Answer:
1.x=-3,-4
2.A
3.-3,-5
4.C
5.A
6.C
7.D
8.C
Step-by-step explanation:
Option C:
The solution of inequality 2x + y < 10 is (5, –3).
Solution:
Given inequality is 2x + y < 10.
Lets substitute the given points in the inequality and find the solution.
Option A: (6, –1)
2(6) + (–1) < 10
12 – 1 < 10
11 < 10
This is false because 11 > 10.
Therefore (6, –1) is not the solution of the inequality.
Option B: (1, 10)
2(1) + (10) < 10
2 + 10 < 10
12 < 10
This is false because 12 > 10.
Therefore (1, 10) is not the solution of the inequality.
Option C: (5, –3)
2(5) + (–3) < 10
10 – 3 < 10
7 < 10
This is true.
Therefore (5, –3) is the solution of the inequality.
Option D: (5, 5)
2(5) + (5) < 10
10 + 5 < 10
15 < 10
This is false because 15 > 10.
Therefore (5, 5) is not the solution of the inequality.
Hence Option C is the correct answer.
The solution of inequality 2x + y < 10 is (5, –3).
Answer:
h(t) = -5*t^2 + 20*t + 2
Step-by-step explanation:
First, we know that the motion equation of the ball will be quadratic, so we write the equation:
h(t) = a*t^2 + b*t + c
Now we need to work with the data in the table.
h(1) = 17
h(3) = 17
h(1) = h(2) = 17
Then we have a symmetry around:
(3 - 1)/2 + 1 = 2
Remember that the symmetry is around the vertex of the parabola, then we can conclude that the vertex of the parabola is the point:
(2, h(2)) = (2, 22)
Remember that for a quadratic equation:
y = a*x^2 + b*x + c
with a vertex (h, k)
we can rewrite our function as:
y = a*(x - h)^2 + k
So in this case, we can rewrite our function as:
h(t) = a*(t - 2)^2 + 22
To find the value of a, notice the first point in the table:
(0, 2)
then we have:
h(0) = 2 = a*(0 - 2)^2 + 22
= 2 = a*(-2)^2 + 22
2 = a*(4) + 22
2 - 22 = a*(4)
-20/4 = -5 = a
Then our function is:
h(t) = -5*(t - 2)^2 + 22
Now we just expand it:
h(t) = -5*(t^2 - 4*t + 4) + 22
h(t) = -5*t^2 + 20*t + 2
The correct option is the first one.
Step-by-step explanation:
general formula
x²-(a+b)x+(ab)
where a is alpha
and b is beta
x=-4+2/6 or x=-4-2/6
x=-1/3 or x=-1
a+b=-1/3 + -1 =-4/3
ab= -1/3 x -1 =1/3
quadratic equation
x²-(-4/3)x + 1/3=0
x² + 4/3x + 1/3=0
multiply through by 3
3x² +4x +1=0
Answer:
-3
Step-by-step explanation:
first distribute 5 to x and 2 =5x+10 then combine like terms to 5x+4x=9x so on one side u have 9x+10 then on the other side of the equation u have 6x+1 now get the whole numbers on one side of the equation and variables on the other.
9x+10=6x+1
-6x -6x
3x+10=1
-10. -10
<u>3x</u>=<u>-9</u>
3. 3
-3=x
