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3 years ago

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Write the equation for the line parallel to the given line 4x-3y=9 and through the point (3, -1). Then Write the answers in slop

e intercept and standard form

1 answer:

Katyanochek1 [597]3 years ago

7 0

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2$

We have:

$4x-3y=9\ \ \ \ |-4x\\\\-3y=-4x+9\ \ \ \ |:(-3)\\\\y=\dfrac{4}{3}x-3\to m_1=\dfrac{4}{3}$

$y=m_2x+b\\\\m_2=m_1\to m_2=\dfrac{4}{3}$

$y=\dfrac{4}{3}x+b$

The line passest through the point (3, -1). Substitute the coordinates of the point to the equation of a line:

$-1=\dfrac{4}{3}\cdot3+b\\\\-1=4+b\ \ \ \ |-4\\\\b=-5$

$y=\dfrac{4}{3}x-5\ \ \ \ |\cdot3\\\\3y=4x-15\ \ \ \ |-4x\\\\-4x+3y=-15\ \ \ \ |\cdot(-1)\\\\4x-3y=15$

Answer: $\boxed{y=\dfrac{4}{3}x-5;\ 4x-3y=15}$

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Math question on big ideas math the 1/3 confuses me I hate fractions

jok3333 [9.3K]

a simple way to do away with denominators, is we can simply multiply both sides by the LCD, in this case the LCD is 3, so let's multiply both sides by 3.

$\bf 3\left( \cfrac{1}{3}x+y \right)=3(4)\implies x+3y=12\implies 3y=12-x
\\\\\\
y=\cfrac{12-x}{3}\implies \stackrel{\textit{distributing the denominator}}{y=\cfrac{12}{3}-\cfrac{x}{3}}\implies y=4-\cfrac{1}{3}x$

6 0

3 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

4 0

2 years ago

Graph the linear equation. X = y + 5

Zina [86]

X = y + 5
-y + x - x = y - y + x + 5
-y = x + 5
y = x - 5

6 0

3 years ago

8-2y=3y-2<br> Help me please

lesya692 [45]

This seems like a lot more work than it is, but here we go
Simplifying<span>8 + -2y = 3y + -2
Reorder the terms: 8 + -2y = -2 + 3y
Solving 8 + -2y = -2 + 3y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right.
Add '-3y' to each side of the equation. 8 + -2y + -3y = -2 + 3y + -3y Combine like terms: -2y + -3y = -5y 8 + -5y = -2 + 3y + -3y
Combine like terms: 3y + -3y = 0 8 + -5y = -2 + 0 8 + -5y = -2 Add '-8' to each side of the equation. 8 + -8 + -5y = -2 + -8
Combine like terms: 8 + -8 = 0 0 + -5y = -2 + -8 -5y = -2 + -8 Combine like terms: -2 + -8 = -10 -5y = -10
Divide each side by '-5'. y = 2
Simplifying y = 2</span><span>

</span>

4 0

3 years ago

Read 2 more answers

What is the simplified form of the quantity 1 over b minus 1 over a all over the quantity 1 over b plus 1 over a?

jolli1 [7]

Option B: (b-a)/(b+a) is the correct answer

Step-by-step explanation:

The given expression is;

$\frac{\frac{1}{b}-\frac{1}{a}}{\frac{1}{b}+\frac{1}{a}}$

First of all we have to take LCM in both numerator and denominator

So,

$=\frac{\frac{b-a}{ab}}{\frac{b+a}{ab}}$

The reciprocal of the denominator will be multiplied with the numerator for simplification

So,

$=\frac{b-a}{ab} * \frac{ab}{b+a}\\= \frac{b-a}{b+a}$

Hence,

Option B: (b-a)/(b+a) is the correct answer

Keywords: Fractions, expressions

Learn more about fractions at:

#LearnwithBrainly

4 0

3 years ago