4. If the determinant delta of a quadratic equation is positive, the equation has two real roots. If the determinant is negative, it has two imaginary roots. In this case, delta=b^2-4ac=(-1)^2-4*1*4=-15. Therefore, this equation has two imaginary roots.
Answer:
x=6/7 and y=18/7
Step-by-step explanation:
If y = 3x and 2x + 4y = 12,
then substitute the value of y with 3x
2x + 4(3x) = 12
2x+12x=12
14x=12
x=12/14=6/7
y=3x=3*(6/7)=18/7
Answer:
-5
Step-by-step explanation:
-10+5b=-35
5b=-35-(-10)
5b=-35+10
5b=-25
b=-25/5
b=-5
Answer: -3.0593
Step-by-step explanation:
The test statistic for the difference between two population mean (when population standard deviations
are known ) is given by :-

where ,
= Sample sizes taken from two populations 1 and 2.
= Difference between two Sample mean.
= Standard deviations of populations 1 and 2.
As per given , we have
We assume that the data follows a normal distribution.
Then, the test statistic will be :-
Hence, the test statistic= -3.0593
Answer:
The point C is 12.68 km away from the point A on a bearing of S23.23°W.
Step-by-step explanation:
Given that AB is 50 km and BC is 40 km as shown in the figure.
From the figure, the length of x-component of AC = |AB sin 80° - BC cos 20°|
=|50 sin 80° - 40 cos 20°|=11.65 km
The length of y-component of AC = |AB cos 80° - BC sin 20°|
=|50 cos 80° - 40 sin 20°|= 5 km
tan
= 5/11.65
=23.23°
AC=
km
Hence, the point C is 12.68 km away from the point A on a bearing of S23.23°W.