Answer:
The equation of the required line is y = x + 5
Step-by-step explanation:
The equation of the given line is y = x - 2
The required line = A line parallel to the given line
The point through which the required line passes = (-3, 2)
The general form of the equation of a straight line, is y = m·x + c
Where;
m = The slope of the line
By comparison, the slope of the given line, m = 1
When two lines are parallel, their slope are equal
Therefore, the slope of the required line = m = 1
The equation of the required line in point and slope form is therefore;
y - 2 = x - (-3) = x + 3
∴y = x + 3 + 2 = x + 5
The equation of the required line is therefore;
y = x + 5.
Times the bottom equation by -4 to cancel out the x’s.
Add the equations.
Solve for y.
Plug in y to find x.
Answer:
Step-by-step explanation:
The equation 
represents the discriminant of a quadratic. It is the part taken from under the radical in the quadratic formula.
For any quadratic:
- If the discriminant is positive, or greater than 0, the quadratic has two solutions
- If the discriminant is equal to 0, the quadratic has one distinct real solution (the solution is repeated).
- If the discriminant is negative, or less than 0, the quadratic has zero solutions
In the graph, we see that the equation intersects the x-axis at two distinct points. Therefore, the quadratic has two solutions and the discriminant must be positive. Thus, we have 
.
Answer: She should blend 98 lbs of high-quality beans.
She should blend 72 lbs of cheaper beans
Step-by-step explanation:
Let x represent the number of pounds of high quality beans that she should blend.
Let y represent the number of pounds of cheaper beans that she should blend.
She needs to prepare 170 lbs of blended coffee beans. This means that
x + y = 170
She plans to do this by blending together a high-quality bean costing $4.75 per pound and a cheaper bean at $2.00 per pound. The blend would sell for $3.59 per pound. This means that the total cost of the blend would be 3.59×170 = $610.3. This means that
4.75x + 2y = 610.3 - - - - - - - - - -1
Substituting x = 170 - y into equation 1, it becomes
4.75(170 - y) + 2y = 610.3
807.5 - 4.75y + 2y = 610.3
- 4.75y + 2y = 610.3 - 807.5
- 2.75y = - 197.2
y = - 197.2/-2.75 = 71.9
y = 72 pounds
x = 170 - y = 170 - 71.9
x = 98.1
x = 98 pounds
Hi there!
In order to solve, we need to use the formula for the area of a circle, and the angle given to find the area of the sector. Then, subtract the area of the triangle to find the area of the segment. We would use the equation : A = x/360 (pi * r^2) - 1/2(b * h). We need to plug in 90 for the angle measurement, 8 for the radius, and 8 for both the base and height.
WORK:
A = 90/360 (pi * 64) - 1/2(64)
A = 1/4(64pi) - 32
A = 16pi - 32 = ~ 18.3ft^2
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
