What is the solution set of the following system of equations?
1 answer:
Answer:
(0, 6) and (-5, -9)
Step-by-step explanation:
y = 3x + 6
y = (x + 4)² - 10
*Perfect square trinomial rule: (a + b)² = a² + 2ab + b²
Using substitution, we can substitute the value of y from the first equation for the value of y for the second equation.
y = (x + 4)² - 10 ⇒ 3x + 6 = (x + 4)² - 10
New equation:
3x + 6 = (x + 4)² - 10
<u>Solve</u>
3x + 6 = (x + 4)² - 10 <== simplify (x + 4)² using the rule listed above
3x + 6 = x² + 2(x)(4) + 4² - 10
3x + 6 = x² + 2(4x) + 4(4) - 10
3x + 6 = x² + 8x + 16 - 10 <== combine any like terms
3x + 6 = x² + 8x + 6 <== subtract 6 from both sides
- 6 - 6
3x = x² + 8x <== rearrange
-x² - 8x + 3x = 0 <== combine any like terms
-x² -5x = 0 <== factor out -x
-x(x + 5) = 0
Find the zeros/x-intercepts of the equation:
-x = 0 x + 5 = 0
/-1 /-1 - 5 - 5
x = 0 x = -5
Therefore, the zeros of the system of equations are: 0 and -5
Next, substitute the x values into y = 3x + 6.
For x = 0:
y = 3(0) + 6
y = 0 + 6
y = 6
(0, 6)
For x = -5:
y = 3(-5) + 6
y = -15 + 6
y = -9
(-5, -9)
The solution sets for the system of equations are: (0, 6) and (-5, -9)
Hope this helps!
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Answer:
A. 60 degrees
Step-by-step explanation:
Solution to sin(x/2)=(/2)
By looking at this equation, I can identify that the answer must be within the first quadrant since the numerator and denominator are both positive.
Since it is in the first quadrant, the range of the value of the answer must be between 0 degrees less than or equal to x less than or equal to 90 degrees.
I can also identify that this is a 30, 60, 90 degree triangle because it has a and 2 as the numerator and denominator; in this case this tells us that we are dealing with a 30, 60, 90 degree triangle because that is the only triangle with those 2 respective sides.
Once identifying those two pieces of information, we can then determine the answer.
Since sin is equal Opposite/Hypotenuse, we can then substitute the sides of the triangle (, 2) to find the angle (unknown).
So the equation would look like this,
Sinx/2=/2 (
representing the opposite side of the angle; 2 representing the Hypotenuse of the triangle)
We can then conclude that 60 degrees is the unknown angle, due to the nature of a 30 60 90 degree triangle.
*Use the attachment for reference
Therefore, the answer, 60 degrees, is a solution to the equation "sin(x/2)=(/2)"
The solutions of the function are:
- When f(x) = -4, the solution is -4
- When f(x) = -2, the solution is -5/2
- When f(x) = 0, the solution is -1
The equation is given as
When x = -4
3/4 * -4 -1
= -12/4 - 1
= -4
When x = -2
3/4*(-4) - 1
= -6/4 - 1/1
Take the lcm
-10/4
= -5/2
When x = 0
3/4(0) - 1
= -1
When f(x) = -4, the solution is -4
When f(x) = -2, the solution is -5/2
When f(x) = 0, the solution is -1
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