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3 years ago

The equation y-4=-3(x+4) is written in point-slope form. What is the y-intercept of the line? *

Mathematics

1 answer:

nataly862011 [7]3 years ago

6 0

Answer:

-8

Step-by-step explanation:

you need to rewrite it in y=mx+b form where b-is the y-intercept

y-4= -3(x+4)

distribute

y-4 = -3x-12

isolate y

y= -3x-8

compare this with the y=mx+b so y-intercept is -8

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Find two positive numbers whose product is 192 and their sum is a minimum.

yuradex [85]

Answer:

8√3

Step-by-step explanation:

Let a, b = the positive numbers, and the sum = s,

(1)---- ab = 192

(2)--- a + b = s

Since we want to find the minimum sum, we'll have to substitute one of the variables (either a or b) from (1) to (2), I'll choose b,

From (1), b = 192/a

Substitute b = 192/a into (2),

s = a + 192/a

Now, we are able to use a concept of calculus (maximum & minimum) to solve it, just remember 2 steps in finding the values of x in maxima minima question:

1) find dy/dx

2) Find x from dy/dx = 0

ds/da = 1 - 192/a²

When ds/da = 0,

1 - 192/a² = 0

a² = 192

a = ±√192

a = 8√3 , -8√3

Since a is positive, a = 8√3

Substitute a into (1),

b = 192/(8√3)

b = 8√3

Therefore, the two positive numbers are 8√3... and 8√3

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the variabity of the sample means will be greater

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3 years ago

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IgorLugansk [536]

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Step-by-step explanation:

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3 years ago

Why do we we tend to spend more with credit than with cash.

IrinaVladis [17]

We tend to spend more with credit than with cash.

There can be following reasons of this:

# It save cash which can used in emergencies.

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These are some of reasons.☝

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3 years ago

Which linear inequality is represented by the graph? (A)y ≤1/3 x − 1 (B)y ≥ x − 1 (C)y < 3x − 1 (D)y > 3x − 1

lubasha [3.4K]

The equation of the line is $\boxed{y \geqslant \frac{1}{3}x - 1}.$

Further explanation:

The linear equation with slope $m$ and intercept $c$ is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ can be expressed as,

$\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

Given:

Explanation:

The line intersects y-axis at $\left( {0, - 1} \right)$ . Therefore, the y-intercept is $-1.$

The line passes through the points $\left( {0, - 1} \right)$ and $\left( {3,0} \right).$

The slope can be obtained as follows,

$\begin{aligned}m&= \frac{{0- \left( {- 1} \right)}}{{3 - 0}}\\&= \frac{1}{3}\\\end{aligned}$

Substitute $\dfrac{1}{3}$ for m, $3$ for $x$ and $0$ for $y$ in equation $y = mx + c$ to obtain the value of $c$ .

$\begin{aligned}0& \frac{1}{3} \cdot 3 + c\\- 1&=c\\\end{aligned}$

To check whether the equation includes origin substitute 0 for x and 0 for y in equation $y \geqslant \dfrac{1}{3}x - 1.$

$\begin{aligned}0&\geqslant \frac{1}{3} \times 0 - 1 \\0&\geqslant - 1\\\end{gathered}$

The statement is true. The equation contains origin.

The equation of the line is $\boxed{y \geqslant \frac{1}{3}x - 1}.$

Learn more:

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers,slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

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4 years ago

Read 2 more answers