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ElenaW [278]
3 years ago
6

HELP WITH THESE SERIES OF QUESTIONS!!

Mathematics
1 answer:
Virty [35]3 years ago
5 0
1. Simplified already
2. 5x^2 x (3x+5)
3. 3x^3 x (3x^4 +11)
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Find the equation of the line that is parallel to the given line and passes through the given point
Sati [7]

Answer:

\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}

Step-by-step explanation:

\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}

\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}

\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}

x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1

\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4

5 0
3 years ago
sam read 75 pages of a new mystery novel in 2 hrs. if the book contains 350 pages and he always reads the same rate, how long wi
Andreyy89
About 8 hours, 37 minutes, and 30 seconds
7 0
3 years ago
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Solve each equation for the unknown <br>1. 5 + y = 7.<br>2. 3.8 = a + 2.5<br>5. + p = 9 1/3 ​
Alexxandr [17]

Answer:

1. 5 + y = 7

⇒ y = 7 - 5

⇒<u>y = 5</u>

2.  3.8 = a + 2.5

⇒ a = 2.5 - 3.8

⇒ <u>a = -1.3</u>

3. 5 + p = 9 1/3 ​

⇒ p = 9 1/3 - 5

⇒ p = 28/3 - 5

⇒ p = 28/3 - 15/3

⇒ p = 13/3

⇒<u> </u><u>p = 4 1/3</u>

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Answer:

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Step-by-step explanation:

What kind of food?

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Please show work for<br>1.5 x 6.3 =​
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Answer: 9.46

Step-by-step explanation:

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