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IrinaVladis [17]
3 years ago
5

The equation 1 – 4⁄3x = 1⁄2(–x + 7) has what type of solution set

Mathematics
1 answer:
Kobotan [32]3 years ago
4 0

Answer:

Unique  

Step-by-step explanation:

Let y₁ = 1 - ⁴/₃x           (1)

and y₂ = ½(–x + 7)     (2)

The slope of Equation (1) is -⁴/₃.

The slope of Equation (2) is -½.

The slopes are different, so there is a unique solution set.

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Answer:

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Step-by-step explanation:

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5 0
3 years ago
Which of the following equations has a graph PARALLEL to the line y = 4x + 7
Kobotan [32]

Answer:

y = 4x - 2

Step-by-step explanation:

This equation has the same slope as the equation given which means that they are parallel lines. This equation also has a y-intercept of -2.

I graphed both equations below to show you that they are parallel.

If this answer is correct, please make me Brainliest!

4 0
3 years ago
|1/2b-8|=|1/4b-1|<br> b=____ and ____
Deffense [45]

Answer:

  b = 12 and 28

Step-by-step explanation:

The absolute value equation |1/2b-8| = |1/4b-1| resolves to a piecewise linear function with three pieces. There are two solutions.

<h3>Domains</h3>

The absolute value function on the left has a turning point where its value is zero:

  1/2b -8 = 0

  b -16 = 0

  b = 16

The absolute value function on the right has a turning point where its value is zero:

  1/4b -1 = 0

  b -4 = 0

  b = 4

For b > 16, both absolute value functions are identity functions. In this domain, the equation is ...

  1/2b -8 = 1/4b -1

For 4 < b < 16, the function on the left negates its argument, so the equation in this domain is ...

  -(1/2b -8) = 1/4b -1

For b < 4, both functions negate their arguments, so the equation in this domain is ...

  -(1/2b -8) = -(1/4b -1)

For the purpose of finding the value of b, this is effectively identical to the equation for b > 16. (The value of b does not change if we multiply both sides of the equation by -1.)

<h3>Solutions</h3>

<u>Domain b < 4 ∪ 16 < b</u>

  1/2b -8 = 1/4b -1

  2b -32 = b -4 . . . . . . . . multiply by 4

  b = 28 . . . . . . . . . . . . add 32-b to both sides

This solution is in the domain of the equation, so is one of the solutions to the original equation.

<u>Domain 4 < b < 16</u>

  -(1/2b -8) = 1/4b -1 . . . . equation in this domain

  -2b +32 = b -4 . . . . . . multiply by 4

  36 = 3b . . . . . . . . . . . add 2b+4 to both sides

  12 = b . . . . . . . . . . . . divide by 3

This solution is in the domain of the equation, so is the other solution to the original equation.

<h3>Graph</h3>

For the purposes of the graph, we have define the function g(b) to be the difference of the two absolute value functions. The solutions are found where g(x) = 0, the x-intercepts. The graph shows those to be ...

  b = 12  and  b = 28

__

<em>Additional comment</em>

Defining g(b) = |1/2b-8| -|1/4b-1|, we can rewrite it as ...

  g(b)=\begin{cases}7-\dfrac{1}{4}b&\text{for }b < 4\\-\dfrac{3}{4}b+9&\text{for }4\le b < 16\\\dfrac{1}{4}b-7&\text{for }16\le b\end{cases}

Then the solutions are the values of b that make g(b) = 0.

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2 years ago
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D and E. An acute angle is any angle that is less than 90(a right angle). A is an obtuse angle(more than 90). And B + C are right angles. Hope this helps you!
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3 years ago
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