1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melisa1 [442]
3 years ago
15

I’m not sure how to answer this in a Graph, Diagram, and Algebra(algebraic reasoning too) for a,b,c, and d. Can someone please h

elp me?

Mathematics
1 answer:
Arlecino [84]3 years ago
3 0

The outline that that illustrate how <em>k</em> values change so that the solutions are the ones in the question are as follows

(a) The number line solution contains zero

Using algebra, we have;

The given quadratic inequality is; -x² + 4 ≥ x + k

The number line solution is the expression of the solution on the number line.

We have;

-x² + 4 ≥ x + k

-x²  - x + 4 - k ≥ 0

Dividing by (-1), we get;

x² + x - 4 + k ≤ 0

When - 4 + k = -2

k = 2, we get;

x² + x - 4 + 2 ≤ 0

x² + x - 2 ≤ 0

(x - 1)·(x + 2) ≤ 0

Given that the result of the product is less than zero, we have;

((-3) - 1)·((-3) + 2) > 0

Therefore, the solution are;

x ≤ 1, or x ≥ -2

Which gives

-2 ≤ x ≤ 1

  • Using diagram;

The solution of the above inequality includes 0 as shown in the attached number line

  • Graphically;    

The graph of the inequality is plotted using MS Excel, showing the solution set, of -2 ≤ x ≤ 1

(b) There are no solution to the inequality

In the present case, we have;

((-1)² - 4×(-1) × (4 - k) <  0

17 - 4·k < 0

k > \dfrac{17}{4}

Let k = 5, we have;

-x² + 4 ≥ x + k

-x² - x + 4 - 5 ≥ 0

-x² - x  -1 ≥ 0

The discriminant, is (1² - 4×(-1)×(-1)) = -3 < 0, therefore, there are no real

roots to inequality, and -x² - x  -1 is not equal to zero.

  • Graphically

Please find attached the graph of the function, which does not intersect with the x-axis, and therefore, has no values at which <em>y</em> = 0

(c) The solution is a single number

-x² + 4 ≥ x + k

When k = x + 5, we have;

0 ≥ x² + 2·x + 1

0 ≥ (x + 1)²

Therefore;

The only solution is; x = -1

Using diagrams:

Please find attached the solution of the function on the number line

  • Graphically

The graph of the function showing only one intercept is attached

Learn more here:

brainly.com/question/11982012

You might be interested in
Name the angle relationship. Find the measure of angle b.
yarga [219]

Answer:

vertical angles b= 86

Step-by-step explanation:

b is equal to 86 since the angles are vertical angles

5 0
3 years ago
Read 2 more answers
What is 7/8 x 1/3 x 2/3? Pls help me.
Step2247 [10]
7/36
Multiply the top together and then the bottom together and the final numbers on top and bottom is your answer.
8 0
3 years ago
Read 2 more answers
20 POINTS 20 POINTS. Will give Brainliest.
Simora [160]

Answer:

using y=mx+c

C=7

y=8

x= -4

we're looking for m

8=-4m +7

1= -4m

m= -1/4

8 0
3 years ago
Read 2 more answers
Does (3,5) and (-3,-5) lie in the same quadrant
Arlecino [84]

Answer:

no they don't one lies in  quadrant 1 while the other is in quadrant 3

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
How to scientific notation to express the number 480 into 1 scientific notaion?
AfilCa [17]

Consider the number 480 in expanded form:

... 480 = 4×100 + 8×10

The left-most digit and multiplier are those that correspond to the ones you use in scientific notation.. You recall that 100 = 10×10 = 10². All this means is that

... 480 = 4.8×10²

5 0
3 years ago
Other questions:
  • What is the value of each number in 1,567.209?
    6·2 answers
  • Lori owes her mom $400. She pays her debt off over 40 weeks.​
    9·2 answers
  • Which of the following method for making a proof does not involve the negation of a statement
    6·1 answer
  • A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center
    14·1 answer
  • A poster measures 9 1/2 inches by 11 3/4 inches estimate the area of poster
    8·1 answer
  • PLEASE HELP! I’ll give brainliest!
    13·1 answer
  • Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • Vbb. Pls help 50 points
    13·1 answer
  • I need help asap T&gt;T
    14·1 answer
  • How high is a weather balloon that is tied to the ground if it is secured by a 15m long rope and the angle between the rope and
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!