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Anvisha [2.4K]
3 years ago
9

Simplify 3-4i/3+4i + 3+4i/3-4i

Mathematics
1 answer:
Shkiper50 [21]3 years ago
4 0

Answer:

-14/25

Step-by-step explanation:

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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
Arlecino [84]

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

3 0
2 years ago
Kevin bought 4/6 pounds of pecans for $50.89. About how much was the cost per pound?
sukhopar [10]

Answer:

$76.33

Step-by-step explanation

1 divided by 4/6 = 3/2 =1.5

50.89 x 1.5 =$76.33

5 0
3 years ago
David bought a cape and mask for each of the 9 boys at his party. The capes cost $5.25 each and the masks cost $4.35 each. How m
Mila [183]
The clown earned$104.75
4 0
3 years ago
Hayley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each
Sindrei [870]

Answer:

After 3 weeks they both will have the same amount in their savings account.

Step-by-step explanation:

Given:

Amount saved by Haley = $155

Amount saved by Hank = $230

Amount saving each week by Haley = $10

Amount spending each week by Hank = $15

We need to find Number of weeks when both both will have same amount in savings account.

Solution:

Let Number of week be 'x'.

Total Amount of Haley can be calculated by Amount saved by Haley plus Amount saving each week by Haley multiplied by number of weeks.

framing in equation form we get;

Total Amount of Haley = 155+10x

Also;

Total Amount of Hank can be calculated by Amount saved by Hank minus Amount spending each week by Hank multiplied by number of weeks.

framing in equation form we get;

Total Amount of Hank = 230-15x

Now we need to find the number of weeks when both will have same amount.

To find the same we will have to make both the equation equal.

So we can say.

155+10x=230-15x

On Solving above equation we get;

We will combine the like terms together;

10x+15x =230-155\\\\25x = 75

Now Dividing both side by 25 using Division property of equality we get;

\frac{25x}{25} = \frac{75}{25}\\\\x=3 \ weeks

Hence, After 3 weeks they both will have the same amount in their savings account.

4 0
2 years ago
95.97 meters is 42% of<br> yards? (1 yard = 0.914 m)
rusak2 [61]

95.97 meters is 42% of 249.89 yards.

6 0
3 years ago
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