Answer:
The larger of the two is 44.67
Step-by-step explanation:
let the first number=x
let the second number=y
We can derive a system of equations using the mathematical statements
Their sum is 33:
x+y=33( call this equation 1)
Sum of first number and four times the second is -2:
x+4y=-2(call this equation 2)
Since the integer coefficients of x in both equations are the same we can quickly subtract one from the other to eliminate it
For this explanation, I choose to subtract equation 1 from 2
(x+4y=-2)-(x+y=33)=3y=-35
y=-35/3
Now plug in the value of y into any equation for that of x. Say we plug into equation 1
x+(-35/3)=33
x-35/3=33( multiply through by 3)
3x-35=99
3x=99+35
3x=134
x=134/3
Therefore,x=134/3 or 44.67 and y=-35/3 or -11.67
Answer:
P = 10%
Step-by-step explanation:
Of means multiply and is means equals
P * 80 = 8
Divide each side by 80
P = 8/80
P = .1
Change to percent form
P = 10%
legs of the triangles
Each triangle 30-60-90 is:
one leg: 15 ft => short diagonal = 2 * 15ft = 30ft
other leg, x:
tan(30) = 15 / x => x = 15 ft / tan(30) = 25.98 ft
=> long diagonal = 2 * 25.98ft = 51.96 ft
side of the rhoumbus = hypotenuse of one triangle
side of the rhombus = √ [ (15)^2 + (25.98)^2 ] = √(900) = 30 ft
Area of the rhombus:
4 * area of one triangle = 4 [base*height/2] = 4*15*25.98/2 = 779.43 ft^2
The shortest distance accross the garden is equal to the side of the rhombus = 30 ft
AREA OF A RECTANGLE IS 42 UNITS
Rectangle: Triangle:
A = L * W A = hb / 2
A = (x-8) * 6 A = (7(x-3)) / 2
A = 6x - 48 A = (7x - 21) / 2
Since the problem states that both rectangle and triangle have the same area.Then:
6x - 48 = (7x - 21) / 2
1) Eliminate the denominator 2 by multiplying both sides by 2.
2 * (6x - 48) = 2 * ((7x - 21) / 2)
12 x - 96 = 7x - 21
Find x. Transfer like numbers and change their signs.
12x - 7x = 96 - 21
5x = 75
5x / 5 = 75 / 5
x = 15
Substitute x by its value:
Rectangle: Triangle
A = (x-8) * 6 - A = (7(x-3)) / 2 Areas of both Rectangle
A = (15 -8 ) * 6 A = (7(15-3)) / 2 and Triangle is the same.
A = 7 * 6 A = (7 * 12) / 2
A = 42 units A = 84 / 2
A = 42 units
