Answer:
See below.
Step-by-step explanation:
Given :-
x² + bx + c = 0 if x₁ + x₂ = -b and x₁x₂ = c
Solving :-
a) x₁ = 1/2 and x₂ = -3/4
=> x² + -(1/2 + -3/4)x + 1/2(-3/4)
=> x² + -(-1/4)x + (-3/8)
=> x² + 1/4x - 3/8
=> 8x² + 2x - 3 = 0
b) x₁ = 1 + √5 and x₂ = 1 - √5
=> x² + -(1 + √5 + 1 - √5)x + (1 + √5)(1 - √5)
=> x² - 2x + 1 - 5
=> x² - 2x - 4 = 0
Answer:
Third option: 12x^2+8x+25
Step-by-step explanation:
s1=8x^2
s2=4x^2+15
s3=8x+10
Total perimeter of the pool edge: P
P=s1+s2+s3
Replacing s1, s2 and s3 in the formula above:
P=(8x^2)+(4x^2+15)+(8x+10)
P=8x^2+4x^2+15+8x+10
Adding like terms:
P=12x^2+8x+25
To find the volume of a cylinder, you use this formula:
V =
h
Plug in your numbers,
V = (3.14 *
) * 13
Exponents:
V = (3.14 * 64) * 13
Parentheses:
V = 200.96 * 13
Multiply:
V = 
The radius to the nearest integer is 22.5 square inches
Answer:
a)120
b)6.67%
Step-by-step explanation:
Given:
No. of digits given= 6
Digits given= 1,2,3,5,8,9
Number to be formed should be 3-digits, as we have to choose 3 digits from given 6-digits so the no. of combinations will be
6P3= 6!/3!
= 6*5*4*3*2*1/3*2*1
=6*5*4
=120
Now finding the probability that both the first digit and the last digit of the three-digit number are even numbers:
As the first and last digits can only be even
then the form of number can be
a)2n8 or
b)8n2
where n can be 1,3,5 or 9
4*2=8
so there can be 8 three-digit numbers with both the first digit and the last digit even numbers
And probability = 8/120
= 0.0667
=6.67%
The probability that both the first digit and the last digit of the three-digit number are even numbers is 6.67% !
