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vichka [17]
3 years ago
10

Solve for e. Give an exact answer. 0.75(8+e)=2-1.25e0.75(8+e)=2−1.25e

Mathematics
1 answer:
mote1985 [20]3 years ago
5 0

Answer:

<h2>e = -2</h2>

Step-by-step explanation:

Given the expression 0.75(8+e)=2-1.25e, to get the value of e, the following steps must be carried out;

0.75(8+e)=2-1.25e\\6+0.75e = 2-1.25e\\collect\ like \ terms\\6-2 = -1.25e-0.75e\\4 = -2e\\Dividing\ both\ sides\ by \ -2\\\frac{4}{-2} = \frac{-2e}{-2}\\ e = -2

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Uestion
Stella [2.4K]

Check the picture below, so the park looks more or less like so, with the paths in red, so let's find those midpoints.

~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ J(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 -3}{2}~~~ ,~~~ \cfrac{ 3 +1}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ 4 }{2} \right)\implies JK=(-1~~,~~2) \\\\[-0.35em] ~\dotfill

~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ L(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad M(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 +5}{2}~~~ ,~~~ \cfrac{ -3 -1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies LM=(2~~,~~-2) \\\\[-0.35em] ~\dotfill

~~~~~~~~~~~~\textit{distance between 2 points} \\\\ JK(\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\qquad LM(\stackrel{x_2}{2}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ JKLM=\sqrt{(~~2 - (-1)~~)^2 + (~~-2 - 2~~)^2} \\\\\\ JKLM=\sqrt{(2 +1)^2 + (-2 - 2)^2} \implies JKLM=\sqrt{( 3 )^2 + ( -4 )^2} \\\\\\ JKLM=\sqrt{ 9 + 16 } \implies JKLM=\sqrt{ 25 }\implies \boxed{JKLM=5}

now, let's check the other path, JM and KL

~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ J(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad M(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 -3}{2}~~~ ,~~~ \cfrac{ -3 +1}{2} \right) \implies \left(\cfrac{ -4 }{2}~~~ ,~~~ \cfrac{ -2 }{2} \right)\implies JM=(-2~~,~~-1) \\\\[-0.35em] ~\dotfill

~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ K(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad L(\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +1}{2}~~~ ,~~~ \cfrac{ -1 +3}{2} \right) \implies \left(\cfrac{ 6 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies KL=(3~~,~~1) \\\\[-0.35em] ~\dotfill

~~~~~~~~~~~~\textit{distance between 2 points} \\\\ JM(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad KL(\stackrel{x_2}{3}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ JMKL=\sqrt{(~~3 - (-2)~~)^2 + (~~1 - (-1)~~)^2} \\\\\\ JMKL=\sqrt{(3 +2)^2 + (1 +1)^2} \implies JMKL=\sqrt{( 5 )^2 + ( 2 )^2} \\\\\\ JMKL=\sqrt{ 25 + 4 } \implies \boxed{JMKL=\sqrt{ 29 }}

so the red path will be  5~~ + ~~\sqrt{29} ~~ \approx ~~ \blacksquare~~ 10 ~~\blacksquare

3 0
2 years ago
Inequality word problem<br><br> 7 less than -2 times a number X is greater than or equal to 41
Lady bird [3.3K]
Less than means minus so 7 less than means -7

-2 times a number x means -2 times x or -2x

is greater than or equal to means <u>></u>

41=41


so
-7+-2x<u>></u>41
-2x-7<u>></u>41
add 7 to both sides
-2x<u>></u>48
divide both sides by -2
remember to flip sign since divided by negative
x<u><</u>-96 
5 0
3 years ago
PLS HELP I WILL GIVE BRAINLIEST
Serjik [45]

Answer:

Easy 10000 like that was so easy

Step-by-step explanatLOLLO

5 0
3 years ago
What is the solution factoring by polynomial (3x+2y)(x+2y)
hodyreva [135]

Answer:

3x²+8xy+4y²

Step-by-step explanation:

Opening brackets,

3x²+6xy+2xy+4y²

=3x²+8xy+4y²

6 0
4 years ago
Suma a patru numere este 600.Primul numar este cu 12 mai mare decat al doilea si cu 12 mai mic decat al treilea.Stiind ca al pat
pashok25 [27]
Salut!
Ai ca a + b + c +d = 600;
a = b + 12 => b = a-12;
a = c - 12 => c = a + 12;
d = (a+b+c)/3 => d = a;
In final, 4a = 600 => a = 150;
b = 138;
c = 162;
d = 150;
Bafta!
8 0
4 years ago
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