8 ( 8x - 4) = -7 (-x

For which values of c does the following polynomial have two complex roots? X^2+4x+C

Grace [21]

For this case we have that by definition, the discriminant of a quadratic expression is given by:

$d = b ^ 2-4 (a) (c)$

If the discriminant is less than zero then the expression has two different complex roots.

In this case we have the following expression:

$x ^ 2 + 4x + c$

So we have to:

$a = 1\\b = 4\\c = c\\$

The discriminant is given by:

$d = 4 ^ 2-4 (1) (c)\\d = 16-4c$

Then, if we want two complex roots it must be fulfilled that:

$16-4c$

Thus, the expression has two complex roots for all values greater than 4.

ANswer:

$c> 4$

5 0

3 years ago

Lynn Jude and Anne were given the function f(x)=2x^2+6, and they were asked to find f(-4). Lynns answer was 38, Judes answer was

Cerrena [4.2K]

Answer:

Lynn's answer 38 is correct

2(-4)^2+6

2(16)+6

32+6=38

Step-by-step explanation:

5 0

3 years ago

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An SRS of 450 450 high school seniors gained an average of ¯ x = 20 x¯=20 points in their second attempt at the SAT Mathematics

maria [59]

Answer: (15.47, 24.53)

Step-by-step explanation:

We know that the confidence interval for population mean is given by :_

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

, where n= sample size.

$\sigma$ = standard deviation.

$\overline{x}$ = sample mean.

z*= Critical value.

Given : n= 450

$\overline{x}=20$

$\sigma=49$

Critical value for 95% confidence = z*=1.96 [From z-value table]

Then, the 95% confidence interval will be :-

$20\pm (1.96)\dfrac{49}{\sqrt{450}}$

$\approx 20\pm (1.96)(2.31)$

$\approx 20\pm 4.53$

$=(20-4.53,\ 20+4.53)=(15.47,\ 24.53)$

Hence, the 95% confidence interval for the mean change in score μ μ in the population of all high school seniors. : (15.47, 24.53)

3 0

3 years ago

Find the measure of each angle.

Galina-37 [17]

Given:

Given that the isosceles trapezoid JKLM.

The measure of ∠K is 118°

We need to determine the measure of each angle.

Measure of ∠L:

By the property of isosceles trapezoid, we have;

$\angle K+\angle L=180^{\circ}$

$118^{\circ}+\angle L=180^{\circ}$

$\angle L=62^{\circ}$

Thus, the measure of ∠L is 62°

Measure of ∠M:

By the property of isosceles trapezoid, we have;

$\angle L \cong \angle M$

Substituting the value, we get;

$62^{\circ}=\angle M$

Thus, the measure of ∠M is 62°

Measure of ∠J:

By the property of isosceles trapezoid, we have;

$\angle J \cong \angle K$

Substituting the value, we get;

$\angle J =118^{\circ}$

Thus, the measure of ∠J is 118°

Hence, the measures of each angles of the isosceles trapezoid are ∠K = 118°, ∠L = 62°, ∠M = 62° and ∠J = 118°

4 0

3 years ago

Shawn and dorian rented bikes from two different rental shops. the prices in dollars, y, of renting bikes from the two different

Hitman42 [59]

They paid $24 each for the rental.

6 0

3 years ago

Read 2 more answers

8 ( 8x - 4) = -7 (-x - 5)