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Rzqust [24]
2 years ago
8

Write the absolute value equations in the form x−b =c (where b is a number and c can be either number or an expression) that hav

e the following solution sets:
two solutions: x=1/2, x=-1/3
one solution: x=-3
all numbers such that x≤5
all numbers that x ≥-1.3

anything helps!
Mathematics
1 answer:
hjlf2 years ago
7 0

All cases rewritten in the form of <em>difference</em> expressions are listed below:

  1. <em>x - 1/2 = 0</em>, <em>x + 1/3 = 0</em>
  2. <em>x + 3 = 0</em>
  3. <em>x - 5 ≤ 0</em>
  4. <em>x + 1/3 ≥ 0</em>
<h3 /><h3>How to translate equalities and inequalities into difference expressions</h3>

Equalities represent relationships between two expressions, in which one expression is equal to another. An equality (<em>x = a</em>) is equivalent to the following <em>difference</em> expression:  

<em>x - a = 0</em>   (1)

And inequalities represent relationships between two expressions, in which one expression is not necessarily to another. An inequality (<em>x < a, x > a, x ≤ a, x ≥ a</em>) is represented by the following <em>difference</em> expression:

<em>x - a = b</em>   (2)

Where b have the following cases:

  1. If <em>x < a</em>, then <em>b < 0</em>.
  2. If <em>x > a</em>, then <em>b > 0</em>.
  3. If <em>x ≤ a</em>, then <em>b ≤ 0</em>.
  4. If <em>x ≥ a</em>, then <em>b ≥ 0</em>.

Now we proceed to rewrite each case in term of <em>difference</em> expressions:

  1. <em>x - 1/2 = 0</em>, <em>x + 1/3 = 0</em>
  2. <em>x + 3 = 0</em>
  3. <em>x - 5 ≤ 0</em>
  4. <em>x + 1/3 ≥ 0</em>

To learn more on inequalities, we kindly invite to check this verified question: brainly.com/question/19491153

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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
andrew-mc [135]

Answer:

f(x):

x =  - 4

g(x)

x = 1

Step-by-step explanation:

When a function is of the form:

f(x) = a {(x - h)}^{2}  + k

The equation of the axis of symmetry is

x = h

The given function is

f(x) = 3 {(x + 4)}^{2}  + 1

We can see that h=-4

Hence the equation of axis of symmetry is

x =  - 4

From the graph, the axis of symmetry of h(x) is the vertical line that divides the parabola into two congruent halves.

This line is

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4 0
2 years ago
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Hunter-Best [27]
<h3>Answer:  Choice D</h3><h3>y = (-1/5)x + 7</h3>

======================================

Work Shown:

We will only focus on the two points that are on the regression line.

Those two points are (10,5) and (15,4)

Let (x1,y1) = (10,5) and (x2,y2) = (15,4)

Find the slope of the line through (x1,y1) = (10,5) and (x2,y2) = (15,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 5)/(15 - 10)

m = -1/5

m = -0.2

Plug m = -0.2, and  (x1,y1) = (10,5) into the point slope formula. Solve for y

y - y1 = m(x - x1)

y - 5 = -0.2(x - 10)

y - 5 = -0.2*x - 0.2*(-10) ... distribute

y - 5 = -0.2*x + 2

y - 5+5 = -0.2*x + 2 + 5 ... add 5 to both sides

y = -0.2*x + 7

y = (-1/5)*x + 7 .... convert -0.2 to -1/5

The equation y = (-1/5)x + 7 is in the form y = mx+b with m = -1/5 = -0.2 as the slope and b = 7 as the y intercept. The y intercept is where the graph crosses the vertical y axis. More specifically, the location of the y intercept in this case is at the point (0,7).

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3 years ago
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Brrunno [24]

Answer:

6 feet in the distance

Step-by-step explanation:

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