x^2 −4x − 4

Factor by grouping  taking x^2 out of the first group and -4 out of the second

0 = x^3 + x^2      −4x − 4

     x^2(x+1)     -4(x+1)

Factor out (x+1)

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

Now we have the difference of squares

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

x+1 is a factor

Answer:

Yes

Step-by-step explanation:

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

x^2 ( x+1) -4 (x+1)

(x^2 - 4) (x+1)

(x-2) (x+2) (x+1)

X= 2 x=-2 x=-1

What are the coordinates of the center of the circle if this is its equation:x2 + y2 - 16x + 6y +53 = 0

Answers

Hello,

x²-16x+y²+6y+53=0
==>x²-2*8*x+8² + y²+2*3*y+3²+53-64-9=0
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Randy is thinking of a number. When he adds 7 to the number, multiplies the sum by 3, then subtracts 2, the result is 13. What is the original number?A. 6
B. -2
C. 2
D. -6

Answers

Answer:

B. -2

Step-by-step explanation:

let the number be x

=7+x

=3(7+x)

=3(7+x)-2

13=3(7+x)-2

solving for  x we have

13=21+3x-2

21+3x-2-13=0

collect like terms we have

21-2-13+3x=0

6+3x=0

6=-3x

x=6/-3

x=-2

The answer is B

B. -2

Two systems of equations are shown below:System A:
6x+y=2
-x-y=-3
System B:
2x-3y=-10
-x-y=-3
Which of the following statements is correct about the two system equations?

A) The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.

B) They will have the same solution because the first equations of both the systems have the same graph.

C) They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.

D) The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding -4 to the first equation of System A and the second equations are identical.

Answers

System A:
6x + y = 2
-x - y = -3

System B:
2x - 3y = -10
-x-y = -3

Solve:
System A:
6x + y = 2
y = 2 - 6x
-x - (2-6x) = -3
-x - 2 + 6x = -3
5x = -3 + 2
5x = -1
x = -1/5
y = 2 - 6(-1/5)
y = 2 + 6/5
y = 2 + 1.2
y = 3.2     System A: x = -1/5 or -0.2  ; y = 3 1/5 or 3.2

System B:
2x - 3y = -10
2x = -10 + 3y
x = -5 + 1.5y
-x - y = -3
-(-5 + 1.5y) -y = -3
5 - 1.5y - y = -3
-2.5y = -3 - 5
-2.5y = -8
y = 3.2
x = -5 + 1.5(3.2)
x = -5 + 4.8
x = -0.2   System B: x = -0.2 ; y = 3.2

B) They will have the same solution because the first equations of both the systems have the same graph.

Answer: I just took the test and got it wrong when I put B, the correct answer is C.

Step-by-step explanation:
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