Answer:
The equation of line with given slope that include given points is 3 y + x - 20 = 0
Step-by-step explanation:
According to Cora , if we know the slope and points on a line then we can write the equation of a line .
Since , The equation of line in slope-intercept form is
y = m x + c
<u>Where m is the slope of line , and if we know the points ( x , y ) which satisfy the line then constant term c can be get and the equation of line can be formed .</u>
So , From the statement said above it is clear that she is correct .
Now , Again
Given as :
Slope of a line is m = - 
That include points ( 2 , 6 )
Now from the equation of line as y = m x + c
∴ 6 = - ( 2 ) + c
Or, 6 = - 
+ c
So , c = 6 +
or, c = 
∴ c = 
So, The equation of line can be written as
y = - x +
Or, 3 y = - x + 20
I.e 3 y + x - 20 = 0
Hence The equation of line with given slope that include given points is 3 y + x - 20 = 0 Answer
Using trigonometric ratio, the value of x is 63.6°
<h3>Trigonometric Ratio</h3>
This is the ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Trigonometric ratio are often coined as SOHCAHTOA
In the given triangle, we need to find the value of x using trigonomtric ratio.
Since we have the value of adjacent and hypothenuse, we definitely need to use cosine
cosθ = adjacent / hypothenuse
adjacent = 4
hypothenuse = 9
Substituting the values into the equation;
cos θ = 4 / 9
cos θ = 0.444
θ = cos⁻¹ 0.4444
θ = 63.6°
Learn more on trigonometric ratio here;
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1000 millilitres = 1 litre
soda= 2 litres
apple juice = 2.5 litres
fruit punch = 1.5 litres
lemonade = 2 litres
2+2.5+1.5+2= 8 litres
10 - 8 = 2 litres
so, the combinations could be:
2 soda, 1 apple juice, 1 fruit punch and 1 lemonade
or
1 soda, 1 apple juice, 1 fruit punch and 2 lemonade
Given:
The quadratic equation is:
To find:
The discriminant of the given equation and the number of real solutions.
Solution:
If a quadratic equation is 
, then the value of discriminant is:
If D<0, then the quadratic equation has no real roots or two imaginary roots.
If D=0, then the quadratic equation has two equal real roots.
If D>0, then the quadratic equation has two distinct real roots.
We have,
Here, 
. So, the discriminant of the given equation is:
Since D<0, therefore the number of real solutions is 0.
Hence, the value of the discriminant is -31 and the number of real solutions is 0.
