Name the line and plane shown in the diagram

The function y = x 2 - 10x + 31 has a ____

katrin [286]

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

$f(x) = x^2-10x+31$

Taking first derivative

$f'(x) = 2x-10$

Now the first derivative has to be put equal to zero to find the critical value

$2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5$

The function has only one critical value which is 5.

Taking 2nd derivative

$f''(x) =2$

$f''(5) = 2$

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

$f(5) = (5)^2-10(5)+31\\=25-50+31\\=6$

Hence,

<u>The function y = x 2 - 10x + 31 has a minimum value of 6</u>

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

8 0

2 years ago

A triangle has side lengths of 34in. 28in. and 42in. Is the triangle acute, right or obtuse?

Paul [167]

I believe the answer is acute. Hope this helps!!

5 0

2 years ago

Triangle JKL has vertices J(2,5), K(1,1), and L(5,2). Triangle QNP has vertices Q(-4,4), N(-3,0), and P(-7,1). Is (triangle)JKL

Tems11 [23]

Answer:

Yes they are

Step-by-step explanation:

In the triangle JKL, the sides can be calculated as following:

J(2;5); K(1;1)

=> JK = $\sqrt{(1-2)^{2} + (1-5)^{2} } = \sqrt{(-1)^{2}+(-4)^{2} } = \sqrt{1+16}=\sqrt{17}$

J(2;5); L(5;2)

=> JL = $\sqrt{(5-2)^{2} + (2-5)^{2} } = \sqrt{3^{2}+(-3)^{2} } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}$

K(1;1); L(5;2)

=> KL = $\sqrt{(5-1)^{2} + (2-1)^{2} } = \sqrt{4^{2}+1^{2} } = \sqrt{1+16}=\sqrt{17}$

In the triangle QNP, the sides can be calculate as following:

Q(-4;4); N(-3;0)

=> QN = $\sqrt{[-3-(-4)]^{2} + (0-4)^{2} } = \sqrt{1^{2}+(-4)^{2} } = \sqrt{1+16}=\sqrt{17}$

Q (-4;4); P(-7;1)

=> QP = $\sqrt{[-7-(-4)]^{2} + (1-4)^{2} } = \sqrt{(-3)^{2}+(-3)^{2} } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}$

N(-3;0); P(-7;1)

=> NP = $\sqrt{[-7-(-3)]^{2} + (1-0)^{2} } = \sqrt{(-4)^{2}+1^{2} } = \sqrt{16+1}=\sqrt{17}$

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

7 0

2 years ago

Read 2 more answers

Ele:

lana66690 [7]

Answer:

The pattern is that, every time a 9 is added. This pattern continuous forever.

Step-by-step explanation:

9 X 1 = 9

9 X 2 = 18 (9+9)

9 X 3 = 27 (9+9+9)

Etc.

5 0

2 years ago

Which number is an irrational number?Help Plzzzzz

Aleonysh [2.5K]

The square root of 15 is irrational.

6 0

3 years ago

Read 2 more answers