MATHEMATICS HIGH SCHOOL

What is the vertex form of y = x^2 - 20x +15

Answers

Answer 1
Answer: so your equation is y = x² - 20x + 15. what you'll want to do is complete the square, so take half of 20 and square it. 20/2 = 10. 10² = 100. add 100 to both sides. and simplify x²-20x+100+15 to (x²-10)²+15. now subtract 100 from both sides to get y alone. this leaves you with y = (x²-10)-85. that's your vertex form.
Answer 2
Answer: Given a function:
y=ax²-bx+c
The vertex is: (-b/2a, f(-b/2a)

In this case:
y=x²-20x+15
-b/2a=20/2=10
f(10)=10²-20(10)+15=100-200+15=-85

Answer: The vertex is (10,-85)

Given a vertex (h,k), the vertex form is :
y=a(x-h)²+k

In this case:
(10,-85)
a=1
 
y=(x-10)²-85

Answer: y=(x-10)²-85

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The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x = number of years since 1900, and y = pounds per person. What cubic model best fits this data? YearPounds Consumed. 19021.959. 19246.373. 19467.29. 198215.817. A. y = 0.00989x3 - 0.0000872x2 + 1.192x + 0.403. B. y = -0.0000872x3 + 0.00989x2 - 0.403x - 1.192. C. y = -0.0000872x3 - 0.00989x2 - 0.403x + 1.192. D. y = 0.0000872x3 - 0.00989x2 + 0.403x + 1.192

Answers

To see what model best represents this data we have to plug in the values for x and y:
Model D :
x = 2, y = 1.959
y = 0.0000872 · 2³ - 0.00989 · 2² + 0.403 · 2 + 1.192 = 1.968
....   ...
x = 82,  y = 15.817
y = 0.000873 · 82³ - 0.00989 · 82² + 0.403 · 82 + 1.192 = 15.818
Answer:
D ) y = 0.0000872 x²- 0.00989 x² + 0.403 x + 1.192
 

The area of the sector formed by the 110 degree central angle is 40 units squared what is the radius

Answers

we know that
area of the circle=pi*r²

if 360° (full circle) has an area of-------------> pi*r²
110°------------------------------> 40 units²
pi*r²=40*360/110--------> pi*r²=130.91------> r²=130.91/pi-----> r²=41.69
r=6.46 units

the answer is
the radius is 6.46 units

How to increase numbers

Answers

Hi There! :)

How to increase numbers?

Multiply by a percentage
Add or multiply another number with that number

Which of the following is NOT a characteristic of an inner planet? A. rocky B. solid surface C. near the sun D. made mostly of gas

Answers

it is D, made mostly of gas. that's an outer planet characteristc.

The correct answer is D. Made mostly of gas. Hope this helps! :)

How do I solve r+11+8r=29

Answers

The solution to the equation r + 11 + 8r = 29 is r = 2.

What is the solution to the equation?

Given the equation in the question:

r + 11 + 8r = 29

To solve the equation r + 11 + 8r = 29, first, collect and combine the x terms on one side of the equation and the constant terms on the other side:

r + 11 + 8r = 29

Collect and add like terms:

r + 8r + 11 = 29

9r + 11 = 29

Subtract 11 from both sides of the equation:

9r + 11 - 11 = 29 - 11

9r = 29 - 11

9r = 18

Isolate r by dividing both sides by 9:

r = 18/9

r = 2

Therefore, the value of r is 2.

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r+11+8r=29
    -11      -11
r+8r=18
   +1=18
    9r=18
        r=2

What is the inverse of the function f(x) = x – 12?

Answers

Final answer:

The inverse of the function f(x) = x - 12 is found by swapping x and y, and solving for y. The inverse is f-1(x) = x + 12.

Explanation:

The inverse of a function 'f' can be found by swapping the x and y. If we consider the original function as y = f(x) = x – 12, the inverse of the function will be found by reversing this as x = y – 12. Solving for 'y' to express the inverse function 'f-1(x)', we add 12 to both sides to get f-1(x) = x + 12. Hence, the inverse of the function f(x) = x – 12 is f-1(x) = x + 12. Keep in mind, the inverse of a function is a reflection of that function across the line y=x, representing a mirror image of the original.

Learn more about Inverse Functions here:

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