Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer:
20 square inches
Step-by-step explanation:
No. of bags Huma has : 4
No. of tiles in one bag: 6
Total no . of tiles in 4 bag = 4 * No. of tiles in one bag
= 4*6 = 24
No of tiles left with huma = 4
Let x be the no of tiles used to cover rectangle
Hence,
sum of no. of tiles left with huma and no of tiles used to cover rectangle should be equal to Total no . of tiles in 4 bag
mathematically
no. of tiles left with huma(4) + no of tiles used to cover rectangle (x) = Total no . of tiles in 4 bag (24)
4 + x = 24
subtracting 4 from both sides
4 + x -4 = 24 - 4
=> x = 20
Thus, 20 square inches tiles are used to cover the rectangle.
This means that area of rectangle is 20 square inches .
Try to do them on math -way
Answer:
18in^3
Step-by-step explanation:
v=<u>πr^</u><u>2</u><u>h</u>
3
where π =3
diameter=3
,r=<u>3</u>
2
=1.5
h=8
v= <u>3</u><u>×</u><u>1</u><u>.</u><u>5</u><u>×</u><u>1</u><u>.</u><u>5</u><u>×</u><u>8</u>
3
v= 18
Answer:
The probability that a person has the virus given that they have tested positive is P(A|B)=0.032.
The probability that a person does not have the virus given that they have tested negative is P(A'|B')=0.999.
Step-by-step explanation:
a) The probability of B: "the person tests positive" is the sum of:
- The probability that a person has the virus and the test is positive.
- The probability that a person don't have the virus but the test is positive.
Then, the probability of B: "the person tests positive" is
We have
Then
The probability that a person has the virus given that they have tested positive is P(A|B)=0.032.
b) The probability P(A'|B') is
We have
Then
The probability that a person does not have the virus given that they have tested negative is P(A'|B')=0.999.
