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blagie [28]
2 years ago
6

Find the interval in which the function is positive.

Mathematics
1 answer:
blsea [12.9K]2 years ago
7 0

Answer:

  (b)  I, III

Step-by-step explanation:

The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).

<h3>General shape</h3>

The leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.

If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.

<h3>Specific shape</h3>

The answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).

  f(2) = 2² -7·2 +10 = 4 -14 +10 = 0

  f(5) = 5² -7·5 +10 = 25 -35 +10 = 0

This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.

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After graduating from college, Jane has two job offers to consider. Job A is compensated at $100,000 a year but
vaieri [72.5K]

Answer: (a)  Job A , by approximately $69, 482

\\ (b)  Job A , by approximately $6,867

 \\(c) Job B , by approximately $ 767,362

  \\ (d) Job A

Step-by-step explanation:

JOB B

\\The starting Salary is $ 10,000

Since there is an increment of 25% at the beginning of each new year. The breakdown of the increment is as follow:

\\First year : 125% of $ 10,000 = $12,500

\\Second year : 125% of $ 12,500 = $15,625

\\Third year : 125% of $15,625= $19,531.25

\\Fourth year: 125% of $19,531.25 = $24,414.06

\\Fifth year : 125% of $24,414.06 = $30,517.58

\\Sixth year: 125% of $30,517.58 = $38,147.00

\\Seventh year: 125% of $38,147.00 = $47,683.75

\\Eight year: 125% of $47,683.75 = $59,604.69

\\Ninth year: 125% of $59,604.69 = $74,505.86

\\Tenth year: 125% of $74,505.86 = $93,132.32

\\Following the same procedure:

\\Eleventh year = $116,415.40

\\Twelfth year = $145,519.25

\\Thirteenth year = $181,899.06

\\Fourteenth year = $227,373.82

\\Fifteenth year = $ 284,217.29

\\Sixteenth year = $355,271.61

\\Seventeenth year = $444,089.51

\\Eighteenth year = $555,111.89

\\Nineteenth year = $693,889.86

\\Twentieth year = $867,362.32

\\(a) Following the analysis above, at the beginning of the fifth year Job A will have a greater annual salary

\\Difference: Salary of Job A at the beginning of fifth year remains $ 100,000 while that of Job B resulted into $ 30,517.58, the difference implies

$100,000 - $ 30,517.58 = $69,482

\\(b) At the beginning of tenth year, Job A is still $100,000, Job B resulted into $93,132.32. Job A is still greater by approximately $6,867

\\(c) At the beginning of the twentieth year, the annual salary of A is still $ 100,000 while the annual salary of B is $ 867,362.32. Job B annual salary is greater by approximately $ 767,362

\\(d) If I were in Jane’s shoe I will take Job A and work for few years to gain more experience the look for a job that pays better. Waiting for many years in case of Job B is risky , market situation is uncertainty.

8 0
3 years ago
Solve the equation below for x. −12(3x−4)=11 A. −1323 B. −813 C. −6 D. 6
geniusboy [140]

-1/2( 3x -4) = 11

Use distributive properties:

-3/2 + 2,= 11

Subtract 2 from both sides:

-3/2x = 9

Divide both sides by -3/2

X = 9/ -3/2

X = -6

The answer is c. -6

3 0
3 years ago
a math student is standing 40 feet from the base of a water tower. the angle of elevation from her horizontal line of sight is 7
Lerok [7]

9514 1404 393

Answer:

  128 ft

Step-by-step explanation:

The height of the tower above eye-height is related to the angle by ...

  Tan = Opposite/Adjacent

  tan(72°) = (tower height above eye height)/(40 ft)

  tower height above eye height = (40 ft)×tan(72°) = 123 ft

Since eye height is 5 ft, the total height of the tower from the ground is ...

  tower height = eye height + height above eye height

  tower height = 5 ft + 123 ft

  tower height = 128 ft

4 0
2 years ago
Find the value of x, y, and z in the rhombus below.
Yuki888 [10]

Solution:

<u>It should be noted:</u>

  • Opposite sides of a rhombus are always equal.
  • Opposite angles of a rhombus are always equal.

<u>Thus:</u>

  • (-y - 10) = 90°
  • 3z - 3 = 90°
  • 4x - 2 = 90°

<u>Finding x:</u>

  • 4x - 2 = 90°
  • => 4x = 90 + 2
  • => 4x = 92
  • => x = 23

<u>Finding y:</u>

  • (-y - 10) = 90°
  • => -y - 10 = 90°
  • => -y = 100
  • => y = -100

<u>Finding z:</u>

  • 3z - 3 = 90°
  • => 3z = 90 + 3
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4 0
2 years ago
Read 2 more answers
The measure of arc EF is —
Dimas [21]

30 plus EF = 180

Ef = 150

circumscribed angle plus the central angle is 180

7 0
2 years ago
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