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Amiraneli [1.4K]
3 years ago
11

Need help just 12 and 14 and answer choices

Mathematics
1 answer:
Lina20 [59]3 years ago
8 0
12) First multiply 354 by 3.


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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4
Dmitry [639]

Answer:

  • \boxed{\sf Standard-form :x + 4y -17=0 }\\

  • \boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

\longrightarrow x + 4y = 7\\

Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;

\longrightarrow 4y = -x + 7  \\

\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\

On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,

\longrightarrow m =\dfrac{-1}{4}\\

\longrightarrow c =\dfrac{7}{4}\\

Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,

\longrightarrow m_{||)}=\dfrac{-1}{4}\\

Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,

\longrightarrow y - y_1 = m(x-x_1) \\

On substituting the respective values ,

\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\

\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\

\longrightarrow 4(y -5 ) =-1(x +3) \\

\longrightarrow 4y -20 = - x -3 \\

\longrightarrow x + 4y -20+3=0\\

\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\

Again the equation can be rewritten as ,

\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5  \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4}  \\

\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{  y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\

6 0
2 years ago
Which is not a property of a parallelogram?
Nookie1986 [14]
"Contains four right angles" is the one among the following choices given in the question that is <span>not a property of a parallelogram. Parallelograms can have angles that are not ninety degrees. The correct option among all the options that are given in the question is the second option or option "B". </span>
3 0
3 years ago
What is 4 over 6 divided by 2 over 4?
djverab [1.8K]
4/3 /......................................................../
7 0
3 years ago
The school that Trevon goes to selling tickets to the annual dance competition. On the first day of tickets sales the school sol
KiRa [710]

Answer:

  both kinds of tickets are $5 each

Step-by-step explanation:

Let s and c represent the dollar costs of a senior ticket and child ticket, respectively. The problem statement describes two relationships:

  12s + 5c = 85 . . . . . revenue from the first day of sales

  6s + 9c = 75 . . . . . . revenue from the second day of sales

Double the second equation and subtract the first to eliminate the s variable.

  2(6s +9c) -(12s +5c) = 2(75) -(85)

  13c = 65 . . . . . simplify

  65/13 = c = 5 . . . . . divide by the coefficient of c

Substitute this value into either equation. Let's use the second one.

  6s + 9·5 = 75

  6s = 30 . . . . . . . subtract 45

  30/6 = s = 5 . . . divide by the coefficient of s

The price of a senior ticket is $5; the price of a child ticket is $5.

5 0
3 years ago
A polygon with 12 sides is called a/an <br> a. dodecagon. <br> b. pentagon. <br> c. undecagon.
Pepsi [2]
The answer is A. dodecagon.
5 0
3 years ago
Read 2 more answers
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