x=4 y=5
if we put two pharases together
the answer is as follows pic :
x=4 y=5
Answer:
48
Step-by-step explanation:
81 - 33 = 48
Slope of line = tan(120) = -tan(60) = - √3
Distance from origin = 8
Let equation be Ax+By+C=0
then -A/B=-√3, or
B=A/√3.
Equation becomes
Ax+(A/√3)y+C=0
Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/√3)y+C)/sqrt(A^2+(A/√3)^2))
Substitute coordinates of origin (x,y)=(0,0) =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/√(4/3) => C=8*2/√3 = (16/3)√3
Therefore one solution is
x+(1/√3)+(16/3)√3=0
or equivalently
√3 x + y + 16 = 0
Check:
slope = -1/√3 .....ok
distance from origin
= (√3 * 0 + 0 + 16)/(sqrt(√3)^2+1^2)
=16/2
=8 ok.
Similarly C=-16 will satisfy the given conditions.
Answer The required equations are
√3 x + y = ± 16
in standard form.
You can conveniently convert to point-slope form if you wish.
The sketch of the garden and the pond is shown below
Area of garden = length × width
Area of garden = [3x + 5] × 3x
Area of garden = 3x[3x+5]
Area of garden = 9x² + 15x
Area of pond = [x-2] × x
Area of pond = x[x-2]
Area of pond = x² - 2x
Area to be re-sod = Area of garden - Area of pond
Area to be re-sod = 9x² + 15x - [x² - 2x]
Area to be re-sod = 9x² - x² + 15x + 2x
Area to be re-sod = 8x² + 17x
The amount of sod needed to be bought would depend on how much in each packaging they are being sold.
Answer:
70
Step-by-step explanation:
Angle Q and angle P are supplementary angles, so they add up to 180 degrees.
6x + 4 + 10x = 180
16x + 4 = 180
16x = 176
x = 176/16
x = 11
Put x in angle Q as 11 and solve.
6(11) + 4
66 + 4
= 70
Angle Q measures 70 degrees.