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OLEGan [10]
3 years ago
12

Solve for y, y-8= -( y-2) / 2

Mathematics
2 answers:
rusak2 [61]3 years ago
8 0

Answer:

y = 6

Step-by-step explanation:

y - 8= - (y - 2) / 2

Expand.

y - 8 = (- y + 2) /2

Multiply both sides by 2.

2(y - 8) = - y + 2

2y - 16 = -y + 2

Add y and 16 on both sides.

2y + y = 2 + 16

3y = 18

Divide both sides with 3.

y = 18/3

y = 6

natta225 [31]3 years ago
7 0

Answer:

y = 6

Step-by-step explanation:

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Determine whether the equation x^3 - 3x + 8 = 0 has any real root in the interval [0, 1]. Justify your answer.
nikdorinn [45]

Answer:

The equation does not have a real root in the interval \rm [0,1]

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if f is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

  1. If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
  2. The image of a continuous function over an interval is itself an interval.

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in \rm [0,1], which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval \rm [0,1], which means to evaluate the equation in 0 and 1:

f(x)=x^3-3x+8\\f(0)=8\\f(1)=6

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval \rm [0,1]. I attached a plot of the equation in the interval \rm [-2,2] where you can clearly observe how the graph does not cross the x-axis in the interval.  

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2 years ago
5 (x + 2) = 3 (x + 8)
aleksley [76]
So first you distribute the 5 to the x and the +2 and get
5x+10=3(x+8)
 then you distribute the 3 to the other x and the +8 and get
5x+10=3x+24
subtract 3x from both sides
2x+10=24
subtract 10 from both sides and get
2x=14
divide both sides by 2 and get
x=7
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jayce runs 2 1/2 miles on monday. Each day after that, he runs the same 1 1/3 mile route every morning. His goal is to run at le
PtichkaEL [24]

Answer:

Step-by-step explanation:

6 < 2 1/2 + 1 1/3R

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Write 53,278 in Expanded Form
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53,278 can be written as:

50,000 + 3,000 + 200 + 70 + 8
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