MATHEMATICS HIGH SCHOOL

The steps below show the incomplete solution to find the value of y for the equation 4y − 2y − 4 = −1 + 13:Step 1: 4y − 2y − 4 = −1 + 13
Step 2: 4y − 2y − 4 = 12
Step 3: 2y − 4 = 12

Which of these is most likely the next step?

2y = 3
2y = 8
2y = 16
2y = 18

Answers

Answer 1

Answer: The next step would be:

2y - 16

Answer 2

Answer:

Answer:

2y=16 Or the Third Option

Step-by-step explanation:

Trust me because i just got done doing my test and i got the question correctly.

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a cylinder with base are 169π ft^2 and a height twice the radius. what is the lateral area and surface area of the cylinder

Answers

$Area\ of\ base:A_B=169\pi\ ft^2\n\nA_B=\pi r^2\ \ \ (r-radius)\n\n\pi r^2=169\pi\ \ \ /:\pi\n\nr^2=169\n\nr=√(169)\n\nr=13\ (ft)\n\nH=2r\to H=2\cdot13=26\ (ft)$

$lateral\ area:A_L=2\pi rH\n\nA_L=2\pi\cdot13\cdot26=676\pi\ (ft^2)\n\nSurface\ area:A_S=2A_B+A_L\n\nA_S=2\cdot169\pi+676\pi=338\pi+676\pi=1014\pi\ (ft^2)$

Area of base = 169 π

r = √Area = 13 ft

Given, height = 2 x 13 = 26 ft.

Lateral surface area of cylinder = 2πrh = 2 x π x 13 x 26 = 676 π ft²

Total surface area = 2πr(r + h) = 2 x π x 13 x 39 = 1014 π ft²

Thus, lateral surface area is 676 ft² and total surface area is 1014 ft²

What are the vertex, focus, and directrix of the parabola with the given equation?12y = x^2 –6x + 45 (1 point)

Answers

Answer:

Vertex is (3,3)

Focus (3,6)

Directrix y=0

Step-by-step explanation:

We are given that an equation of parabola

$12y=x^2-6x+45$

Subtract 45 on bot sides then we get

$12y-45=x^2-6x$

To make complete square on right side

We add 9 on both sides

$12y-45+9=x^2-6y+9$

$12y-36=(x-3)^2$ ( $(a-b)^2=a^2+b^2-2ab,(x-3)^2=x^2-6x+9)$

$12(y-3)=(x-3)^2$

Compare it with the equation of parabola along y- axis

$(x-h)^2=4p(y-k)$

Then, we get h=3,k= $3$

$4p=12$

$p=(12)/(4)=3$

Vertex of parabola =(h,k)=(3,3)

Focus of parabola=(x,p+k)=(3,3+3)=(3,6)

Equation of directrix of parabola ,y=k-p=3-3=0

y=(((x^2)-(6*x)+45)/12)

Choose the correct classification of 2x + 10x2 − x3 by number of terms and by degree.Third degree trinomial
Fourth degree trinomial
Sixth degree polynomial
First degree binomial

Answers

Answer:

(A)Third degree trinomial

Step-by-step explanation:

The given expression is:

$2x+10x^2-x^3$

Now, Degree of the expression is defined as the highest power of the variable given in the expression, thus in the given expression that is $2x+10x^2-x^3$ the variable is x and the highest power of x is 3, therefore it is a third degree expression.

Also, Trinomial is an expression which consists of three terms, and also the given expression $2x+10x^2-x^3$ consists of three terms that are $2x, 10x^2 and -x^3$ therefore, the given expression is a third degree trinomial.