Unit circle , finding the angle please help

How many solutions does the equation |x + 6| − 4 = c have if c = 5? If c = −10? Complete the explanation

mixer [17]

Answer:

<h2>For c = 5 → two solutions</h2><h2>For c = -10 → no solutions</h2>

Step-by-step explanation:

We know

$|a|\geq0$

for any real value of a.

|a| = b > 0 - two solutions: a = b or a = -b

|a| = 0 - one solution: a = 0

|a| = b < 0 - no solution

|x + 6| - 4 = c

for c = 5:

|x + 6| - 4 = 5 add 4 to both sides

|x + 6| = 9 > 0 TWO SOLUTIONS

for c = -10

|x + 6| - 4 = -10 add 4 to both sides

|x + 6| = -6 < 0 NO SOLUTIONS

Calculate the solutions for c = 5:

|x + 6| = 9 ⇔ x + 6 = 9 or x + 6 = -9 subtract 6 from both sides

x = 3 or x = -15

5 0

3 years ago

The first three steps in determining the solution set of the system of equations algebraically are shown in the table. y = −x2 +

lianna [129]

You have a system of equations $\left \{ {{y = -x^2+2x-9} \atop {y =-6x+6}} \right.$ .

1. Substitude right side of second equation into the left side of the first equation: $-6x+6=-x^2+2x-9$ .

2. Solve this equation:
$x^2-2x+9-6x+6=0, \\ x^2-8x+15=0, \\ D=(-8)^2-4\cdot 1\cdot 15=64-60=4, \\ \sqrt{D}=2, \\ x_{1,2}=\dfrac{8\pm 2}{2 } =3,5$ .

3. Find y:
for $x_1=3, y_1=-6\cdot 3+6=-18+6=-12$ ,
for $x_2=5, y_2=-6\cdot 5+6=-30+6=-24$ .

4. The solutions of the system are: (3,-12) and (5,-24).
Answer: Correct choice is A.

7 0

3 years ago

Read 2 more answers

Law of sines: How many distinct triangles can be formed for which m∠A = 75°, a = 2, and b = 3? No triangles can be formed. One t

Vinvika [58]

We have been given angle A as 75 degrees and sides a = 2 and b = 3.

Using Sine rule, we can set up:

$\frac{Sin(A)}{a}=\frac{Sin(B)}{b}$