Let's solve your system by substitution.
y=2x+1;y=4x−1
Step: Solve y=2x+1for y:
y=2x+1
Step: Substitute2x+1foryiny=4x−1:
y=4x−1
2x+1=4x−1
2x+1+−4x=4x−1+−4x(Add -4x to both sides)
−2x+1=−1
−2x+1+−1=−1+−1(Add -1 to both sides)
−2x=−2
−2x
−2
=
−2
−2
(Divide both sides by -2)
x=1
Step: Substitute1forxiny=2x+1:
y=2x+1
y=(2)(1)+1
y=3(Simplify both sides of the equation)
Answer:
x=1 and y=3
Answer:
10. y=2x+1 y = -1/2x +1
11. y=-1/3x +6 y = 3x -4
12. y=-5x-18 y=1/5x + 14/5
Step-by-step explanation:
To write the equation of a line we must have a slope and a point. To find the slope, we use the slope from the equations for parallel lines and modify it for perpendicular lines.
10. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope here is 2. The parallel slope is 2 and the perpendicular slope is the negative reciprocal or -1/2.
Parallel Perpendicular
(y-1)=2(x-0) (y-1)==-1/2(x-0)
y-1=2x y-1 = -1/2 x
y=2x+1 y = -1/2x +1
11. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope here is -1/3. The parallel slope is -1/3 and the perpendicular slope is the negative reciprocal or 3.
Parallel Perpendicular
(y-5)=-1/3(x-3) (y-5)=3(x-3)
y-5=-1/3x+1 y-5 = 3x - 9
y=-1/3x +6 y = 3x -4
12. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope here is -5. The parallel slope is -5 and the perpendicular slope is the negative reciprocal or 1/5.
Parallel Perpendicular
(y-2)=-5(x--4) (y-2)=1/5(x--4)
y-2=-5(x+4) y-2 = 1/5(x +4)
y-2=-5x -20 y-2 = 1/5x +4/5
y=-5x-18 y=1/5x + 14/5
<em>What you need to find is the extra amount of plywood. To do that, you must find the area of the square and the area of the circle and subtract them to find the answer.</em>
Formulas:
area of a square: A = bh
area of a circle: A =
square measurements:
b = 28
h = 28
circle measurements:
(≈3.14)
r = 14
A = (28)(28)
A = 784
area of square = 784 in^2
A = 3.14 (
)
A = 3.14 (196)
A = 615.44 in^2
784 - 615.44 = 168.56
The amount of plywood left over is 168.56 in^2.
The answer should be X= 3.60m
Answer:
2.5 Teaspoons of vanilla are needed.
Step-by-step explanation:
If 3 cups of flour is 1.5 teaspoons of vanilla. 1.5 /3=.5 Meaning there is .5 teaspoons of vanilla per cup of flour.
If you have 5 cups of flour 5 x .5= 2.5 (teaspoons)
