All categories

2 years ago

What is the vertex of f(x)=(x-8)(x-2)

Mathematics

1 answer:

igor_vitrenko [27]2 years ago

5 0

Hello!

To find the vertex of f(x), we can simplify this function into standard form.

f(x) = (x - 8)(x - 2)

f(x) = x² + -10x + 16

With the equation in standard form, we use the formula: x = -b/2a. Then, we substitute the value of x into the equation to solve for the y-value.

x = -(-10) / 2(1)

x = 10 / 2

x = 5

Then, we substitute x = 5 into the original equation.

f(x) = (5 - 8)(5 - 2)

f(x) = -3(3)

f(x) = -9

Therefore, the vertex of f(x) is (5, -9).

You might be interested in

What is the value to 370

MAXImum [283]

Answer:

Answer is on the pic

Step-by-step explanation:

I hope it's helpful!

5 0

2 years ago

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bou

Novay_Z [31]

Answer:

$P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a} , a \leq X \leq b$

And for this case we can write the probability like this:

$P(X$

And then the final answer for this case would be $\frac{2}{3}=0.667$

Step-by-step explanation:

For this case we define our random variable X "price of gasoline for a city in the USA" and we know the distribution is given by:

$X \sim Unif (a=3.5, b=3.8)$

And for this case the density function is given by:

$f(x) = \frac{x}{b-a}= \frac{x}{3.8-3.5}=, 3.5 \leq X \leq 3.8$

And we want to calculate the following probability:

$P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a} , a \leq X \leq b$

And for this case we can write the probability like this:

$P(X$

And then the final answer for this case would be $\frac{2}{3}=0.667$

5 0

2 years ago

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel: A quadrilateral ABCD is shown with the

algol [13]

A Quadrilateral A B C D in which Sides AB and DC are congruent and parallel.

The student has written the following explanation

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SAS.

The student has also written

angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Postulate SAS completely describes the student's proof.

Because if in a quadrilateral one pair of opposite sides are equal and parallel then it is a parallelogram.