MATHEMATICS HIGH SCHOOL

Write a quadratic function in standard form containing the point (6,5) and x-intercepts 5 and 11.​

Answers

Answer 1
Answer:

Answer:

\sf y = -x^2 + 16x - 55

Step-by-step explanation:

In order to write a quadratic function in standard form, we can use the factored form of a quadratic equation and then expand it.

The factored form of a quadratic equation is:

\sf y = a(x - r_1)(x - r_2)

Where:

  • (r1, 0) and (r2, 0) are the x-intercepts.
  • (6, 5) is a point on the quadratic function.

Given that the x-intercepts are 5 and 11, we can write:

y = a(x - 5)(x - 11)

Now, we'll use the point (6, 5) to find the value of 'a':

5 = a(6 - 5)(6 - 11)

5 = a(1)(-5)

5 = -5a

Now, solve for 'a' by dividing both sides by -5:

\sf a =(-5)/(5)

a = -1

Now that we have the value of 'a', you can write the quadratic function in standard form:

y = -1(x - 5)(x - 11)

Now, expand and simplify the expression:

\sf y = -1(x^2 - 16x + 55)

\sf y = -x^2 + 16x - 55

So, the quadratic function in standard form containing the point (6, 5) and x-intercepts 5 and 11 is:

\sf y = -x^2 + 16x - 55
Answer 2
Answer:
\bold{ANSWER:}
f(x) = -x^2 + 16x - 55.


\bold{SOLUTION:}

• To write a quadratic function in standard form, we can use the factored form of a quadratic equation:

f(x) = a(x - r1)(x − r2),

• where r1 and r2 are the x-intercepts. We are given that the x-intercepts are 5 and 11, so we can substitute these values into the equation:

f(x) = a(x-5)(x - 11).

• Now, we need to find the value of 'a' and substitute the coordinates of the given point (6, 5) to solve for 'a'.

• Substituting the point (6, 5) into the equation, we get:

5a(65) (6 - 11).

• Simplifying further:

5 = a(1)(-5).

5 = -5a

• Dividing both sides by -5

a = -1

• Now that we have found the value of 'a', we can substitute it back into the equation:
f(x)=-1(x-5)(x - 11).

• Expanding the equation:

f(x) = -1(x^2 - 11x - 5x + 55).

• Simplifying:

f(x) = -x^2 + 16x - 55.

Therefore,

The quadratic function in standard form that contains the point (6, 5) and x-intercepts 5 and 11 is:

f(x) = -x^2 + 16x - 55.

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A square pool has an area of 292 square feet. To the nearest tenth, what is the length of one side of the pool?

A.
8.5 feet

B.
17.1 feet

C.
73.0 feet

D.
146.0 feet

Answers

Since the pool is square, the four sides are equal.
Therefore the length of one side = sqrt(292) = 17.1 to the nearest tenth.

The sum of a rational number and a rational number is rational. A.Always True
B.Sometimes True
C.Never True

Answers

Answer:

A

It is always true that:

rational number + rational number = rational number.

The answer is option A.

Answer:

a

Step-by-step explanation:

100%

According to David Taylor of the Bank Administration Institute, about _____ percent of households with annual incomes over $50,000 have PCs equipped with modems.

Answers

According to David Taylor of the Bank Administration Institute, about 40 percent of households with annual incomes over $50,000 have PCs equipped withmodems.

Answer:

40

Step-by-step explanation:

A rectangular swimming pool with a flat bottom is 20 feet by 12 feet. How long will it take to fill the swimming pool to 5 feet if water is being pumped into the pool at 30 cubic feet per minute?

Answers

The given dimensions of the rectangular swimming pool are =

Length = 20 feet

Width = 12 feet

Height upto which the water should be filled up = 5 feet

So, the total volume of water needed to fill the pool will be =

20*12*5=1200 cubic feet

The water is pumped at a speed of = 30 cubic feet per minute.

So, to fill 1200 cubic feet, the time taken will be = (1200)/(30) =40

Hence, it will take 40 minutes to fill the pool.
20 feet * 12 feet * 5 feet
= 20 * 12 * 5 feet ^3
= 1200 feet^3

1200 feet^3 / (30 feet^3 / minute)
= (1200 / 30) minutes
= (120 / 3) minutes
= 40 minutes

A = bh; solve for h
h =

Answers

Answer:

The value of h is

h = A/b.

The population of rabbits doubles every 3 months. If there were initially 150 at the bunny farm, how many will there be after 3 years?

Answers

First you need to find how many months there are in 3 years. You multiply 3 by 12 to find out how many months there are(there are 12 months in a year) 3*12 = 36. Next you need to find out how many times the population doubles. You can do this by dividing the total amount of months by 3(36/3=12). You can then multiply the starting population by 2 to the amount of times you double (150*(2^(12))). Giving you an answer of 49152.
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