Answer:
Solution set of the quadratic equation is, Empty set
Step-by-step explanation:
Given the quadratic equation: 
Subtraction property of equality states that you subtract the same number to both sides of an equation.
Subtract both sides by 1 we get;
Simplify:
Division property of equality states that you divide the same number to both sides of an equation.
Divide both sides by 6 we get;
Simplify:
For any x in real number there does not exist any number x which satisfy
, therefore, there is no solution for this set of the quadratic inequality or in other word we can say that set of the solution is Empty set.
Answer: s=36
Step-by-step explanation:
To solve for s, we can use our algebraic properties to solve.
[subtract both sides by 14]
[multiply both sides by 3]
Answer:
The -1 came from factoring.
The equation is multiplied by 8 because 8 could be pulled from 16x-8.
16 can be divided by 8 2 times and 8 can only divided by 8 once.
so factoring it makes the equation 8(2x-1)
<u>vertex</u>
y = 3(x - 2)² - 4
y = 3((x - 2)(x - 2)) - 4
y = 3(x² - 2x - 2x + 4) - 4
y = 3(x² - 4x + 4) - 4
y = 3(x²) - 3(4x) + 3(4) - 4
y = 3x² - 12x + 12 - 4
y = 3x² - 12x + 8
3x² - 12x + 8 = 0
x = <u>-(-12) +/- √((-12)² - 4(3)(8))</u>
2(3)
x = <u>12 +/- √(144 - 96)</u>
6
x = <u>12 +/- √(48)
</u> <u> </u> 6<u>
</u>x =<u> 12 +/- 6.93</u>
<u /> 6
x = 2 +/- 1.155
x = 2 + 1.155 x = 2 - 1.155
x = 3.155 x = 0.845
y = 3x² - 12x + 8
y = 3(3.155)² - 12(3.155) + 8
y = 3(1.334025) - 3.786 + 8
y = 4.002075 - 3.786 + 8
y = 0.216075 + 8
y = 8.216075
(x, y) = (3.155, 8.216075)
or
y = 3x² - 12x + 8
y = 3(0.845)² - 12(0.845) + 8
y = 3(0.714025) - 10.14 + 8
y = 2.142075 - 10.14 + 8
y = -7.857925 + 8
y = 0.142675
(x, y) = (0.845, 0.142675)
<u>y-intercept</u>
y = 3x² - 12x + 8
y = 3(0)² - 12(0) + 8
y = 3(0) - 0 + 8
y = 0 - 0 + 8
y = 0 + 8
0 = -y + 8
y = 8
(x, y) = (0, 8)
-------------------------------------------------------------------------------------------
<u>vertex</u>
y = 4(x - 5)² = 1
y = 4(x - 5)² - 1
y = 4((x - 5)(x - 5)) - 1
y = 4(x² - 5x - 5x + 25) - 1
y = 4(x² - 10x + 25) - 1
y = 4(x²) - 4(10x) + 4(25) - 1
y = 4x² - 40x + 100 - 1
y = 4x² - 40x + 99
4x² - 40x + 99 = 0
x = <u>-(-40) +/- √((-40)² - 4(4)(99))</u>
2(4)
x = <u>40 +/- √(1600 - 1584)</u>
8
x = <u>40 +/- √(16)</u>
8
x = <u>40 +/- 4</u>
8
x = 5 +/- 1/2
x = 5 + 1/2 x = 5 - 1/2
x = 5 1/2 x = 4 1/2
y = 4x² - 40x + 99
y = 4(5 1/2)² - 40(5 1/2) + 99
y = 4(30 1/4) - 220 + 99
y = 121 - 220 + 99
y = -99 + 99
y = 0
(x, y) = (5 1/2, 0)
or
y = 4x² - 40x + 99
y = 4(4 1/2)² - 40(4 1/2) + 99
y = 4(20 1/4) - 180 + 99
y = 81 - 180 + 99
y = -99 + 99
y = 0
(x, y) = (4 1/2, 0)
<u>y-intercept</u>
y = 4x² - 40x + 99
y = 4(0)² - 40(0) + 99
y = 4(0) - 0 + 99
y = 0 - 0 + 99
y = 0 + 99
y = 99
(x, y) = (0, 99)
--------------------------------------------------------------------------------------------
<u>vertex</u>
y = (x - 1)² = 2
y = (x - 1)² - 2
y = ((x - 1)(x - 1)) - 2
y = (x² - x - x + 1) - 2
y = x² - 2x + 1 - 2
y = x² - 2x - 1
x² - 2x - 1 = 0
x = <u>-(-2) +/- √((-2)² - 4(1)(-1))</u>
2(1)
x = <u>2 +/- √(4 + 4)</u>
2
x = <u>2 +/- √(8)</u>
2
x = <u>2 +/- 2.83</u>
2
x = 1 +/- 1.415
x = 1 + 1.415 x = 1 - 1.415
x = 2.415 x = 0.415
y = x² - 2x - 1
y = (2.145)² - 2(2.145) - 1
y = 4.60125 - 4.029 - 1
y = 0.57225 - 1
y = 0.42775
(x, y) = (2.415, 0.42775)
or
y = x² - 2x - 1
y = (0.415)² - 2(0.415) - 1
y = 0.172225 - 0.83 - 1
y = -0.657775 - 1
y = -1.657775
(x, y) = (0.415, -1.657775)
<u>y-intercept</u>
y = x² - 2x - 1
y = (0)² - 2(0) - 1
y = 0 - 0 - 1
y = 0 - 1
y = -1
(x, y) = (0, -1)
Answer:
C or 8
Step-by-step explanation:
Once again, first you ant to simplify the equation before putting in the numbers. So the simplified equation is mh + mp -p/h +m. Then you put the numbers in. mh is actually 3(-1), which is -3. mp is really 3*4, which is 12. p/h is 4/-1, which is -4, and then you add m. So when you put the numbers is it ends up as -3 + 12 - 4 +3, which simplified is 8, or C
