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notsponge [240]
3 years ago
6

How do you solve this equation? x/2 - x = x/4 + 6

Mathematics
1 answer:
fenix001 [56]3 years ago
4 0

Answer:

x= - 8

Step-by-step explanation:

multiply both sides by 4 to get rid of the fractions. you should then get:

2x-4x=x+24

then get all the x terms to one side by subtracting by x on each side:

2x-4x-x=24

then simplify:

-3x=24

divide by -3 on each side:

x= - 8

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Find the area of a plane figure bounded by lines
natulia [17]

Answer: 4.5

<u>Step-by-step explanation:</u>

First, find the points of intersection by solving the system.

y = x² + 2x + 4

y = x + 6

Solve by substitution:

x² + 2x + 4 = x + 6   ⇒   x² + x - 2 = 0   ⇒   (x + 2)(x - 1) = 0   ⇒   x = -2, x = 1

Now, integrate from x = -2 to x = 1

\int\limits^1_2 {(x+6)-(x^{2}+2x+4) } \,    <em>the bottom of the integral is -2 </em>

= \int\limits^1_2 {x+6-x^{2}-2x-4 } \,

= \int\limits^1_2 {-x^{2}-x+2 } \,  

= \frac{-x^{3}}{3} - \frac{x^{2}}{2}+2x\int\limits^1_2 {} \,

= (\frac{-1^{3}}{3} - \frac{1^{2}}{2}+2(1)) - (\frac{-(-2)^{3}}{3} - \frac{(-2)^{2}}{2}+2(-2))

= (\frac{-1}{3} - \frac{1}{2} +2) - (\frac{8}{3} -\frac{4}{2} -4)

= \frac{-9}{3} + \frac{3}{2} +6

= -3 + 1.5 + 6

= 4.5


3 0
3 years ago
Please help taking a test and can’t figure it out!!!
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I’m pretty sure the answer would be A
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Ms. Augustine is playing a game with her class. When a student tells her a number, she uses a rule to determine the new number.
Degger [83]

Answer:

When a student tells her a number, she uses a rule to determ

Step-by-step explanation:

Get the answers ... When a student tells her a number, she uses a rule to determine the new number. Ms. Augustine always uses the same rule. The table below shows some of the results. What would the number be when the student says 8? A. 58. B. 56. C. 54

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The variable Z is directly proportional to X. when X is 15, Z has the value of 45. what is the value of Z when X=23
IrinaVladis [17]
If\ Z\ is\ directly\ proportional\ to\ X\ then\ \frac{Z}{X}=const.\\------------------------\\X=15\ and\ Z=45\\\\X=23\ and\ Z=?\\\\\frac{Z}{23}=\frac{45}{15}\to\frac{Z}{23}=3\ \ \ \ |multiply\ both\ sides\ by\ 23\\\\\huge\boxed{Z=69}
8 0
3 years ago
5000 is 1/10 of what
KatRina [158]
<span>The correct answer is 50,000.

Explanation<span>:
We can set up the equation 5000=1/10x to represent this situation.

To solve, we will divide both sides by 1/10:
5000</span></span>÷<span><span>(1/10) = (1/10x)</span></span>÷<span><span>(1/10)
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To divide fractions, flip the second one and multiply; this gives us
5000*(10/1) = x
50000 = x.</span></span>
8 0
3 years ago
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