The projection of 
onto 
is
We have
A - price of the senior citizen ticket
b - price of the student ticket
{4a+5b=102
{7a+5b=126
3a=24 → a=8
5b=102-32
5b=70
b=14
price of the senior citizen ticket is $8
price of the student ticket is $14
Answer: The value of X is 1000
Step-by-step explanation:
X98 = 98,000 means a variable 'X' multiplied by 98 is equal to 98000
ie X x 98=98,000
To get the value of X, divide both sides by 98
X98/98 = 98,000/ 98
X = 1000
Thus, 1000 x 98 is truly equal to 98000
Answer:
15/50
Step-by-step explanation:
5*3=15
5*10=50
so 15/50.
To find out which equation has no real solutions, we need to calculate the discriminant for each of these given equations.
For calculating the discriminant, we need to first compare these equations with the general formula which is <u>ax²+bx+c.</u>
So, let's get started.
1) x² + 4x + 16 = 0
a=1, b=4, c=16
D = b²-4ac
= (4)² - 4(1)(16)
= 16-64
= -48
√D = √-48
2) 4x² + 4x - 24 = 0
a=4, b=4, c=-24
D = b²-4ac
= (4)² - 4(4)(-24)
= 16 - 16(-24)
= 16 + 384
= 400
√D = √400 = +20 or -20
3) 5x² + 3x - 1 = 0
a=5, b=3, c=-1
D = b²-4ac
= (3)² - 4(5)(-1)
= 9 + 20
= 29
√D = √29
4) 2x² - 4x + 4 = 0
a=2, b=-4, c=4
D = b²-4ac
= (-4)² - 4(2)(4)
= 16 - 32
= -16
√D = √-16
Now from all these above calculations, we can see that discriminant was negative in first equation and in last equation.
If D<0 then roots does not exist, as the square root can not contain a negative value or the equation does not have any real solutions.
Roots in such case can be calculated but those roots are known as imaginary roots, which is a higher concept.
So Final answer is,
Equation 1 => x² + 4x + 16 = 0
and
Equation 4 => 2x² - 4x + 4 = 0
has no real solutions.
