X - 4 = 1/3(6x

Twelve more than the product of 5 and a number x? x is 20

inn [45]

5 * 20 + 12 = ?

5 * 20 = 100

100 + 12 = 112

5 * 20 + 12 = 112

8 0

3 years ago

Read 2 more answers

For the function, find all critical numbers and then use the second-derivative test to determine whether the function has a rela

Serhud [2]

Answer:

relative maximum: x = 1

relative minimum: x = 7

Step-by-step explanation:

Critical points:

Values of x for which f'(x) = 0.

Second derivative test:

For a critical point, if f''(x) > 0, the critical point is a relative minimum.

Otherwise, if f''(x) < 0, the critical point is a relative maximum.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$f(x) = x^{3} - 12x^{2} + 21x - 8$

Finding the critical points:

$f'(x) = 3x^{2} - 24x + 21$

$3x^{2} - 24x + 21 = 0$

Simplifying by 3

$x^{2} - 8x + 7 = 0$

So $a = 1, b = -8, c = 7$

$\bigtriangleup = (-8)^{2} - 4*1*7 = 36$

$x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7$

$x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1$

Second derivative test:

The critical points are x = 1 and x = 7.

The second derivative is:

$f''(x) = 6x - 24$

$f''(1) = 6*1 - 24 = -18$

Since f''(1) < 0, at x = 1 there is a relative maximum.

$f''(7) = 6*7 - 24 = 18$

Since f''(x) > 0, at x = 7 there is a relative minumum.

8 0

3 years ago

Molly read 50 out of the 200 pages in her fiction book. Joel is also reading a fiction book, but his book has 280 pages in total

katrin [286]

Answer:

$x = 70$

Step-by-step explanation:

Given

Molly: 50 out of 200

Joel: x out of 280

Required

Find x

Start by representing the giving parameters as ration

Molly= 50 : 200

Joel = x : 280

From the question, the ratios are equivalent. So,

$50 : 200 = x : 280$

Convert to fractions

$\frac{50}{200} = \frac{x}{280}$

Solve for x

$x = \frac{50}{200} * 280$

$x = \frac{1}{4} * 280$

$x = \frac{280}{4}$

$x = 70$

5 0

3 years ago

PLEASE HELP I HAVE 3 MINS LEFT FAST!!!! ILL MARK BRAINLIEST!!!

GenaCL600 [577]

A-1500
B-1500
C-1500+1500=3000

7 0

3 years ago

8. Based on the multiplication rule for independent events, what is the probability of getting an airplane in both boxes? Explai

Furkat [3]

Answer:

$P(A and B ) = \frac{1}{4}* \frac{1}{4}=\frac{1}{16}$

Step-by-step explanation:

We assume the following problem: "Consider the following ways students might create their lists using the notation:

B for block, W for watch, R for ring, and A for airplane. The first letter represents the toy found in the first box, and the second letter represents the toy found in the second box. The first column represents getting the block in the first box, followed by each one of the other toys. The second column represents getting the watch in the first box, followed by each one of the other toys. The third column is developed with the ring in the first box, and the fourth column is developed with the airplane in the first box"

And the possible outcomes are:

BB WB RB AB

BW WW RW AW

BR WR RR AR

BA WA RA AA

As we can see we have 16 possibilities.

For this case if we use the independence of events we have the following rule. If A and B are independent events then:

$P(A and B) = P(A) *P(B)$

Let A = Select an airplane from the total of 4 for the first box

B= Select an airplane from the total of 4 for the second box

For this case probability of getting an airplane selected in the first box is 1 out of 4 since we have just one outcome possible and 4 possible.

$P(A) = \frac{1}{4}$

And the probability of getting an airplane selected in the second box is also 1/4 since for the first box selected we have the same number of optiosn for the second box , 4.

$P(B) = \frac{1}{4}$

So then we have this:

$P(A and B ) = \frac{1}{4} \frac{1}{4}=\frac{1}{16}$

5 0

4 years ago

X - 4 = 1/3(6x - 54)