Answer: 2, 6
<u>Step-by-step explanation:</u>
Triangle Inequality Theorem states that the sum of two sides must be GREATER than the third side.
RS + ST > RT and RS + RT > ST and ST + RT > RS
2x + 4x > 12 2x + 12 > 4x 4x + 12 > 2x
6x > 12 12 > 2x 12 > -2x
x > 2 6 > x -6 < x
2 < x x < 6 invalid
Answer: 2 < x < 6
Graph: O----------------------O
2 6
<em> Note: -6 is invalid because you cannot have a negative length. </em>
Answer:
y = 1/2x + 2
Step-by-step explanation:
for x=10, y=7
for x=20, y=12
for x=30, y=17
y = 1/2x + 2
Answer:
7+5 first because of pemdas
7+5 = 12
12+4 x 13-2
then 4 x 13
4 times 13 = 52
12+52-2
then add
12+52 = 64
64-2
then subtract
64-2 = 62
Step-by-step explanation:
Pemdas
Answer:
a) 0.5514
b) 0.0058
Step-by-step explanation:
Data provided in the question:
Probability that the the selected person is righthanded, P(R) = 0.82
Therefore,
Probability that the the selected person is not righthanded, P(R') = 1 - 0.82
= 0.18
Now,
a. They are all right-handed
P (They are all right-handed) = P(R) × P(R) × P(R)
= 0.82 × 0.82 × 0.82
= 0.5514
b) None of them is right-handed
P (None of them is right-handed) = P(R') × P(R') × P(R')
= 0.18 × 0.18 × 0.18
= 0.0058
1. to create your own quadratic you have to just make up any numbers. so off the top of my head:
y = -5x^2 + 10x - 3
2. the equation to find the x value of the vertex uses is the equation -b/2a. You may notice that this is similar to the quadratic formula except for you take away the plus or minus square root part. if you think about it, it makes sense that this would be the vertex because the plus or minus parts are an equal distance away from the center of the parabola. so using the form ax^2 + bx + c we can plug in the a and b:
x = -10/2 (-5)
x = -10/-10
x = 1
so we have x and can plug into equation to get y value:
y = -5 (1)^2 + 10(1) -3
y= -10 + 10 - 3
y = -3
vertex is at point (1, -3)
3. the axis of symmetry is the line that runs straight up and down at the center of a parabola. the center of the parabola is the vertex so the line runs straight up and down through vertex. for a line to run straight up and down it is a constant x value. since the x of the vertex is 1, the line is:
x = 1
4. using quadratic formula :
x = [-b (+-) sqrt (b^2 - 4ac)]/2a
we get:
x = [-10 (+-) sqrt (10^2 - 4 (-5)(-3)]/2 (-5)
x = [-10 (+-) sqrt (100 - 60)]/-10
x= [-10 (+-) sqrt (40)]/-10
x= [-10 (+-) 2* sqrt (10)]/-10
x= [5 (+-) sqrt (10)]/5
that is the answer. You can use a calculator to solve easily.
5. the discriminant is the solution to what is under the squareroot sign. so the square root part was:
sqrt (b^2 - 4ac)
so discriminant is :
b^2 - 4ac
so for this function it is:
10^2 - 4 (-5)(-3)
solving this the discriminant is 40
