MATHEMATICS HIGH SCHOOL

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

Answers

Answer 1

Answer:

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

Answer 2

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

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HELP!!!!Carissa takes a square piece of cardboard and cuts 5 in. by 5 in. squares out of each corner. She folds the sides up to make a box without a top. What equation can Carissa use to determine the volume of the box, where x is the side length of the original piece of cardboard? Express the equation in standard form.

-16+5n=-7(-6+8n)+3

what is the work for this ?? this is the like only one i cant get

Answers

-16 + 5n = -7(-6 + 8n) + 3 Given
-16 + 5n = 42 - 56n + 3 Distribute
-16 + 5n = 45 - 56n Collect like terms
61n = 61 Add 56n to the left side and add 16 to the right side
n = 1 Divide 61 from both sides

The answer is n = 1. Remember that when you have a number beside two or more numbers in parentheses, you have to distribute, or multiply the number outside the parentheses by each number inside the parentheses.

Hope this helps!

Solve for A A/20 = 7

Answers

Answer:

A = 140

Step-by-step explanation:

Answer:

in my opinion the answer is A=140

Step-by-step explanation:

Ron lives 6 miles due north of the ball field, and Stan lives 8 miles due west of the ball field. What is the straight line distance between their homes? (It makes a right triangle.)8 miles

10 miles

20 miles

50 miles

Answers

You would use Pythagoras' theorem (a^2 + b^2 = c^2) because it is a right-angled triangle. 6^2 + 8^2 = 36 + 64 = 100. √100 = 10. So your answer is 10 miles, I hope this helps!

I think it's 20 miles but I don't know if it is

A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule (3xy)(7xy²), where y represents the number of white tiles.Which simplified expression represents the number of colored tiles used for a path of length x feet?

Answers

the number of colored tiles needed to make it is calculated using the rule: (3xy)(7xy²) where x is the length of the path in feet y represents the number of white tiles

(3xy) (7xy^2)

= 21(x^2)(y^3) is the simplified expression represents the number of colored tiles

Which quantity would not be labeled with a vector?A. kilometers/hour B. miles/hour C. miles/gallon D. centimeters/second

Answers

$Speed-velocity\ would\ be\ lebeled\ with\ a\ vector\n\nv=(d)/(t)\n\nd-distance\nt-time\n\nA.\ (km)/(h)\to(d)/(t)\n\nB.\ mph\to(d)/(t)\n\nC.\ (miles)/(gallon)\to(d)/(V)\ (V-volume)\n\nD.\ (cm)/(s)\to(d)/(t)\n\nAnswer: \fbox{C.}$

C. miles/gallon
.....................

The mean score on a calculus exam was 40, and the standard deviation was 5. The teacher decided to double everyone’s score and then added 7 points. What are the values of the mean and standard deviation of the distribution of transformed exam scores? (Options: mean = 80 and standard deviation = 5, mean = 80 and standard deviation = 10, mean = 87 and standard deviation = 5, mean = 87 and standard deviation = 10, mean = 87 and standard deviation = 17)

Answers

The new mean becomes 87 (40*2+7), while the new standard deviation becomes 10 (5*2). The correct option is then option D.

hope this helps! please give brainliest :)

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