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2 years ago

slide 1) Write an equation in point slope form that passes through the point (1,8) & slope of -3 y-y,=m(x-x₁) 2) Write the e

quation in slope intercept form.

Mathematics

1 answer:

pentagon [3]2 years ago

4 0

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{8})\qquad \qquad \stackrel{slope}{m}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-3}(x-\stackrel{x_1}{1}) \\\\\\ y-8 = -3x+3\implies y=-3x+11$

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If the first chapter of a certain book is 16 pages long and makes up 4% of the book, how many pages does the entire book have?

galina1969 [7]

If 16 pages equal to 4%, how many pages will equal to 100%?

4/100 = 16/x
4x=1600
X= 400

So total pages should be 400.

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2 years ago

PLS HELP Simply the expression by combining like terms. 6x+9+2x+4=

sukhopar [10]

Answer:

Combine like terms: 18x + 15x = 33x

(45 + 33x + 6x2)

Step-by-step explanation:

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2 years ago

A card is selected randomly from a jar that contains 15 cards, numbered from 25 to 39. What is the probability that the card sel

VikaD [51]

Answer:

The probability that the card selected bears a number less than 34 is 0.3333.

Step-by-step explanation:

Let random variable X be defined as the number on the selected card.

There are N = 15 total cards.

The number on the cards are as follows:

S = {25, 26, 27,..., 38, 39}

The probability of an event, E is the ratio of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

In this case we need to compute the probability that the card selected bears a number less than 34.

The favorable outcomes are:

s = {25, 36, 37, 38, 39}

n (X < 34) = 5

Compute the probability that the card selected bears a number less than 34 as follows:

$P(X$

$=\frac{5}{15}\\\\=\frac{1}{3}\\\\=0.3333$

Thus, the probability that the card selected bears a number less than 34 is 0.3333.

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3 years ago

Solve the equation. -4(7x + 8) = 192

AleksAgata [21]

-8 is the answer ........

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3 years ago

Perform a first derivative test on the function f(x)equals2 x cubed plus 3 x squared minus 120 x plus 6; [minus5,8]. Bold

maria [59]

Answer:

a) Critical points

x = 4 and x = -5

b) x = 4 corresponds to a minimum point for the function f(x)

x = - 5 corresponds to a maximum point for the function f(x)

c) The minimum value of f(x) in the interval = -298

The maximum value of f(x) in the interval = 431;

Step-by-step explanation:

f(x) = 2x³ + 3x² - 120x + 6 in the interval [-5, 8]

a) To obtain the critical points, we need to obtain the first derivative of the function with respect to x. Because at critical points of a function, f(x), (df/dx) = 0

f'(x) = (df/dx) = 6x² + 6x - 120 = 0

6x² + 6x - 120 = 0

Solving the quadratic equation,

x = 4 or x = -5

The two critical points, x = 4 and x = -5 are in the interval given [-5, 8] (the interval includes -5 and 8, because it's a closed interval)

b) To investigate the nature of the critical points, we obtain f"(x)

Because f'(x) changes sign at the critical points

If f"(x) > 0, then it's a minimum point and if f"(x) < 0 at c, then it's a maximum point.

f"(x) = (d²f/dx²) = 12x + 6

at critical point x = 4

f"(x) = 12x + 6 = 12(4) + 6 = 54 > 0, hence, x = 4 corresponds to a minimum point.

at critical point x = -5

f"(x) = 12x + 4 = 12(-5) + 4 = -56 < 0, hence, x = -5 corresponds to a maximum point.

c) At x = 4,

f(x) = 2x³ + 3x² - 120x + 6 = 2(4)³ + 3(4)² - 120(4) + 6 = -298

At x = - 5

f(x) = 2x³ + 3x² - 120x + 6 = 2(-5)³ + 3(-5)² - 120(-5) + 6 = 431

7 0

3 years ago