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coldgirl [10]
2 years ago
7

WILL GIVE BRAINLIEST

Mathematics
1 answer:
Montano1993 [528]2 years ago
3 0

Step-by-step explanation:

Use the compound interest formula:

A = P( 1 + r/n)^nt

A is the amount at the end

P is the principal or original amount.

R is annual rate as a decimal (you have to convert)

N is the # of compounding periods in a year (quarterly means 4)

T is time in years

A = 500( 1 + 0.0475/4)^(4×20)

This would be $1285.64 when fully computed.

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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
Please help <br>cos40∘=sin(x+30∘)​
iVinArrow [24]

Answer:

x = 20 degrees.

Step-by-step explanation:

cos40∘=sin(x+30∘)​

sin (x + 30) = 0.766

x + 30 = arcsin 0.766 = 50

x = 50 - 30 = 20.

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2 years ago
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Scaling up a 4 inch by 6 inch image by 50% results in which of the following image size
Monica [59]
50% or 1/2 of 4 is 2 50% or 1/2 of 6 is 3 so then just add them to the respective number since its going up by 50% or 2 in by 3 in \[\frac{ 6 }{ 9}\]
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sammy [17]

Answer:

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Step-by-step explanation:

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3 years ago
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If a = i - 9k and b = j + k , find ab .
Orlov [11]

Answer:

solution

given a=1_9k and b=j+k

Now,ab=(1_9k)(j+k)

=1((j+k)-9k(j+k)

=j+k_9jk-9k^2

=k_9k^2+j_9jk

=k((1_9k)+j(1_9k)

=(1_9k)(k+k)

5 0
3 years ago
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